metamaterials for multi-spectral infrared absorbers govind dayal

Metamaterials for Multi-spectral Infrared Absorbers

A Thesis Submitted

in Partial Fulfilment of the Requirements

for the Degree of

DOCTOR OF PHILOSOPHY

by

GOVIND DAYAL SINGH

to the

DEPARTMENT OF PHYSICSINDIAN INSTITUTE OF TECHNOLOGY KANPUR, INDIA

JUNE, 2014

This thesis is dedicated to

MY FAMILY

[ My Beloved Parents ]

Dedication

INDIAN INSTITUTE OF TECHNOLOGY KANPURDEPARTMENT OF PHYSICS, INDIA - 208016

STATEMENT

I hereby declare that the matter manifested in this thesis entitled: "Metamaterials

for Multi-spectral Infrared Absorbers", is the result of research carried out by me in

the Department of Physics, Indian Institute of Technology Kanpur, India under the

supervision of Prof. S. Anantha Ramakrishna.

In keeping with the general practice of reporting scientific observations, due ac-

knowledgement has been made wherever the work described is based on the findings

of other investigators.

IIT Kanpur Govind DayalJune, 2014 Ph.D. Student

Roll No : Y9109067

INDIAN INSTITUTE OF TECHNOLOGY KANPURDEPARTMENT OF PHYSICS, INDIA - 208016

Professor S. Anantha Ramakrishna Office : +91 512 2597449Lab : +91 512 2596601Email : [email protected]

CERTIFICATE I

It is certified that the work contained in this thesis entitled: "Metamaterials for

Multi-spectral Infrared Absorbers", has been carried out by Govind Dayal Singh under

my supervision and the same has not been submitted elsewhere for a degree.

IIT Kanpur Prof. S. Anantha RamakrishnaJune, 2014 (Thesis Supervisor)

Acknowledgement

"It is good to have an end to journey toward; but it is the journey that matters, in the end." - Ernest

Hemingway

This dissertation took almost five years from conception to completion and it’s just like climbing a

high peak, step by step, accompanied with bitterness, hardships, countless cycles of inquiry, exploration,

confusion and encouragement. Though, it will not be enough to express my gratitude in words to all

those people who helped me in this journey, I would still like to give my many, many thanks to all these

people.

First of all, I offer my sincerest gratitude to my supervisor, Prof. S. Anantha Ramakrishna for

exposing me a very exciting and interesting field of research which instilled confidence in me. I owe

a great deal of devotion to him, not only introducing me from the infancy of Metamaterials, but also

for his moral support, ’optics feelings’, optimism and constant encouragement and being the source

of inspiration for me. He has oriented and supported me with promptness and care, and has always

been patient and encouraging in times of new ideas and difficulties; he has listened to my ideas and

discussions which led to key insights. His fresh view on science and positive attitude have always been

very stimulating.

I am extremely indebted to "peers" Prof. H. Wanre and Prof. R. Vijaya who have helped with their

suggestions and critical comments which enabled me to shape my thesis. I owe special thanks to Prof. J

Ramkumar, for his instruction, insights and supervision for the laser micromachining experiments.

I must acknowledge Prof. V. Subrahmanyam, Prof. Sutapa Mukherji, Prof. Avinash Singh and

Dr. S. Damodaran for teaching me interesting and informative courses during the period of coursework

here. I also want to convey my sincere thanks to all my teachers during my school and college life prior

to IIT-K. Through classroom teaching they shaped my mind, nurtured my thoughts and nourished my

research potential.

A token of thanks to my Lab Post Docs Dr. Jeyadheepan, Dr. P. Mandal and Dr. Sriram for their

friendly attitude and academic support. I offer my special thanks to my dear lab mates Dheeraj, Ganga,

Jhuma, Prince, Rameshwari, Raghwendra and Rajesh for their help and nice efforts to make the lab

enthusiastic place for research. They shared with me their intellect and the basic tools of the trade. My

special thanks goes to Jhuma for helping me in many depositions, in particular, with glancing angle

deposition, Dheeraj for AFM measurements and also Nadeem for providing me many initial mask to

start with the laser micromachining experiments.

I am very thankful to IIT Kanpur for the great research infrastructure and CSIR for providing me

the research fellowship and offering me financial support.

I express my profound thanks to Mrs. Kanchan (Ma’am) and Jyoti to provide me a homely atmosphere

and lively company on various occasions.

Completing this work would have been all the more difficult were it not the invaluable network of

supportive, forgiving, generous and loving friends Sunil, Nikhil, Dushyant, Gyanendra, Prabhakar,

Subhankar, Gopal, Upkar, Bahadur, Pranati, Vandana, Seema, Nimisha, Reeta, Shraddha etc. at IIT K.

I have always been fortunate enough to have very good friend like Arun, Ratnesh, Gopi, Subhash with

whom I have shared many a tense moment and bouts of joy and they always wished well for me. I am

eternally grateful to Sushma for her constant encouragement, affection, care and support.

No words of appreciation could express my gratitude for my family, who have always been with me

although they were miles away from me. Whatever I am today is because of their unconditional love,

care, guidance, encouragement and moral support. To put in one line, the script of my success remains

incomplete without their huge sacrifices.

Lastly but definitely not the least, I owe a debt of gratitude to the Almighty to sail the journey and

made this possible by being with me all the time.

I seek pardon for all whose names are missed out unintentionally in spite of their immense and

persistent support. While grateful to the people who have bring this thesis to fruition, all the mistakes

and flaws that remain are my own.

Thank You!

i

Synopsis

Electromagnetic metamaterials are composite arrays of resonant structures of sub-

wavelength size designed to have specific optical properties. The electromagnetic

properties of a metamaterial depend mainly on the geometry of individual unit cells

through the resonances of the structure. Many unique effects such as negative refractive

index , sub-wavelength imaging, cloaking, perfect absorption etc, that are not possible

to achieve with natural materials, have been obtained by carefully designing the unit

cell for the specified frequencies. The sub-wavelength size of the unit cells allows meta-

materials to be characterized by a complex valued effective medium parameters such

as the electric permittivity and the magnetic permeability. Due to resonant nature of

the metamaterials, the effective medium parameters are usually frequency dispersive.

Much of the work in metamaterials has focused on the effects that arise due to the

real part of electric permittivity and magnetic permeability, for example, which can

be manipulated to be negative form a material with a negative index of refraction.

However, the imaginary part of the electric permittivity and magnetic permeability

can also be manipulated to create unusual properties. In particular, the electric permit-

tivity and magnetic permeability of metamaterials can be manipulated to create very

strong absorbers. By adjusting the electric permittivity and magnetic permeability, a

metamaterial can be impedance-matched to free space, minimizing reflectivity. By ma-

nipulating electric and magnetic resonances independently, it is possible to effectively

absorb radiation through the electric and magnetic field components. The use of perfect

absorbers may provide a method of exceeding the blackbody radiation limit imposed

by most current uncooled thermal detectors. Metamaterials with near unity absorp-

ii

tion are highly desirable for many applications including micro-bolometers, sensors,

thermal imagers, and absorbers used in thermal photo-voltaic solar energy conversion.

Landy et. al. (Phys. Rev. Lett 100 (20): 207402 (2008)) proposed and demonstrated the

first microwave metamaterial absorber.

Metamaterials based on metallic elements are particularly efficient as absorbing

media, because both the electrical and the magnetic properties of a metamaterial can

be tuned by structural design. One example of highly absorbing metamaterial design,

extensively investigated in this thesis, is that of a tri-layer structure, which consists

of a conducting metallic patch separated from a conducting (ground) plane by a di-

electric spacer layer. The tri-layer structure supports a series of cavity-like resonances

analogous to a grounded patch antenna, in which the electromagnetic field is localized

within the gap between the ground plane and the metallic patch element. The fun-

damental mode of sub-wavelength size metallic resonator is a dipole mode, however,

with a moderator size resonator fundamental as well as higher order modes can also be

excited. The structured units on the top act as electric resonators driven by the electric

field of the incident radiation. Assuming the metallic patch as a polarizable dipole,

an image dipole is induced in the bottom metallic film in response to the presence of

a metallic patch. The in-plane (parallel to the film) dipole moments of the image are

opposite to those of the metallic patch. These two anti-parallel currents along with the

displacement field in the intervening dielectric act to form circulating current loops

with a confined magnetic field in between to give rise magnetic resonance. When the

electric and magnetic dipole resonances occur at same frequency, then a strong localiza-

tion of electromagnetic energy results in the metamaterial structure and a consequent

strong absorption occurs in the presence of metallic regions.

The work presented in this thesis aims at the design, fabrication and characterization

of metamaterial absorber structures as novel materials for the multi-spectral absorption

at infrared frequencies. Numerical and experimental approaches are used to demon-

iii

strate multi-spectral absorption across the infra-red spectrum from short wave infrared

(SWIR) to long wave infrared (LWIR) and the mechanisms that allows such structures

to produce near unity absorption via the excitation of electromagnetic resonances in

structures are elucidated. The salient results of this thesis are the development of

multi-band metamaterial absorbers, ITO based broadband IR absorber and thermally

switchable metamaterials. Some novel micro fabrication techniques based on the ex-

cimer laser micromachining and shadow mask deposition have been utilized for the

fabrication of the metamaterials.

Chapter 1 presents a theoretical background to metamaterial and the control of

electromagnetic radiation by such artificial structured materials, and is intended to

establish a context for the detailed discussion of metamaterial absorbers that follows.

Section 2 is dedicated to exploring in detail the different mechanisms of resonances

which underpin the selective absorption possible with metamaterials. The charac-

teristics required for a material to be absorbing are discussed, and the conventional

approaches to designing such materials are covered. This is followed by a review of

current research in the area of absorbing materials.

Chapter 2 presents the methods used by us for the design, fabrication and character-

ization of metamaterial absorbers. The first section focuses on the use of finite element

modeling as a tool for the design of metamaterial absorbers and specifically on COM-

SOL Multiphysics software. The basis of the finite element method is described and the

manner in which COMSOL Multiphysics software applies the finite element approach

to simulate electromagnetic problems is detailed. The specific modeling tactics em-

ployed to simulate the behavior of each variant of the metamaterial is also covered in

detail. In the next section, we present a detailed description of the fabrication methods

used in this thesis. The metamaterials with micro-sized unit cells have been fabricated

with shadow mask techniques. The free standing shadow masks have been fabricated

using Excimer laser micro-machining. The laser micro machining of high aspect ratio

iv

features on polymers as well as on thin plasmonic metal films is discussed in detail.

In Chapter 3, we investigate the optimal designs of highly absorbing metamate-

rial at infra-red frequencies optimized from both the point of view of metamaterial

performance as well as fabrication process. A detailed study of the behavior of these

structures as a function of frequency, polarization state and incident angles is presented.

The finite element model is used to investigate the form of the resonant modes excited.

In particular, the effect of ground plane thickness and the physical phenomenon of

electromagnetic resonance in the tri-layer system is exhaustively considered. We also

further extended our design strategy for extending the usable bandwidth of metama-

terial absorber whereby a more detailed understanding of the phenomenon resulted.

Stacked metal-dielectric-metal multi-layered structures with different dielectric spacers

can support multiple resonant modes and are presented as building blocks of multi-

band metamaterials.

All the design studies in literature have considered only the fundamental electric

and magnetic dipole resonances or LC resonances of the tri-layer structure. In chapter

4, we demonstrate a simple metamaterial absorber design that behaves as a multi-

band perfect absorber at infra-red frequencies due to excitation of the fundamental

as well as higher order electromagnetic resonances in the tri-layer structure. The

metamaterials were fabricated using shadow mask deposition techniques, an attractive

low-cost technology for making large-area samples. A detailed numerical analysis was

carried out for further understanding the nature of these modes for perfect impedance

matching to that of vacuum for the spectrally selective “perfect” absorption of infrared

light. In the next section, we demonstrated a metamaterial absorber design fabricated

on flexible polymer substrates. The metamaterials were fabricated using glancing angle

deposition (GLAD) on pre-patterned polymer substrates that were fabricated using

excimer laser micromachining. The principle of the GLAD is based on the shadowing

effect such that only the exposed areas are coated by a directional incoming vapor flux

v

of material. The fabricated metamaterials had multi-band spectral absorption similar

to the earlier fabricated metamaterials.

A simple design paradigm for making broad-band ultra-thin infrared metamaterial

absorbers that are transparent to visible radiation is introduced in Chapter 5. The

absorber’s unit cell is composed of a conducting metallic patch separated from a semi-

conducting indium tin oxide (ITO) film by a dielectric spacer layer, resulting in nearly

100% absorbance at mid wave infrared (MWIR) frequencies and high absorbance over

a broad frequency range. The semi-conducting film acts as reflective metal at infrared

frequencies while it behaves as a transparent dielectric at visible frequencies. The

broadening in the absorption spectrum is found to be arise from the small variation

of dielectric permittivity of the semi-conducting ITO films at infrared frequencies as

compared to a plasmonic metal film. As a consequence of this, the dispersion of

metamaterial structure is quite broad in nature and results in a metamaterial absorber

with over 3 µm FWHM bandwidth.

In chapter 6, we present designs of a switchable metamaterial absorber that changes

its state from a absorbing state to reflecting state at a particular threshold of intensity.

The design consists of a multi-layered metal/dielectric/metal structure with one of

the layers being a switchable medium that can change its property from metallic to

insulating or vice-versa with some external stimulus. In one adaptation, the dielectric

placed in between the metal is a smart material like vanadium dioxide (VO2) that

changes its state from a dielectric to a metallic state via a phase transition at a particular

temperature. The change in phase of dielectric material to metallic material leads to

change the metal/dielectric/metal absorbing structure to become a metal/metal/metal

structure with a low impedance resulting in high reflectivity. The finite element model is

used to explore the character of the absorption and heat generation, and hence predict

their threshold intensity at which phase transition will occur. In the next section,

we experimentally demonstrated a tunable metamaterial absorber design in another

vi

adaptation where the bottom film of the tri-layer structure is a phase-change material

(VO2). In its insulating phase the tri-layer is a metal/dielectric/dielectric structure with

a 60% absorption, however, when heated externally across the phase transition of the

VO2 the tri-layer changes to a metal/dielectric/metal structure with over 90% absorption

within the metamaterial absorption band.

ContentsSynopsis i

Chapter 1 : Theoretical Background of Metamaterials and its application as Per-fect Absorber 13

1.1 Introduction to Metamaterials 131.1.1 Optical properties of metal and Semi conductors 201.1.2 Plasma-like metamaterials 241.1.3 Magnetic response at higher frequencies 26

1.2 Waves at interface between two media 29

1.3 Total light absorption in structured metal surfaces 311.3.1 Anti-reflection coatings based absorber 321.3.2 Resonant absorbers 341.3.3 Surface plasmon based absorbers 35

1.4 Metamaterial based Perfect Absorber 371.4.1 Realization of perfect absorption in metamaterial 381.4.2 Equivalent circuit for a pair of stacked patches 421.4.3 Recent advances in metamaterial perfect absorber 45

1.5 References 49

Chapter 2 : Simulation, Fabrication and Characterization Techniques 53

2.1 Introduction 53

2.2 The finite element method (FEM) and its implementation byCOMSOL 55

2.2.1 The Finite Element Method 552.2.2 Implementing the FEM in COMSOL 592.2.3 A benchmark problem 63

2.3 Fabrication of Metamaterials 652.3.1 Excimer Laser Micromachining 652.3.2 Experimental Procedures for Excimer laser microma-

chining 67

vii

viii CONTENTS

2.3.3 Micro Machining of Single Micrometer Features 68

2.3.4 Laser micromachining of polyimide films 70

2.3.5 Measurement of Material Removal Rate for MachiningHoles 73

2.3.6 Laser micromachining of thin metallic films 77

2.3.7 Laser micromachining of ITO thin film 79

2.3.8 Shadow lithography using a laser machined shadow mask 80

2.4 Fourier Transform Infrared Spectroscopy (FTIR) 83

2.5 References 86

Chapter 3 : Design of metamaterial absorbers for infrared frequencies 89

3.1 Introduction 89

3.1.1 Choice of the resonant absorption band 90

3.2 Design of dual-band absorbers 98

3.3 Design of multi-band absorbers 103

3.3.1 Metal/dielectric/metal disks stack based absorber 108

3.4 Conclusions 109

3.5 References 111

Chapter 4 : Fabrication of Metamaterial absorbers with multiband absorbancefrom multipole resonances 115

4.1 Introduction 115

4.2 Fabrication of a perfect absorber by shadow mask deposition 116

4.3 IR absorbing properties of the Metamaterials 117

4.4 Computer modeling and discussion of multiband absorption 120

4.5 Fabrication and Characterization of Flexible metamaterials 128

4.6 Excimer laser micromachining and Glancing angle deposition 129

4.7 Conclusions 133

4.8 References 134

Chapter 5 : Broadband infrared metamaterial absorbers with visible transparencybased on ITO 135


5.2 Material and design considerations for a broadband metama-terial 136

CONTENTS ix

5.3 Computational modeling of the metamaterial absorber withthe ITO ground plane 138

5.4 Fabrication and characterization of the metamaterial 141

5.5 Conclusions 143

5.6 References 146

Chapter 6 : Thermally switchable metamaterials 147


6.2 Design of a metamaterial saturable absorber 149

6.3 Experimental demonstration of switchable metamaterials 153

6.4 Conclusions 157

6.5 References 158

Chapter 7 : Future Directions 161

List of Figures

1.1 Material parameter space characterized by electric permittivity (ε) and

magnetic permeability (µ). 19

1.2 Dispersion of the real and imaginary parts of the dielectric permittivity

of Au, Al and ITO at infrared wavelengths. 22

1.3 An array of infinitely long thin metal wires of radius r and a lattice

period of a behaves as a low frequency plasma for the electric field

oriented along the wires. 24

1.4 The schematic diagram of split-ring structure proposed by Pendry et

al.5. 24

1.5 Some geometries of metal particles used to realize artificial magnetic

materials (a) Split ring resonator, (b) u-shaped resonator, (c) cut-wire

pairs. 28

1

2 LIST OF FIGURES

1.6 (a) The case of a perfect electric conductor (PEC) and a lossless dielec-

tric. As there is no absorption and no penetration into the metal, the

reflectivity equals unity at all wavelengths. (b) An absorbing dielectric

on a PEC substrate supports an absorption resonance assuming that

the losses are relatively small. (c) A lossless dielectric on a substrate

with finite optical conductivity (for example, Au at visible frequencies)

can support a resonance owing to the non-trivial phase shifts at the in-

terface between medium 2 and medium 3, but the total absorption is

small because the only loss mechanism is the one associated with the

finite reflectivity of the metal. (d), An ultrathin absorbing dielectric on

Au at visible frequencies can support a strong and widely tailorable

absorption resonance.24 35

1.7 The figure shows the charge and currents distributions of the sym-

metric (electric dipole resonance) and anti-symmetric (magnetic dipole

resonance). 41

1.8 Equivalent circuit of metal-dielectric-metal nanosandwich for asym-

metric mode. 43

1.9 Schematic structure of three layers metamaterial absorber (a)the layer

of metamaterial;(b) the bottom metallic layer;(c)the unit structure in-

clude the dielectric layer. Figure adapted from N. L. Landy et al.43. 46

1.10 Simulated absorbance for metamaterial perfect absorber design as shown

in Fig. 1.9. R(ω) (green), A(ω) (Red) are plotted on the left axis and T(ω)

(blue) is plotted on the right axis. Figure taken from N. L. Landy et al. 47

2.1 3D finite element model for the tri-layer metamaterial structure unit cell. 62

LIST OF FIGURES 3

2.2 Schematic diagram of the simulated unit cell with geometrical param-

eters, ay = az = 310 nm, h = 50 nm, d = 10 nm. Right: Simulated ab-

sorbance as a function of wavelength. 64

2.3 Schematic diagram of the experimental setup for laser machining 66

2.4 Top left panel shows the topography of the sample of arrays of 2 µm

diameter holes with a period of 4 µm machined on a Kapton sheet

measured by AFM. Right panel: The SEM image of an array of 1 µm

holes with 2 µm period. These large scale arrays have a total array

area of 1 mm × 1 mm with excellent uniformity throughout. Bottom

left panel shows optical microscopic image of ablation in photoresist in

the reflection mode. Bottom right panel shows the SEM image of the

3µm disk on polymer film. 68

2.5 Schematic diagram showing the resolution of imaging two distinct

spots about the focal plane of two adjacent focused beams. 69

2.6 Optical microscopic images of the micro machined structures on a Kap-

ton sheet placed at various planes above and below the focal plane. 71

2.7 Top left panel shows optical microscopic image of 2 µm wide lines in

the reflection mode. Right panel shows the AFM image of the fabricate

long lines in polymer. Bottom left panel show SEM image of an array

of 2 µm diameter square holes in polyimide film over 1 mm X 1 mm

area. Bottom right panel show optical microscopic image of the 20µm

square holes in the polymer. 73

4 LIST OF FIGURES

2.8 Top left: Plot showing the depth of the holes in an array of 1 µm holes

machined at various energies and with 5, 10, or 15 pulses. Top right:

shows the machined hole-depths with respect to the number of pulses

at various pulse energies (The lines shown are only a guide to the eye.).

Bottom panel: shows the same data (top right) against the total energy

= pulse energy × the number of pulses. 74

2.9 Top left: SEM of an array of 3µm diameter holes in 40 nm thin gold film

over 1 mm×1 mm area (b) Right: The transmission optical microscope

image of a 3 µm holes in 40 nm thin gold film. Bottom left: SEM image

of an array of 10µm diameter holes in 40 nm thin gold film over 1

mm×1 mm area (b) Right: The transmission optical microscope image

of a 10 µm holes in 40 nm thin gold film. 79

2.10 SEM image of the ITO disk arrays fabricated using laser micromachin-

ing of ITO thin film. 80

2.11 Schematic diagram of the shadow mask deposition technique, the yel-

low arrows represent the incoming vapor flux. 83

2.12 Left: SEM image of shadow mask after the deposition, Right: Trans-

mission optical microscope image of an array of 3 µm diameter holes

on a 8 µm square lattice. 83

2.13 Schematic of the far-field characterization setup composed of a FTIR

spectrometer equipped with a IR-microscope. 85

3.1 Temperature dependent refractive index dispersion of zinc sulphide

(ZnS) and zinc selenide (ZnSe). Figure adopted from Ref.15 91

LIST OF FIGURES 5

3.2 Electromagnetic quantities calculated for absorbing structures with h

= 100 nm, t = 150 nm, d = 60 nm, r = 1 µm and a = 2µm at the resonant

wavelength 5.34 µm are shown (a) Electric field magnitude, (b) surface

currents density, (c) Magnetic field magnitude, (d) power flow given

by Poynting vector, (e) resistive heating in the material. 93

3.3 Simulated Absorbance spectra of the designed absorber structures for

(a) different thicknesses of dielectric film, (b) angle independence of

the absorbance for different polarization, (c) and (d) different thick-

nesses of ground plane and dielectric layer thickness of 60 nm, (e) dif-

ferent thickness of gold disk with dielectric layer 60 nm. (a) to (e) are

for metamaterial structure with continuous dielectric layer and gold

ground plane. 95

3.4 Left: Schematic diagram of the unit cell of a metamaterial absorber

with geometrical parameters are, ay = az = 2 µm, h =200 nm, d = 150

nm, r =1 µm, t = 50 nm. Right: Calculated absorbance as a function of

wavelength for normal incidence. 98

3.5 Left: Schematic diagram of the unit cell of a dual band absorber with

geometrical parameters are, ay = az = 2 µm, h =200 nm, d = 150 nm, r =1

µm, t1 = 80 nm, t2 = 50 nm, t3 = 100 nm. Right: Calculated absorbance

as a function of wavelength for normal incidence for the dielectric pair

of spacers as ZnS and Ge (black), and ZnS and GaAs (red) 99

3.6 Electromagnetic quantities calculated for the absorbing structure as

shown in Fig. 3.5: (a) Electric field magnitude, (b) Magnetic field mag-

nitude and (c) Poynting vector at 4.98 µm; (d) Electric field magnitude,

(e) Magnetic field magnitude and (f) Poynting vector at 8.5 µm. 101

6 LIST OF FIGURES

3.7 Calculated reflectance of an array of gold disks of 1 µm diameter and

100 nm thickness in a square lattice of period 2 µm on various sub-

strates as shown in legend. The dielectric permittivity used for differ-

ent substrate were εZnS=2.2, εGaAs=3.29 and εGe=4.0038. 103

3.8 Calculated absorbance for the dual band metamaterial absorber shown

in Fig. 3.5 at 4.98 µm (left) and at 8.5 µm (right) as a function of inci-

dence angle for different polarizations, with ZnS as one dielectric and

Ge as second dielectric layers. Black lines are meant to guide the eye

only. 104

3.9 Calculated absorbance and reflectance spectra for multi-band absorber

for 1 µm disks with dielectric layer thicknesses dZnS = 35 nm, dZnTe =

50 nm, dGaAs = 90 nm, and dGe = 150 nm. 105

3.10 Calculated absorptivity and reflectivity for the design shown in Fig. 3.10

with two gold disks of diameter 0.8 µm and 1 µm with ZnS as one di-

electric layer material and Ge as the material for the second dielectric

layer. 106

3.11 Schematic diagram of the sub-lattice design with same geometrical pa-

rameters are, a= 2.5 µm, r1 = 1 µm, r2 = 0.9 µm, and d= 100 nm and layer

thicknesses same as shown in Fig. 3.5; and Electric field magnitude at

(a) 3.64 µm, (b) 6.92 µm and (c) 7.12 µm wavelengths. 107

3.12 Left: shows the broadband absorbance for stacks of MDM disk with

same geometrical parameters as shown in Fig. 3.2 Right: shows the

broadband absorbance for stacks of MDMDM disk with geometrical

parameters as shown in Fig. 3.5. 109

3.13 Top panels: surface current within the metal disk and continuous metal

film for wavelengths 5 µm, 5.45 µm and 6 µm. Bottom panels: Surface

currents for metal/dielectric/metal disks. 110

LIST OF FIGURES 7

4.1 Top left: Schematic of unit cell of an absorbing metamaterial with t=100

nm, d=280 nm, h=60 nm, disk diameter = 3.2 µm and periodicity in X-

Y directions are 8 µm. Top middle: SEM image shows the top view of

the of fabricated metamaterial structure (Au/ZnS/Au tri-layer). The

bar indicator is 8 µm long. Top right: Optical microscope image of fab-

ricated tri-layer structure in transmission mode. The 60 nm gold film

allows for some transmission of light and the Au disk on top appears

dark. Bottom left: SEM image of the fabricated metamaterial struc-

ture with Au disk on top. Bottom Middle: AFM image of the top Au

disk. Bottom right: Measured profile of the disk and its data process-

ing showing small diffusion of evaporated flux. 118

4.2 Measured power absorption versus the wavelength from the fabri-

cated metamaterials absorber structures consisting of Au/Al disks sep-

arated from a 60 nm gold thin film by a 280 nm ZnS film. Right: Simu-

lated absorbance for the Au-ZnS-Au disk metamaterial structure. 119

4.3 Left: Optical microscopic image of fabricated metamaterial structure

in reflection mode. The bar indicator is 15 µm long. Right: Measured

absorbance versus the wavelength from the fabricated metamaterial

with an array of Al disk diameter of 5 µm separated from a 100 nm

gold thin film by a 280 nm ZnS film. 120

4.4 Field distributions for the three modes at resonant wavelength 12.58

µm, 5.4 µm, and 3.35 µm for the normal incident angle. Fig. (a), (d), (g)

represent the electric field in top disk. Fig. (b), (e) and (h) represent the

magnitude of the magnetic field in tri-layer. Fig. (c), (f) and (i) show

the distribution of the electric field field in z-direction. Fig. (j), (k), (l)

represent the multipolar nature of the electric field in the top disk at

6.16 µm, 5.88 µm and 4.45 µm respectively. 121

8 LIST OF FIGURES

4.5 Schematic diagram showing charge distribution for different orders.

All odd order modes possess a finite dipole for all the incident angles,

however even order modes can only possess a net dipole for oblique

angle. 125

4.6 Top: Simulated power for Au/ZnS/Au structure (left) and for Au disk

on the SiO2 substrate (right). Bottom: Simulated absorbance versus

the angle of incidence for the designed Au-ZnS-Au disk metamaterial

absorber. The wavelength in the plot cases is 5µm, disk size = 3.2µm

and period of the array is 8µm. 127

4.7 Schematic of fabrication process: (a) a polymer substrate (b) micro-

pillars fabricated using laser micromachining (c) snowfall deposition

of metal followed by ZnS on micro-pillars as well as on side walls (d)

schematic of GLAD deposition (e) metallic disk deposited on top of

metal/dielectric coated pillars. Unit cell of an absorbing metamate-

rial with t=100 nm, d=280 nm, h=50 nm, disk diameter = 3.8 µm and

periodicity in X-Y directions are 8 µm. SEM images of fabricated meta-

material structure. 128

4.8 Top Left: SEM images of array of high aspect ratio disks after snow-

fall deposition of gold thin film. Uniform deposition of metal on the

sides as well as top of micro- and nano-pillars. (b) shows deposition

of metal caps fabricated via oblique angle deposition. (c) Metal disk

deposition on continuous gold/ZnS film by continuously rotating the

pre patterned substrate at an oblique angle.Bottom Left: Optical mi-

croscopic image (5X) of the fabricated metamaterial wrapped around

a pen. Right: higher magnification (50X) view of the left panel. 130

LIST OF FIGURES 9

4.9 Left: Measured power absorption versus the wavelength from the fab-

ricated metamaterials absorber structures consisting of Al disks sepa-

rated from a 100 nm modulated gold thin film by a 280 and 300 nm

ZnS film. Right: measured absorbance for the fabricated metamaterial

wrapped around a pen as shown in Fig. 4.7. 131

5.1 Left panel: Drude dispersion of the real and imaginary parts of the

dielectric permittivity of Au (ωp/2π = 2176 THz, εb = 5.7 and γ/2π =

6.5 THz), Al (ωp/2π = 3464 THz, εb = 5.1 and γ/2π = 19.41 THz) and

ITO (ωp/2π = 461 THz, εb = 3.9, γ/2π = 28.7 THz). The right panel

shows dispersion for ITO in an expanded view. 138

5.2 Left panel: Schematic of unit cell of an absorbing metamaterial with h

= 200 nm, d = 380 nm, t = 100 nm, disk diameter = 3 µm and periodicity

in X-Z directions are 8µm. 139

5.3 Left panel: Simulated absorption versus the wavelength for the meta-

materials absorber structures designed. Right panel: Measured ab-

sorption from the fabricated metamaterials absorber structures and the

reflectance of plane ITO film. 139

5.4 Left: Electric field magnitude, Right: Magnetic field magnitude in tri-

layer of Al/ZnS/ITO metamaterial at 4.6 µm wavelengths. The nature

of the m = 3 mode is apparent with three current loops. 140

5.5 Left: Electric field magnitude, Right: Magnetic field magnitude in tri-

layer of ITO/ZnS/ITO metamaterial at 6.16 µm wavelengths. The field

penetration inside ITO disk and ground plane can be seen. 141

10 LIST OF FIGURES

5.6 Left panel: SEM image of the fabricated structure with disk diameter

= 3 µm and periodicity in X-Z directions are 8µm. The bar indicator is

8 µm long. Inset: Diffraction of a He-Ne (632.8 nm) laser transmitted

through the structure with a zeroth order transmittance of 45%. Right:

The atomic force microscope scan shows a disk height of about 100

nm. Bottom: Optical microscope image of fabricated metamaterial in

transmission mode. The structure absorb the IR radiation and diffract

through the visible radiation. 142

6.1 Top left: Schematic of unit cell of an absorbing metamaterial with h =

100 nm, t = 200 nm, d = 200 nm, disk diameter = 2 µm and periodicity

in Y-Z directions are 4 µm. (A) shows the absorbance and reflectance of

the metamaterial for insulating and metallic VO2 phases, (B) shows the

surface currents (arrow) and the magnetic fields (slice), and (C) power

flow in the structure for 10.22 µm. (D) and (E) shows the electric fields

and magnetic fields for metallic VO2 phase respectively. 150

6.2 (a) Heat source in dielectric phase of VO2 (b) heat source in metallic

phase of VO2, (c) temperature distribution for dielectric phase of VO2 ,

and (d) temperature distribution for metallic phase of VO2 151

6.3 Left: shows the measured reflectance of the insulating and metallic

VO2 thin films on a SiO2 substrate at 400C and 800C respectively, Right:

shows the measured reflectance from the 380 nm thin ZnS on top of

VO2 thin film at 400C and 800C respectively. 154

LIST OF FIGURES 11

6.4 Top: Schematic of unit cell of an switchable metamaterial. Bottom left:

shows the measured reflectance of the metamaterial with insulating

and metallic VO2 phases at 400C and 800C respectively. Right: Simu-

lated reflectance by assuming a metallic phase of VO2 in the metama-

terial structure. 156

CHAPTER1Theoretical Background ofMetamaterials and its application asPerfect Absorber

1.1 Introduction to Metamaterials

Electromagnetic metamaterials are composite arrays of sub-wavelength scale features

that can provide the means to engineer fundamental optical parameters of a medium

such as permittivity, permeability, impedance, and index of refraction1,2. The structural

elements that make up a metamaterial can be engineered to exhibit both electric and

magnetic resonances at a pre-determined frequencies3–5. Just as the property of a bulk

material is essentially determined by the chemical elements and bonds in the material,

the unique properties of metamaterials arise from the resonances supported by the

geometry (size and shape) of the meta-atoms embedded in the medium. This implies

that one can tune the characteristics of medium and achieve exceptional properties by

carefully designing the structure. Due to the sub-wavelength size of the unit cells, the

radiation does not sense the individual unit cells in the composite, but only responds to

some average polarization and magnetization that develops in the medium. Hence, the

medium can be characterized by effective medium parameters such as the dielectric

ε(ω) and the magnetic permeability µ(ω) at the macroscopic level. The ability of

metamaterials to exhibit strong magnetic responses at high frequencies, where natural

materials don’t show any magnetic response, has enabled us to explore several exotic

13

14 CHAPTER 1

phenomenon that require magnetic response. Many unique effects such as negative

refractive index7, sub-wavelength imaging8, cloaking, perfect absorption etc., that are

impossible to achieve with natural materials, have been obtained by carefully designing

the unit cell for the specified frequencies.

Homogenization theories attempt to assign effective material parameters (in meta-

materials studies, especially effective permittivity and permeability) to materials of

mixed and heterogeneous micro-structure9,10. This is possible to a certain extent, if the

characteristic length of the inhomogeneities in the mixture is sufficiently smaller than

the wavelength of the operating electromagnetic field e.g., if the average feature size

’l’ of meta-atoms is small enough in order not to be resolved by the electromagnetic

wave that they are interacting with. If λ be the wavelength of the electromagnetic

field involved, then we must have l << λ. Usually the minimum requirement for a

medium to be considered homogeneous is set as: l = λ/4 to λ/6. This condition is

very important since it allows us to leave out scattering and diffraction, regarding only

single beam refraction as the dominant phenomenon. A number of homogenization

approaches have been developed for predicting the effective medium electromagnetic

response. In this way, we can analyze such a structured material with complicated

geometries as an electromagnetically uniform (homogeneous) medium which can be

described through constitutive homogeneous parameters: electric permittivity ε(ω)

and magnetic permeability µ(ω). As Maxwell equations suggest, the signs of ε(ω) and

µ(ω) play a fundamental role in the wave propagation behavior.

The time dependent Maxwell’s equations in a material medium are

∇ ·D(r, t) = ρ, (1.1)

∇ · B(r, t) = 0, (1.2)

1.1. Introduction to Metamaterials 15

∇ × E(r, t) = −∂B(r, t)∂t

, (1.3)

∇ ×H(r, t) = J(r, t) +∂D(r, t)∂t

, (1.4)

Where E and H are the electric and magnetic field intensities, and D and B are the

electric and magnetic flux densities. The quantities ρ and J are the macroscopic free

charge density and free current density (charge flux) of any external charges. SI units

are assumed for all the quantities in Eq. 1.1–1.4. The displacement current, ∂D∂t in

Ampere’s law is essential in predicting the existence of propagating electromagnetic

waves and to establishing charge conservation. The right-hand side of the second

equation 1.2 is zero because there are no magnetic monopole charges.

It is important to note that these expressions contain information expressing the

conservation of charge in a relation known as the equation of continuity:

∇ · J = −∂ρ

∂t. (1.5)

For time independent fields, and isotropic and linear media, the relation between

the electric field and the electric displacement is given by the material equation:

D = ε0E + P = ε0(1 + χe)E = ε0εrE, (1.6)

where χe is the dielectric susceptibility and P = χeE is the dipole moment density

or polarization density. The relation between the magnetic field and the magnetic

induction is given by

B = µ0(H + M) = µ0(1 + χm)H = µ0µrH, (1.7)

16 CHAPTER 1

where χm is the magnetic susceptibility and M = χmH is the dipole moment density or

magnetization density.

The electric polarization vector P describes how the material is polarized when an

electric field E is present. It can be interpreted as the volume density of electric dipole

moments. P is generally a function of E. Some materials can have a nonzero P also when

there is no electric field present. The magnetization vector M similarly describes how

the material is magnetized when a magnetic field H is present. It can be interpreted

as the volume density of magnetic dipole moments. M is generally a function of H.

Permanent magnets, however, have a nonzero M also when there is no magnetic field

present.

From the above discussion, we note that the knowledge of the permittivity (ε) and

permeability (µ) of materials is essential to predict response of the medium to electro-

magnetic fields. If those values are known then material performance is completely

determined.

In most materials, the time dependent displacement field D is directly and linearly

proportional to the applied electric field E, and is a function of the material in which

the field propagates. Due to the mass of the electrons in the medium that introduce a

certain inertia in the response, D does not vary instantaneously with E, but instead is

a function of the entire time history of how the electric field polarized the medium. A

somewhat general form for D can therefore be written in the following form

D(r, t) = ε(r, t) ∗ E(r, t) =

∫ t

−∞

ε(t − t′) · E(r, t′)dt′. (1.8)

In an analogous manner, for the applied field H and the magnetic field B, a similar

relationship can be written out as

B(r, t) = µ(r, t) ∗H(r, t) =

∫ t

−∞

µ(t − t′) ·H(r, t′)dt′. (1.9)


In order to properly define wave propagation in dispersive media we also need the

constitutive relations in frequency domain. The frequency domain can be defined such

as

E(r, t) =

∫∞

−∞

E(r, ω)eiωtdω, (1.10)

D(r, t) =

∫∞

−∞

D(r, ω)eiωtdω, (1.11)

H(r, t) =

∫∞

−∞

H(r, ω)eiωtdω, (1.12)

B(r, t) =

∫∞

−∞

B(r, ω)eiωtdω. (1.13)

We will now briefly describe the fundamental equations governing the evolution of

electromagnetic fields in the absence of any free charges, and free currents. Assuming

a time harmonic dependence E(r, t) = E0exp(−iωt) and H(r, t) = H0exp(−iωt), where ω

denotes the wave frequency, and substituting in Eq. 1.3 and Eq. 1.4, we get

∇ × E(~r) = iωµ0µrH(~r), (1.14)

∇ ×H(~r) = −iωε0εrE(~r). (1.15)

We may combine the two curl Eq. 1.14 and Eq. 1.15 in the Maxwell equations to

yield wave equations in the frequency domain for the electric and the magnetic fields,

respectively,

∇ × (µr−1∇ × E(~r)) − k0

2εrE(~r) = 0, (1.16)

18 CHAPTER 1

∇ × (εr−1∇ ×H(~r)) − k0

2µrH(~r) = 0. (1.17)

where k0 denotes the wave number of free space k0 = ω√ε0µ0 = ω

c0and c0 is the speed

of light in free space. Assuming that the material is homogeneous, then we can use the

refractive index n to rewrite

∇ × (∇ × E(~r)) − k02n−2E(~r) = 0, (1.18)

where n2 = εrµr is defined as the refractive index of the medium. The propagation of

electromagnetic wave inside the medium will eventually depend upon the sign of the

εr and µr.

We can conveniently characterize most electromagnetic materials by the quadrant

where they lie in the permittivity εr and permeability µr plane as shown in Fig. 1.1:

(1) A medium with both positive permittivity and permeability (ε(ω) > 1 &µ(ω) > 1)

which include most dielectric materials is called Double Positive Medium (DPM).

Electromagnetic radiation can propagate through these media and the vectors E, H,

and k form a right-handed triad.

(2) A medium with permittivity less than zero and permeability greater than zero

(ε(ω) < 1 & µ(ω) > 1) is called as Epsilon negative (ENG) medium. Plasmas are

common examples of such media. It is well known that a plasma screens the interior of

a region from electromagnetic radiation and, all electromagnetic waves are evanescent

inside a plasma for frequencies below the plasma frequency. This is directly expressed

by the dispersion relation, which reduces to k2 < 0. Inside such a ENG medium, no

real solutions for the wave vector are possible. Some dielectric materials e.g. SiC

with Lorentz dispersion near an excitonic or optical phonon resonance can also exhibit

(ε(ω) < 1) over a small frequency band above the resonance frequency.

(3) A medium with permittivity greater than zero and permeability less than zero


Figure 1.1: Material parameter space characterized by electric permittivity (ε) and magneticpermeability (µ).

(ε(ω) > 1 &µ(ω) < 1) is called asµ-negative (MNG) medium. Here, also a wave incident

on a medium of this family decays evanescently within the medium and no propagating

modes can be sustained. Due to the absence of magnetic monopoles, there can be no

exact analogue of an electric plasma, but there are natural examples of some anti-

ferromagnetic and ferrimagnetic materials with a resonance at microwave frequencies

that exhibit Re(µ) <0 within a frequency band above the resonance frequency.

(4) A medium with simultaneously positive permittivity and permeability less than

zero (ε(ω) < 1 & µ(ω) < 1) is called as Double negative (DNG) medium. This class

of materials have only been demonstrated with artificial constructs. Such a material

is also termed as left-handed media and the phenomenon of backward wave propa-

gation is exhibited. The propagation constant (k) for DNM is real and the transverse

electromagnetic wave propagates with a phase velocity c/n (where n is the refractive

20 CHAPTER 1

index)1,12,14.

1.1.1 Optical properties of metal and Semi conductors

In optical metamaterials, most of the designs being studied incorporate metals in the

unit structure of the metamaterial. In this section, we briefly review the physical

processes involved in light-metal interactions and emphasize the modification of metal

behaviors at the different frequency range. In metals, the electrons of the valence

band are loosely bound and can become "free of the nuclei" to pursue random motions

through the metal so that average velocity of the electron due to thermal fluctuation

(vt) is zero. The electromagnetic response of a metal is largely determined by the

collective movement of free electrons of number density (N) that moves against a fixed

background of positive ion cores. In the presence of an electric field (E) the electrons

acquire a drift velocity (vD) which is superimposed on the thermal motion.

The Drude free-electron model provides a realistic model of metal behavior at

optical (high) frequencies than does the ideal conductor model as the inertial effects of

a finite electronic mass become important. The Drude model is classical in its approach

and considers the material to be a ’gas’ of free electrons interspersed among some

arrangement of relatively heavy positive ions. The combination of these positive ionic

cores and the mobile ’gas’ of electrons makes the medium neutral overall and can

be considered to be a plasma. In the Drude model, it is assumed that the electrons

do not interact with each other or with the positive nuclei, with the exception of

random electron collisions with the nuclei. The electrons oscillate in response to the

applied electromagnetic field, and their motion is damped via collisions occurring with

a characteristic collision frequency γ = 1/τ. With a time harmonic incident electric field,

E0 exp(−iωt), the equation of motion for a free electron is


mx(t) + mγx(t) = −eE, (1.19)

where ‘m’and ‘e’represent the effective mass and the charge of the electron, respectively,

and ‘γ’is the damping constant. The first term relates to the effects of inertia, the

second to dissipation due to collisions and the right hand side represents the driving

electric force experienced by the electrons. It is assumed that the wavelength of light is

large compared with the distance travelled by the electron, so that it effectively sees a

spatially constant field and the velocities involved are sufficiently low so that the effects

of the magnetic field can be neglected. Solving this differential equation, we obtain the

displacement x(t) of the electron from its original position as:

x(t) = −em

1ω(ω + iγ)

exp(−iωt) (1.20)

The polarization density P defined as the total dipole moment per unit volume can

be calculated as P = Nex, with N being the density of the free-electron gas and x(t) is

the displacement of the electron from its original position. As discussed in the previous

section, the macroscopic polarization P can be expressed as

P = ε0χeE, (1.21)

and

D = ε0E + P = ε0εE. (1.22)

Substituting the value of the polarization P in Eq. 1.22, we get

D = ε0E + P = ε0E −Ne2

mE

ω(ω + iγ)(1.23)

and the relative permittivity of the metallic material, ε(ω), is given by

22 CHAPTER 1

Figure 1.2: Dispersion of the real and imaginary parts of the dielectric permittivity of Au, Aland ITO at infrared wavelengths.

ε(ω) = εb −ω2

p

ω(ω + iγ)(1.24)

where ωp is the volume plasma frequency at which the density of the electron gas

oscillates and is given by

ωp =

√Ne2

mε0(1.25)

From the above expression for ωp, it is clear that the plasma frequency of a material

depends on number density of the free electron carriers of the metal. For most metals,

the free electron density is of the order of 1023 cm−3, and the plasma frequency lies in

the range of visible to ultraviolet frequencies. The dielectric permittivity is negative up

to ωp and the plasma shields the interior from electromagnetic radiation. This is why

metals are highly reflecting at visible frequencies below ωp. For frequencies above the

ωp the medium behaves as an ordinary positive dielectric media. The plasma frequency

fp and the collision frequency γ of common metals are listed in the table 1.1.


Material Plasma frequency ( fp) Collision frequency (γ)Al 3570 THz 17.5 THzAu 2175 THz 6.5 THzAg 2175 THz 14.1 THzITO 462 THz 28 THz

Table 1.1: Plasma frequency and collision frequency for metals and semiconductor.

However, the semi-conducting materials whose conductivity can be increased and

controlled by doping with impurities, offer a flexible manner to tune the plasma fre-

quency. The optical properties of doped semiconductors are determined by the free-

carrier density that determine the plasma frequency and damping constant as defined

in the Drude free electron model. As doped semi-conductor materials have a lower

charge carrier density ( 1020 cm−3) relative to typical metals ( 1023 cm−3), their plasma

frequency are observed to lie in the near-infrared spectral region. The frequency de-

pendent behavior of permittivity of gold, aluminum and indium tin oxide (ITO), a com-

monly used material for metamaterials at near-IR and visible frequencies, are shown in

Fig. 1.2. From the Fig. 1.2, we note that magnitudes of the dielectric permittivity ε(ω)

of Au, Al at mid-IR frequencies is much larger than the permittivity of the ITO. Metals

such as aluminum, gold, and silver are characterized by a large electrical and thermal

conductivity and a high reflectivity in the visible spectral range. The permittivity in

a conductor has a large imaginary part and this means that the losses are large. The

fields, attenuate rapidly within the conductor and are confined to a thin surface layer of

few tens of nano-meters. In case of ITO, due to the the lower carrier concentration and

hence small plasma frequency as compared to noble metals, the dispersion in the rela-

tive permittivity of ITO is comparatively small as shown in Fig. 1.2. The bulk plasmon

frequency of ITO is located in the near-infrared range at a wavelength of ∼ 1 µm for

carrier densities around 1020 cm−3. Thus, this material is reflective in the mid-IR region

and transparent in the visible region. ITO has been shown to be a potential plasmonic

material in the NIR region.

24 CHAPTER 1

Figure 1.3: An array of infinitely long thin metal wires of radius r and a lattice period of abehaves as a low frequency plasma for the electric field oriented along the wires.

Figure 1.4: The schematic diagram of split-ring structure proposed by Pendry et al.5.

1.1.2 Plasma-like metamaterials

In the previous section, we saw that the plasma frequency of semiconductors can be

increased by doping the medium, the inverse can also be done to reduce the plasma

frequency to obtain negative permittivity materials at low frequencies by literally dop-

ing the vacuum with metal. It was proposed by Pendry et. al.3,4 that metamaterials

consisting of dilute arrays of thin metallic wires behave as a low frequency plasma with


a frequency stop-band from zero up to a cutoff frequency that can be attributed to the

motion of the electrons in the wires only. The proposed structure is an array of very

thin wires in 1D, 2D or 3D arrays, structured on truly sub-wavelength length-scales and

can be effectively homogenized as schematically shown in Fig. 1.3. Due to electrons

confinement to the wire only and the low density of wires, the effective electron density

is considerably reduced and the effective electron mass is increased because of the large

self-inductance of the thin wire.

Let us consider the response to an electric field applied parallel to one set of wires

as shown in Fig. 1.3. The first effect is that the effective electron density is reduced

because only part of the space is filled by metal. The reduced effective electron density

Neff is given by Nπr2

a2 , where ’N’ is the density of conduction electrons in the metal,

’r’ is the radius of the wire and ’a’ is the cell side of the square lattice on which the

wires are arranged. There is a second equally important effect to be considered, that is

the enhancement of the effective mass of the electrons, caused by magnetic (inductive)

effects is given by

meff =µ0r2e2N

2ln(

ar

) (1.26)

The above expression shows that thin wires have high effective mass of electrons as the

inductance of wires is large.

The effective relative permittivity of the system still obeys the Drude-Lorentz model,

with an effective plasma frequency

ωp =

√Neffe2

meffε0. (1.27)

Therefore, using thin wires it is possible to bring plasma frequency literally down into

the microwave region.

26 CHAPTER 1

1.1.3 Magnetic response at higher frequencies

In this section, we will very briefly overview the basic elements of magnetic response

of a material or metamaterial to the electromagnetic radiation. Magnetism in materials

has a quantum-mechanical origin intimately related to the spin and angular motion

of electrons in the orbitals. The orbital motion of electrons about the nucleus of an

atom results in magnetic effects similar to those of current flow in a closed circuit.

The magnetic coupling to an atom is proportional to the Bohr magneton µB = αea0/2,

while the electric coupling is ea0. The induced magnetic dipole also contains the fine

structure constant α=137, so the effect of light on the magnetic permeability is α2 times

weaker than light’s effect on the electric permittivity. In many practical applications

they may be considered frequency independent until the operating wavelengths re-

mains substantially greater than the characteristic scale of the material micro-structure

or nanostructure. Landau and Lifshitz gave an insightful reason of why a magnetic

response resulting from orbital currents in atoms should be negligible at optical frequen-

cies, and consequently, the magnetic permeability ceases to have any physical meaning

at relatively low frequencies of few GHz: There is certainly no meaning in using the

magnetic susceptibility for normal atomic/molecular media at optical frequencies, and

in discussion of such phenomena we usually set µ(ω) = 1. Natural magnetics materials

such as ferromagnetic materials have very high permeability at dc ("direct current" at

zero frequency) and low frequencies, e.g. iron has static permeability µ(ω = 0)= 5000,

and falls practically to unity at 1 GHz.

Before the inception of metamaterials, the magnetic response of materials at higher

frequencies is simply neglected and the wave propagation inside the medium is purely

characterized by the dielectric response of the medium to the incident radiation. Victor

Veselago, in a paper published in 1967, pondered the consequences for electromagnetic

waves interacting with a hypothetical material for which both the electric permittivity,


ε(ω), and the magnetic permeability, µ(ω), were simultaneously negative13. It was

observed that a medium with simultaneously negative permittivity and negative per-

meability [ε(ω) < 0 & µ(ω) < 0] shows some exceptional phenomenon that a natural

occurring material does not show. But this remained only a thought experiment until

1999, when Smith et.al. demonstrated a medium with simultaneous negative permit-

tivity and permeability at microwave frequencies.

In magnetostatics, it is well-known that a current loop carrying a current ’i’ generate

magnetic dipole moment, which is given by the product of the area of the coil and the

current, i.e., m ∝ (current)(area). Due to weak magnetic coupling the induced current

in the inductive circuit is negligible and materials are assumed to be non-magnetic. Sir

John Pendry5 and co-workers proposed and demonstrated a simple method of enhanc-

ing the induced current to engineering magnetic response of a medium by periodic

arrangement of sub-wavelength size micro-structures, made from non-magnetic con-

ducting sheets, known as split ring resonator as shown in Fig. 1.4. The structure was

designed to have a LC resonance with the inductor being a single winding of a wire coil,

and the capacitor formed by the gap at the split of the wire. The time varying magnetic

field, normal to SRR plane as shown in Fig. 1.4, induces a circulating current in the split

ring resonator, which produces a magnetic flux opposing the external magnetic field.

The split in the ring was purposefully introduced to enhance the magnetic response

by virtue of the LC resonance. They derived the effective magnetic permeability, on

the assumption that the rings are sufficiently close together and that the magnetic lines

of force are due to currents in the stacked rings, are essentially the same as those in a

continuous cylinder. The effective relative magnetic permeability of the SRR, can be

calculated by estimation of the equivalent inductance (L) and capacitance (C) within

each element, is given by

µeff(ω) = 1 +fω2

ω20 − ω

2 − iωγ(1.28)

28 CHAPTER 1

Figure 1.5: Some geometries of metal particles used to realize artificial magnetic materials (a)Split ring resonator, (b) u-shaped resonator, (c) cut-wire pairs.

where ω0 =√

3dµ0ε0επ2r3 is the resonance frequency that arises from the LC resonance of

the system and f = πr2

a2 is the filling fraction of the material.

Split-ring structure uses non-intrinsic resonances together with plasma resonances

to achieve an effective magnetic response of the medium at high frequencies. Be-

sides SRR’s, other geometric arrangements such as square rings, u-shapes, cut-wire

pair etc.15,16 can also exhibit magnetic response at optical frequencies excited via time-

varying electromagnetic fields. One of the most popular design for achieving a mag-

netic resonance toward the optical regime is based on arrays of single SRRs lying in

a plane perpendicular to the direction of wave propagation. This configuration was

a popular choice for researchers at microwave and THz frequencies due to well es-

tablished 3D fabrication techniques for millimeters sized structures. The fabrication

techniques for SRR depend largely on the wavelength of operation. For radio and

microwaves, the geometrical sizes of are millimeters or even centimeters in size, and

can readily be made using printed circuit board technology. However, they are not

very popular choice for achieving magnetism at infrared and optical frequency where

the micro and nano-scale SRRs lying flat on a substrate present a challenge for current

fabrication techniques. In contrast to the standard SRR operation, where a magnetic

field normal to the SRR plane is required to excite the magnetic response, the single

in-plane SRRs may act as magnetic dipoles without the involvement of the incident

magnetic field at all. When the electric field is parallel to the gap-bearing side of the

1.2. Waves at interface between two media 29

SRR, there is an asymmetric current mode in the two arms of the ring, and a magnetic

dipole can be obtained18. An alternative metamaterial design is the double-wire or

the cut-wire pair that can support an anti-parallel current resonance and thus produce

a magnetic moment to achieve magnetic activity at higher frequency as shown in the

Fig. 1.5. The fabrication difficulties in making such a structure based on micro- or

nano-fabrication techniques are obvious. The magnetic response of cut-wire structure

is discussed in the detail in the Section 3.2.

1.2 Waves at interface between two media

In this section, we will focus on the physical mechanisms that can enhance the ab-

sorption of electromagnetic radiation in the medium. When an electromagnetic wave

strikes an object, a number of things can happen. The electromagnetic radiation can be

absorbed, reflected, scattered, refracted, or transmitted. Assuming that the surface has

an average roughness (Ra) that is much smaller than the characteristic wavelength so

that there is no scattering from the roughness, incident wave may be reflected [R(ω)],

transmitted [T(ω)], or absorbed [A(ω)]. According to Kirchhoff’s rule, the sum of

the transmittance, reflectance and absorbance must follow the relationship given as

A(ω) = 1 − R(ω) − T(ω).

By solving Maxwell’s equations inside the ambient medium and vacuum together

with the boundary condition of the field continuity, it is easy to obtain the complex

amplitude reflection and transmission coefficient. When a plane wave propagating in

a homogeneous medium encounters an interface with a different medium, a portion of

the wave is reflected from the interface while the remainder of the wave is transmitted.

Fresnel equations that determine the reflectance from a planar interface from a

material of (ε1, µ1) to a one with (ε2, µ2) at an angle θ from the surface normal, for both

transverse electric (TM) and transverse magnetic (TE) polarizations are given by,

30 CHAPTER 1

rTM =

√µrεr − sin2(θ) − εr cos(θ)√µrεr − sin2(θ) + εr cos(θ)

(1.29)

and

rTE =µr cos(θ) −

√µrεr − sin2(θ)

µr cos(θ) +

√µrεr − sin2(θ)

(1.30)

where εr = ε2ε1

and µr =µ2

µ1are the relative permittivity and permeability of the two

media respectively.

Now consider an interface between a medium and the air. Assuming normal

incidence at the interface from air side, the reflectivity can be derived as

r =1 −√µrεr

1 −√µrεr

. (1.31)

Let us now introduce the impedance (Z) as another optical quantity relevant to

describe the relationship between the electric and the magnetic fields, and how it

changes upon the wave travelling into matter. The ratio of the electric field E to the

magnetic field H for a plane wave at position z defines the load presented to the wave

by the medium beyond the point z. The wave impedance can be further simplified

to reduce Z =µ0

ε0 = 377 Ω is the impedance of medium 1 (vacuum). The Reflectance

from an interface between two mediums having characteristic impedances of Z1 and

Z2 respectively can now be written as

r =Z2 − Z1

Z2 + Z1, (1.32)

where Z1 =√

µ1

ε1and Z2 =

√µ2

ε2are the impedances of the medium 1 and medium 2

respectively.

1.3. Total light absorption in structured metal surfaces 31

The Fresnel reflection coefficient has complex amplitude and the reflectance R(ω) from

the medium can be calculated by

R(ω) = r · r∗, (1.33)

From the expressions for R(ω), we conclude that if the impedance of the medium is

matched to the impedance of the surrounding medium (Z = Z0 =√

µ0

ε0for wave incident

from free-space), the wave does not reflect from the medium and we have R(ω) = 0.

Since the impedance is defined as Z = Z0

√µr

εr, one expects to have an impedance-

matched medium for the case where the real parts of the effective permittivity and

the permeability are equal (µr = εr). Unfortunately, there are no natural materials that

can precisely meet such requirements. Thus one need to look at artificially engineered

structures to precisely engineer the E & H.

1.3 Total light absorption in structured metal surfaces

Electromagnetic absorbers have wide applicability in light harvesting, thermal detec-

tion and electromagnetic energy conversion devices. These devices play an increasingly

important role in the everyday lives right from microwave to optical frequencies. For

instance, microwave absorbers have been traditionally used for EMI reduction, antenna

pattern shaping, radar cross reduction and in military applications for several decades.

In comparison, THz technology is relatively new with numerous potential applications

in imaging and spectroscopy for medical diagnostics and biology, high-bandwidth com-

munication, security and defence, and non-destructive evaluation. Similarly, Infrared

part of the radiation is also very important for the chemical and biological sensing and

thermal imaging. At optical frequencies, the conversion of sunlight to electricity via

light trapping is also of particular interest for enhancing the efficiency of thin film solar

32 CHAPTER 1

cells for solving the energy problem that our society faces. It is important to emphasize

that all of these devices have absorbers as an integral part of the devices and a highly

absorbing material is an ideal candidate to significantly enhanced the performance of

the device.

In this section, we will describe the salient principles of different types of EM

absorbers as well as the recent advances on metamaterial and plasmonic absorbers.

In order to achieve total absorption of the incident energy, one needs to achieve a

suppression of the transmission and the reflection. Complete dissipation of the incident

energy in the concerned medium should be possible. The zero transmission condition

can be provided by using an optically thick metal film. Therefore, one of the main

challenge is to design and fabrication of a structure with zero reflection from the

surface of the medium.

1.3.1 Anti-reflection coatings based absorber

In absorbers based on anti-reflection coatings, a thin film of transparent material of a

specially chosen thickness is coated on a metal surface so that interference effects in the

coating cause the wave reflected from the top surface to be out of phase with the wave

reflected from the metal surfaces19–22. The zero transmission condition is provided by

the optically thick metal layer. When the incident wave impinges on the front surface of

the dielectric some proportion of it is reflected while some is transmitted: the proportion

that is reflected determined by the mismatch between the intrinsic impedance of free-

space and the input impedance of the material: greater the difference in impedance, the

larger is the reflection. This transmitted wave then propagates through the dielectric

eventually reaches the metal backing whereupon it is perfectly reflected (assuming a

perfect metal) and propagates back towards the dielectric-air interface. In accordance

with reciprocity, the same proportion of the wave energy originally reflected at the


outer surface of the dielectric is reflected internally at the dielectric-air boundary, the

remainder couples back into the surrounding air. The wave coupled back into air

then interferes with that initially reflected at the air-dielectric interface. This process

repeats multiple times between the two interface within the optical cavities, with some

light leaking out at every bounce. Light that is reflected from the dielectric surface

interferes (both constructively and destructively) with light reflected from the anti-

reflection layers. The destructive interference effects rely on possible phase reversals

of multiple reflection of the light between the two interface within the optical cavities

formed by the dielectrics film and the optical path difference (OPD) between the two

beam. This phase reversals situation arises since the metal plate constitutes a perfect

electric conductor and has a reflection coefficient of -1, the wave suffers a phase change

of π radians upon reflection.

The required thickness and refractive index for zero reflection of a dielectric film

coated on metal can be derived using Fresnel’s formula for the reflection of light from

a single dielectric film on a metal. For a quarter wavelength anti-reflection coating

of a transparent material with a refractive index ‘n ’coated on a perfectly conduction

material and light incident on the coating with a free-space wavelengthλ0, the thickness

‘d ’which causes minimum reflection is calculated by:

r =r1 + r2exp(−2iδ)1 + r1r2exp(−2iδ)

(1.34)

where r1 and r2 are the Fresnel reflection coefficient at air-film interface and film sub-

strate (metal) respectively, and δ is the phase difference between the reflected waves

given by

δ =2πndλ0

(1.35)

From above equation, we note that zero reflection condition for a single dielectric

34 CHAPTER 1

interface is fulfilled when nd=λ0/4. It is important to note that such types of absorbers

do not rely on the precise value of the permittivity and permeability of the bulk layer,

but instead depend on the destructive interference of the multiple reflections through

a thin film of appropriate thickness.

Recently, Kats et. al.24 demonstrated another type of planar absorber by putting a

dielectric thin film/structure on a noble metal substrate Fig. 1.6. The thickness of the

ultra-thin highly absorbing dielectric is far less than a quarter of the wavelength of light

propagating within the dielectric media. The reason of light absorption was ascribed to

the non-trivial interface phase shifts produced by the large optical attenuation within

the highly absorbing dielectrics. They called it an asymmetric FP cavity as only the

bottom of the cavity is adjacent to metal as shown in Fig. 1.6. In their work, examples

of such kind of absorbers working at visible frequencies have been demonstrated by

coating few nanometers thick film of germanium on top of a gold substrate. By tuning

the germanium film thickness from 7 to 25 nm, the color of the sample changes from

light pink to light blue.

1.3.2 Resonant absorbers

One of the earliest absorber type which is inherently narrow-band is known as the Sal-

isbury screen25,26. The Salisbury Screen consists of a resistive sheet placed at distance

of an odd multiple of λ0/4 wavelengths in front of a metal (conducting) backing, and

usually separated by an air gap. In terms of transmission line theory, the quarter wave-

length transmission line transforms the short circuit at the metal into an open circuit

at the resistive sheet. The effective impedance of the structure is the sheet resistance.

(If the gap is a half wavelength then the short circuit reappears and perfect reflection

occurs). If the sheet resistance is 377 ohms/square (i.e. the impedance of air), then good

impedance matching occurs. A Salisbury screen has a narrow band of absorption. A


Figure 1.6: (a) The case of a perfect electric conductor (PEC) and a lossless dielectric. As there isno absorption and no penetration into the metal, the reflectivity equals unity at all wavelengths.(b) An absorbing dielectric on a PEC substrate supports an absorption resonance assumingthat the losses are relatively small. (c) A lossless dielectric on a substrate with finite opticalconductivity (for example, Au at visible frequencies) can support a resonance owing to the non-trivial phase shifts at the interface between medium 2 and medium 3, but the total absorptionis small because the only loss mechanism is the one associated with the finite reflectivity of themetal. (d), An ultrathin absorbing dielectric on Au at visible frequencies can support a strongand widely tailorable absorption resonance.24

material with higher permittivity can replace the air gap. This decreases the required

gap thickness at the expense of bandwidth. Improved performances over broader

range of frequencies is obtained by combining multiple layers, yielding the Jaumann

absorber. Improvement in the structure thickness can be achieved by merging the re-

sistive sheet and the periodic structure to have resistive cell elements. In general, most

such absorbers based on interference effects will be wavelength dependent (dispersive)

with narrow band widths.

1.3.3 Surface plasmon based absorbers

In 1902, Wood27, based on purely visual evidence, suggested that when a metallic

grating comprising of array of metallic elements, with periodicity of the order of the

incident wavelength at optical frequencies, is illuminated by a monochromatic plane

wave with the magnetic field parallel to the grooves, it exhibits a strong absorption for

36 CHAPTER 1

some particular values of the angle of incidence. However, he was unable to provide

any interpretation to these phenomena and thus termed them "singular anomalies".

In 1907, Rayleigh explained these Wood’s anomaly according to the grating formula28

and conjectured that the reflection of light passes off at sharply defined wavelengths.

This type of reflection dips are purely dependent on the grating period. In 1941, Fano

made a breakthrough on explaining Wood’s anomaly and addressed that, in addi-

tion to Rayleigh’s conjecture, there exists a forced resonance supported by the specific

metallic grating which causes the reflection valleys to broaden at wavelengths other

than those predicted according to the grating formula29. In 1976, the total absorption

of light was experimentally shown and theoretically explained30,31 for a metal diffrac-

tion grating. The physical phenomena of total light absorption is mainly due to the

excitation of surface plasmon polaritons (or SPPs, for short), which are collective os-

cillations of free electrons supported at the interface between the metal and dielectric.

These ideas were later extended both theoretically and experimentally to a variety of

metallic nanostructures different configurations32–34 including doubly periodic metal

gratings35,36,38, diffraction gratings consisting of cylindrical cavities in a metallic sub-

strate 35, metal-semiconductor-metal nanostructures41, multi-layers of ordered metallic

nanoparticles39, as well as partially disordered metallic nanoparticle arrays42. Grating

based absorbers are sensitive to the angle of incidence. In contrast, localized plas-

monic resonances, e.g., in metallic nanoslits or nanoparticles, exhibit an absorption

independent of the angle of incidence. In particular, sub-wavelength structures based

on metal-insulator-metal (MIM) involving Fabry-Perot-like resonances are often used

to get a total absorption.

1.4. Metamaterial based Perfect Absorber 37

1.4 Metamaterial based Perfect Absorber

An inspection of Fresnel’s coefficients immediately reveals that a perfectly absorbing

medium can normally be characterized by its electric permittivity and magnetic per-

meability. Hence, in order to achieve perfect impedance matching over larger ranges

of frequencies, one will need to engineer the value and the dispersion of the electric

permittivity and the magnetic permeability of the medium1. The dispersion in ε(ω) is

readingly available since it is exhibited by many metals about their plasma frequency.

The crucial issue is to design sub-wavelength sized structures whose resonances can be

driven by the magnetic component of the electromagnetic field so that the correspond-

ing effect can be reflected in the dispersion of the magnetic permeability µ(ω)5.

Artificial structured materials, where we can engineer the effective medium param-

eters (permeability and permittivity) to have a desired dispersion, provide excellent

flexibility, robustness and tunability to efficiently control and manipulate the absorp-

tion of electromagnetic energy in unprecedented ways compared to natural absorbing

materials. The origin of perfect absorption in a metamaterial is by adjusting the mag-

netic resonance µ(ω) resulting from the structural design in addition to the electric

response ε(ω) of the material. By independently manipulating these resonances in

metamaterial, it is possible to engineer both the real and imaginary components of

ε and µ to effectively absorb incident radiation through both the incident electric and

magnetic fields43. The permittivity of metamaterials is complex and is generally written

as ε = ε′ + iε′′. The permittivity arises from the dielectric polarization of the material.

The quantity ε′ is sometimes called the dielectric constant which is something of a

misnomer as ε′ can vary (disperse) significantly with frequency. The quantity ε′′ is a

measure of the attenuation of the electric field cause by the material. The electric loss

38 CHAPTER 1

tangent of a material is defined as

tan(θe) =ε′′

ε′(1.36)

The greater the loss tangent of the material, the greater is the attenuation as the wave

travels through the material. Analogous to the electric permittivity is the magnetic

permeability which is written as µ = µ′ + iµ′′, with magnetic loss tangent defined as

tan(θm) =µ′′

µ′(1.37)

It is important to mention here that, maximizing the absorption is surprisingly

complicated: increasing the imaginary part of the refractive index of the medium does

not simply equate to increased absorption as we can see from the Fresnel coefficient for

reflection of a wave incident from vacuum as equation written below;

R =n′ + i · n” − 1n′ + i · n” + 1

(1.38)

where n’ and n" are the real and imaginary part of the refractive index of the medium.

Note that n’+in" =√εµ. For a highly absorbing medium, n" has to very large as

compared to the n’. But as n" approaches∞, R approaches to take a value of −1. Hence

the medium becomes highly reflective as in case of the metal at low frequencies. Thus

one has to be careful to impedance match the medium with ambient medium properties

to achieve perfect absorption.

1.4.1 Realization of perfect absorption in metamaterial

The most popular design of metamaterial absorber structure is based on simultaneous

resonant excitations of an electric dipole and a magnetic dipole. The design typically

consists of a tri-layer system with top metallic layer structured at sub-wavelength


scales43. In this respect, metal-dielectric-metal nano-sandwiches have been theoreti-

cally and experimentally investigated because they show strong resonant enhancement

in light scattering or extinction and also because of the possibility of strong electromag-

netic field-enhancement effects in the structures. When the top layer consist of metallic

patches are brought in close proximity, the coupling between between the structured

patch and bottom metal film induces a symmetric high-frequency hybrid mode with

the electric field oscillates in phase in the two metallic patch normal to their axis and

an antisymmetric low frequency hybrid mode with the electric field oscillates with

opposite phase in the two metallic patch normal to their axis. The frequencies of the

two modes of oscillation for the coupled system is analogous to a coupled harmonic

oscillators. As illustrated in Fig. 1.7(left), the symmetric mode with the in phase cur-

rents in the two nanodisks, is characterized by a net electric dipole P. The asymmetric

mode, arising from a current distribution with the currents in the two nanodisks out of

phase is characterized as a sum of magnetic dipole (M) and electric quadrupole (Q) as

shown in Fig. 1.7(right) below44. The induced magnetic dipole couple to the external

magnetic field and gives rise to desired dispersion in magnetic permeability of the

effective medium. In this way, one can obtain a magnetic resonance as well as a electric

response at a desired frequency by appropriate design of the metamaterial structure.

Each layer of the designed metamaterial plays an important role in the engineering the

electromagnetic response of the medium. Let us discuss the role of each layer one by

one.

The structured units on the top act as electric resonators driven by the electric field

of the incident radiation. The incident electric field excite the collective oscillation of

the free electrons in the structured unit. Since, the structured unit has a certain shape

and bound geometry, the excited modes show resonant characteristics known as cavity

resonances. These surface modes have highly confined field near the edges of metallic

structures, which enables strong coupling to the electric field of the incident radiation.

40 CHAPTER 1

At low frequencies, where metals are almost perfectly conducting and the skin depth

is zero, the structured unit on top acts as a classic dipole antenna, for which the current

defining the input impedance is given by the conduction current on the surface of the

patch of highly conductive metal. The classical antenna theory predicts a resonance

at λnm = 2l√εr/√

n2 + m2, where l is the geometrical length of the top metallic patch,

n,m are positive integers with m2 + n2 ,0 and εr is the permittivity of the surrounding

dielectric medium46. However, at higher frequencies, the behavior of the antenna

changes qualitatively as the electromagnetic wave penetrates a large portion of the

total volume and the assumption of surface currents only is not valid.

Recently, there has been great interest in the extension of antenna concepts from

radio frequencies to the visible and infrared portions of the electromagnetic spectrum

that enables us to analyze both computationally and analytically modes in patch.

Novotny47 derived a simple linear scaling law for λeff given by

λeff = n1 ∗ λ + n2, (1.39)

where n1 and n2 are coefficients that depend on the antenna geometry and static di-

electric properties. For a given length of the antenna, multiple half-wavelength current

oscillations can develop at wavelengths with resonances m*λeff/2 = L with m = 1,2,3,4

etc. The structured metal layer may be square, rectangular, thin strip (dipole), circular,

elliptical or any other configuration. Square, rectangular, strip and circular configu-

rations are the most common because of ease of analysis and fabrication, and well

characterized radiation characteristics. These geometries have been adopted for the

demonstration of the perfect absorption at microwave and THz frequencies, where the

designed unit can easily be fabricated by well established printed circuit board (PCB)

techniques.

The dielectric spacer layer placed in between the top and bottom conducting mate-


rial plays an important role in capacitive coupling of the tri-layer structure. As we have

seen that the electric resonance of the top structured layer depends on the dielectric

properties, the resonance frequency of the electric resonator can be adjusted by capaci-

tive loading. This provides a simple way of tuning the resonance of metamaterial by a

tunable dielectric material. The spacer layer also plays a significant role in dissipation

of the absorber radiation via inherent dielectric loss. At lower frequencies, where metal

are almost perfectly conducting and very little loss occurs in the metallic structures the

absorbed energy has to be dissipated in the dielectric spacer material. Based on the nu-

merical studies at microwave and THz frequencies in which the dielectric contribution

to the absorption is analyzed, the role of dielectric loss in absorption has been found to

be considerably larger than that of the ohmic losses in the metal.

Figure 1.7: The figure shows the charge and currents distributions of the symmetric (electricdipole resonance) and anti-symmetric (magnetic dipole resonance).

The role of the ground plane is best described as a perfect conductor that produces

the mirror image of the charge distribution in the top structured layer. In this case

of time varying fields, the oscillating dipoles constitute time varying currents. Two

surface currents flowing in opposite directions along with the displacement current at

the edges constitute a circulating current loop. This circulating current loop can be

driven by a magnetic field lying in the perpendicular plane. This phenomenon leads to

the magnetic excitation, thereby, determining the effective permeability of the structure.

The role of the ground plane has been extensively studied in antenna theory, where

the presence of a ground plane redirects half of the radiation into the normal direction,

42 CHAPTER 1

improving the antenna gain by as much as 3dB, and partially shielding objects on the

other side. However, if the antenna is too close to the conductive surface, the phase of

the impinging wave is reversed upon reflection, resulting in destructive interference

with the wave emitted in the other direction. This is equivalent to saying that the

image currents in the conductive sheet cancel the currents in the antenna, resulting

zero reflection. A ground plane can also be a specially designed artificial surface,

for example, a cut-wire metamaterial. A ground-plane is one half of a dipole above a

conducting plane, which is called a “ground plane” because historically the conducting

plane for radio antennas was the surface of the Earth.

1.4.2 Equivalent circuit for a pair of stacked patches

The response of an artificial magnetic inclusion is due to resonant oscillating currents,

and a common way to describe this is to model the inclusion by an equivalent effective

resistor-inductor-capacitor (RLC) circuit45. In the simplest sense, the unit cell of a

metamaterial array is designed to be an individual RLC circuit. Let us consider a system

of a pair of metallic patches as we will primarily use this system for our absorbers as

shown in Fig. 1.8. This system is excited by a magnetic field with a time harmonic

dependence H = H0e−iωt and is applied perpendicular to the plane in which the patches

lies. The incident light, assumed to be polarized along the length of the patch, generates

a sinusoidal potential, V = V0e−iωt. At the magnetic resonance of the structure anti-

parallel currents are excited in the two stacked patches, these anti-parallel currents

along with the displacement currents creates an effective loop current. Moreover, this

current results in the accumulation of opposite charges at the two upper (and at the two

lower) sides of the pair, creating the situation of a parallel plate capacitor. The structure

thus can be approximated by an equivalent effective resistor-inductor-capacitor (RLC)

circuit, of inductance L, (the inductance of the loop current), and capacitance C, (the


capacitance of the two capacitive regions). Since all the components are in principally

series, the total potential across the circuit equals the sum of the potentials across the

individual components. Writing Kirchoff’s law for the loop, we obtain

Figure 1.8: Equivalent circuit of metal-dielectric-metal nanosandwich for asymmetric mode.

VL + VC + VR = V (1.40)

Where, VL, VC and VR are the voltage drops across the inductance L, capacitance C, and

the resistor R of the equivalent circuit respectively.

Substituting the voltage drops across the individual components in terms of the

charge Q = Q(ω) on the capacitor and the current I = I(ω) in the loop, we get

LdIdt

+ RI +Q(t)

C= V (1.41)

Assuming that L, R, C and V are known, this is still one differential equation in two

unknowns, I(ω) and Q(ω). However the two unknowns are related by I = dQdt so that,

d2Qdt2 + R

dQdt

+QC

= V (1.42)

which has a solution for time harmonic fields given by

Q(ω) =1/L

ω2 − 1LC −

iRωL

V (1.43)

Now, differentiating with respect to t and substituting dQdt = I,

44 CHAPTER 1

I(ω) =iω/L

ω2 − 1LC −

iRωL

V (1.44)

The current in the loop I(ω) generates a magnetic field and has a magnetic moment

defined as:

m = I(ω).A =−iω/L

ω2 − 1LC −

iRωL

A (1.45)

where A is the area of the inductive loop.

Now, consider a uniform magnetic field B passing through the inductive loop. Let

the area vector be A = An, where A is the area of the surface and n its unit normal. The

magnetic flux through the surface is given by surface

φ = B ·A = µ0H0e−iωt A cos(θ) (1.46)

Faraday’s law relates the induced EMF V in a circuit to the time rate of change of the

magnetic flux φ through the circuit. That is,

V = −dφdt

= −iωµ0H0e−iωt A cos(θ) (1.47)

Substituting the value of V in Eq. 1.44, we get the induced magnetic moment, m, in

terms of incident magnetic field.

m = A.I(t, ω) =Fω2

ω2 − ω02 − iγωo

H (1.48)

whereω0 = 1LC and γ = R

L are the resonance frequency and damping constant of the LCR

circuit respectively. The strength of the resonance partially depends upon the metal

resistance, which will dampen the effects. The value of R, L and C depends upon the

material properties and dimensions of the metallic patch.


Finally, using m = χmH, χm = 1 + µr the magnetic susceptibility, Eq. 1.48 is obtained

as

µr = 1 −Fω2

ω2 − ω02 − iγωo

(1.49)

From the above expression, we note that metal-dielectric-metal stacked structure with a

2D pattern on top provides the possibility of observing a negative effective permeability

over a finite frequency range. The magnetic resonance of these structures are because

of an internal capacitance and inductance within each element that depends on their

geometrical parameters, and thus metamaterials can be designed that have magnetic

resonances at frequencies where there are no magnetic resonances in existing natural

materials.

1.4.3 Recent advances in metamaterial perfect absorber

The first metamaterial based absorber was proposed by N. L. Landy et al.43 in the

microwave band. The unit cell of the absorber consisted of two distinct metallic ele-

ments separated by a dielectric spacer layer, the top layer is an electric-ring resonator

(ERR) and the bottom layer is a rectangular metal strip as shown in Fig. 1.9. The

absorption mechanism of the absorber is as follows: The top layer consisting of the

ERR couple strongly to incident electric field aligned along the ERR resonators arms

and gives rise to enhancement and dispersion in the electric permittivity ε(ω). This

time-varying electric field will induce currents in the ERR arms. The induced currents

in the central arm of the ERR will create a mirror image in the metal strip at the bottom

of the dielectric spacer. These two anti-parallel currents along with the displacement

currents at the capacitive gap across the dielectric spacer forms a circulating current

loop. The incident time varying magnetic field couple to the induced magnetic dipole

through the circulating current loop, thus yielding a Lorentz-like magnetic response.

By tuning the geometry of the ERR and the thickness of the spacer, it is possible to

46 CHAPTER 1

Figure 1.9: Schematic structure of three layers metamaterial absorber (a)the layer of meta-material;(b) the bottom metallic layer;(c)the unit structure include the dielectric layer. Figureadapted from N. L. Landy et al.43.

match the ε and µ to the ambient medium out side at the same frequency, leading to

the matching of the impedance Z(ω) of the composite medium to the impedance of free

space. Second, the electromagnetic waves will not pass through the metallic ground

plane, giving rise to zero transmission too. The simulated absorptivity A(ω) calculated

from T(ω) and R(ω) was shown to reach a maximum of 96% at the frequency, ωmax =

11.5 GHz see Fig. 1.10. The designed metamaterial was fabricated with printed circuit

board (PCB) technology using photosensitive FR4, a common method for fabrication

of metamaterials operating in the microwave frequency range. Experimentally, Landy

et. al. were able to achieve a peak absorption of 88%. The authors claimed that the

discrepancies between simulation and measurement results were due to fabrication

errors. Authors also carried out numerical simulation to investigate the loss mecha-

nism in the metamaterial structure and found that dielectric loss occurring between the

two layers far exceeded the Ohmic loss and was mainly concentrated in the center of

the metamaterial unit cell beneath the strip of the ERR. In principle, the metamaterial

absorber could absorb 100% of the narrow-band electromagnetic waves.

Metamaterial absorber designs can be scaled up or down to both low and high

frequencies, to operate at microwaves, THz, infrared and optical range48,49. This can be


Figure 1.10: Simulated absorbance for metamaterial perfect absorber design as shown inFig. 1.9. R(ω) (green), A(ω) (Red) are plotted on the left axis and T(ω) (blue) is plotted onthe right axis. Figure taken from N. L. Landy et al.

achieved by just changing the dimensions of the metamaterial structure and properties

of each device depending on the particular application. A similar design was realized in

the THz frequencies, utilizing the down-scaling of the design of microwave absorber to

achieve a resonance approximately at 1.3 THz50. The absorption mechanism is identical

as that of the original microwave absorber design, with the ERR and cut-wire coupling

strongly to the incident electric field and the magnetic field coupling to anti-parallel

currents in the central arm of ERR and the cut-wire. The simulation of optimized design

predicted an absorptivity of 98% at 1.12 THz; however the experimental absorptivity of

nearly 70% at 1.3 THz was shown due to the fact that the deposited dielectric thickness

was smaller than the optimized one.

After the first experimental demonstrations at microwave and terahertz frequencies,

down scaling approaches have been theoretically put forward to extend these ideas to

higher frequencies. The first metamaterial absorber at infrared frequencies consisting of

three layers including a ’cross’ resonator (gold), a ground plane (gold), and a layer of di-

electric material (aluminum oxide, Al2O3) in between, achieved an absorptivity of 97%

at a wavelength of about 6µm51. In this design the bottom metallic layer is a continuous

ground plane that is thicker than the penetration depth of the light, thus preventing

transmission while the cross resonator and ground plane combination provides the

48 CHAPTER 1

impedance matching necessary for zero reflectivity. The thickness of demonstrated ab-

sorbers are approximately an order of magnitude thinner than the operating free space

wavelength and is thus much thinner than the conventional absorbers mentioned in

earlier sections. Since then several designs have been fabricated and characterized to

demonstrate perfect absorption across the electromagnetic spectrum.

The effective constitutive parameters [ε(ω), µ(ω), Z(ω)] are typically retrieved from

the complex reflection and/or transmission coefficients obtained from the metamaterial

tri-layers under the assumption of homogeneous media. However, this viewpoint is

not appropriate for metamaterial using a thick ground plate because the transmission

coefficients vanishes and we are only left with the complex reflection cofficient to

determine the effective parameters of effective medium52. Additionally, the ambiguity

in the MM thickness also poses a problem in calculating with the presence of a semi-

infinite ground plane. Further, the effective medium parameters retrived from reflection

and transmission coefficients of the single unit cell are not very appreciable.

1.5. References 49

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[11] V. M. Shalaev, W. Cai, U. K. Chettiar, H. Yuan, A. K. Sarychev, V. P. Drachev, andA. V. Kildishev, "Negative index of refraction in optical metamaterials," Opt. Lett.30, 3356, 2005.

[12] S. A. Ramakrishna and Oliver J.F. Martin, "Choice of the wave-vector in negativerefractive media: The sign of

√Z," Opt. Lett. 30, 2626, 2005.

[13] V. G. Veselago, "The electrodynamics of substances with simultaneously negativevalues of ε and µ," Sov. Phys. Usp. 10, 509, 1968.

[14] G. Dolling, M. Wegener, C. M. Soukoulis, and S. Linden, "Negative-index meta-material at 780 nm wavelength," Opt. Lett. 32, 53, 2007.

50 CHAPTER 1

[15] G. Dolling, C. Enkrich, M. Wegener, J. F. Zhou, C. M. Soukoulis, and S. Linden,"Cut-wire pairs and plate pairs as magnetic atoms for optical metamaterials," Opt.Lett. 30, 3198, 2005.

[16] S. Linden, C. Enkrich, G. Dolling, M. W. Klein, J. Zhou, T. Koschny, C. M. Soukoulis,S. Burger, F. Schmidt, and M. Wegener, IEEE J. Sel. Top. Quantum Electron. 12,1097, 2006.

[17] S. Chakrabarti and S. A. Ramakrishna, "Magnetic Response of Split Ring Res-onator Metamaterials: from effective medium dispersion to photonic bandgaps,"Pramana–J. Phys. 78, 483, 2012.

[18] D. Schurig, J. J. Mock, and D. R. Smith, "Electric-field-coupled resonators fornegative permittivity metamaterials ," Appl. Phys. Lett. 88, 041109, 2006.

[19] G. Hass, H. H. Schroeder, A. F. Turner, "Mirror Coatings for Low Visible and HighInfrared Reflectance," J. Opt. Soc. Am., 46, 31, 1956.

[20] J. T. Cox, G. Hass, J. B. Ramsey, "Improved dielectric films for multilayer coatingsand mirror protection," J. Phys. Radium, 25, 250, 1964.

[21] R. N. Schmidt, K. C. Park, "High-Temperature Space-Stable Selective Solar Ab-sorber Coatings," Appl. Opt., 4, 917, 1965.

[22] R. E. Peterson, J. W. Ramsey, J. Vac. Sci. Technol., 12,174, 1975.

[23] O. S. Heavens, Optical Properties of Thin Solid Films, Butterworths, London (1955).

[24] M. A. Kats, R. Blanchard, P. Genevet and F. Capasso, "Nanometre optical coatingsbased on strong interference effects in highly absorbing media," Nature Materials,12, 20-24, 2013.

[25] W. W. Salisbury, US Patent 2599944, 1952.

[26] B. A. Munk, J. B. Pryor, Proc. Symp. EM Mats., 2, 163, 2003.

[27] R. W. Wood, "On a remarkable case of uneven distribution of light in a diffractiongrating spectrum," Phil. Mag. & J. Sci., 4, 396, 1902, .

[28] L. Rayleigh, "On the dynamical theory of gratings," Proc. Royal Soc. (Lond.) 79,399-416, 1907.

[29] U. Fano, "The Theory of Anomalous Diffraction Gratings and of Quasi-StationaryWaves on Metallic Surfaces (Sommerfeld’s Waves)," J. Opt. Soc. Am. 31, 213-222,1941.

[30] M. C. Hutley and D. Maystre, "The total absorption of light by a diffraction grating,"Opt. Commun. 19, 431-436, 1976.

1.5. References 51

[31] D. Maystre and R. Petit, "Brewster incidence for metallic gratings" Opt. Commun.17, 196-200, 1976.

[32] L. B. Mashev, E. K. Popov, and E. G. Loewen, "Total absorption of light by asinusoidal grating near grazing incidence," Appl. Opt. 27, 152-154, 1988.

[33] E. K. Popov, L. B. Mashev, and E. G. Loewen, "Brewster effects for deep metallicgratings" Appl. Opt. 28, 970-975, 1989.

[34] E. Popov, L. Tsonev, and D. Maystre, "Lamellar metallic grating anomalies" Appl.Opt. 33, 5214-5219, 1994.

[35] N. Bonod, G. Tayeb, D. Maystre, S. Enoch, and E. Popov, "Total absorption of lightby lamellar metallic gratings," Opt. Express 16, 15431-15438, 2008.

[36] G. H. Derrick, R. C. McPhedran, D. Maystre, and M. Nevi’re, "Crossed gratings:A theory and its applications," Appl. Phys. 18, 39-52, 1979.

[37] W.-C. Tan, J. R. Sambles, and T. W. Preist, "Double-period zero-order metal gratingsas effective selective absorbers," Phys. Rev. B 61, 13177-13182, 1999.

[38] E. Popov, D. Maystre, R. C. McPhedran, M. Nevi‘ re, M. C. Hutley, and G. H.Derrick, "Total absorption of unpolarized light by crossed gratings," Opt. Express16,6146-6155 2008.

[39] T. V. Teperik, V. V. Popov, and F. J. Garcia de Abajo, "Total light absorption inplasmonic nanostructures," J. Opt. A: Pure Appl. Opt. 9, S458-S462, 2007.

[40] N. Bonod and E. Popov, "Total light absorption in a wide range of incidence bynanostructured metals without plasmons," Opt. Lett. 33, 2398-2400, 2008.

[41] S. Collin, F. Pardo, R. Teissier, and J.-L. Pelouard, "Efficient light absorption inmetal-semiconductor-metal nanostructures," Appl. Phys. Lett. 85, 194-196, 2004.

[42] S. Kachan, O. Stenzel, and A. Ponyavina, "High-absorbing gradient multilayercoatings with silver nanoparticles," Appl. Phys. B 84, 281-287, 2006.

[43] N. I. Landy, S. Sajuyigbe, J. J. Mock, D. R. Smith, and W. J. Padilla, "Perfectmetamaterial absorber," Phys. Rev. Lett. 100, 207402, 2008.

[44] D. J. Cho, F. Wang, X. Zhang, and Y. Ron Shen, "Contribution of the electricquadrupole resonance in optical metamaterials, " Phys. Rev. B 78, 121101, 2008.

[45] A. Isenstadt and J. Xu, "Subwavelength metal optics and antireflection," Elec. Mat.Letters, 9, 125-132, 2013.

[46] C. A. Balanis, Antenna Theory: Analysis and Designs (John Wiley & Sons, Inc.,Singapore, 2005.

52 CHAPTER 1

[47] L. Novotny, "Effective Wavelength Scaling for Optical Antennas," Phys. Rev. Lett.98, 266802, 2007.

[48] C. M. Watts, X. Liu and W. J. Padilla, "Metamaterial Electromagnetic Wave Ab-sorbers," Adv. Mat. 24, OP98-OP120, 2012.

[49] Y. Cui, Y. He, Y.Jin, F. Ding, L. Yang, Y. Ye, S. Zhong, Y. Lin, S. He, "Plasmonic andMetamaterial Structures as Electromagnetic Absorbers," arXiv:1404.5695, 2014.

[50] H. Tao, N. I. Landy, C. M. Bingham, X. Zhang, R. D. Averitt, and W. J. Padilla, “Ametamaterial absorber for the terahertz regime: design, fabrication and character-ization,” Opt. Express 16, 7181-7188, 2008.

[51] X. Liu, T. Starr, A. F. Starr and W. J. Padilla, “Infrared spatial and frequencyselective metamaterial with near-unity absorbance,” Phys. Rev. Lett. 104, 207403,2010.

[52] A. Kildishev, V. Drachev, U. Chettiar, D. Werner, Do-Hoon Kwon, and V. Shalaev,"Comment on Negative Refractive Index in Artificial Metmaterials," Opt. Lett. 32,1510, 2007.

CHAPTER2Simulation, Fabrication andCharacterization Techniques

2.1 Introduction

As we have seen, metamaterials gain their properties not only from their intrinsic

constituent material properties or composition, but primarily from their extrinsic com-

position of a designer structure that possess an effective permittivity and permeability

of a desired value1. Many exceptional phenomenon have been theoretically proposed

e.g. negative refraction, left-handed media, perfect lens or superlens, invisibility cloak

and transformation optics devices. These phenomena would be no more than an illu-

sion or a dream unless we could fabricate the real structures with specified properties.

Unlike metamaterials for microwave and terahertz frequencies, whose unit cell can

be easily fabricated by well established printed circuit board technologies and photo

lithography, the difficulties in the fabrication of optical metamaterials becomes severe

as the typical size of a metamaterial resonator for optical frequencies would be of the

order of a few hundred nanometers. Even at IR frequencies of 10 µm wavelength, the

metamaterial structures are of the order of couple of micrometers, which pushes any

current micro-fabrication technique to its extreme limits. Hence, the requirement of

simple designs and fabrication of metamaterial structures that operate at optical or IR

frequencies has posed a serious challenge for research community to observe many

spectacular phenomena2. In this sense, the rapid progress in optical metamaterial re-

53

54 CHAPTER 2

search is only possible because of advances in numerical simulation techniques and

state-of-the-art micro and nano-fabrication technologies developed during the past two

decades.

In first section of this chapter, we will describe the numerical method used to opti-

mized the geometrical parameters of metamaterial absorber. Numerical modelling has

emerged as a powerful tool that supports metamaterials research for identifying new

designer materials in the development of novel or improved applications. It provides

many key informations that can not be measured experimentally. One advantage of

numerical simulation is that an optimized structure can be designed and the behaviour

predicted without unnecessary fabrication iterations. The reliability and the accuracy

in numerical simulations depends on the validity of the simulation model to predict

experimental data.

In the second section, the development of the fabrication techniques used in this the-

sis to fabricate the designed metamaterial are discussed in detail. Conventional surface

patterning of materials to fabricate metamaterials and photonic structures rely on com-

plicated techniques such as electron-beam lithography (EBL), focused ion beam milling

(FIB), nanoimprint lithography (NIL), laser interference lithography (LIL), direct laser

writing (DLW) and thin film processing to form micro/nanostructures. The most com-

mon fabrication techniques used for fabrication of metamaterial at higher frequencies,

where the dimensions of the unit cells are of the order of few hundred nanometer, are

electron beam lithography and focused ion beam. Both EBL and FIB offer tremendous

flexibility in creating high resolution of nanostructure patterns. However, their major

drawback is the low-throughput for patterning large areas. Photo lithography and laser

micromachining are two high throughput methods developed for integrated circuit and

circuit boards is the semiconductor industry that replicate a pattern rapidly from mask

to work piece. The mask is irradiated by ultra-violet (UV) light/optical light or high

intensity laser pulse and the features on the mask are transferred to work piece with

2.2. The finite element method (FEM) and its implementation by COMSOL 55

or without a demagnification. However, photo lithography involves several process

steps, for example, application of photo-resist, exposure, development, evaporation of

a thin film, and lift off. In comparison, direct laser machining by ablation is a dry pro-

cess that directly translates the features at the mask to the work piece by direct ablation

of the material with far fewer intermediate steps. The fabrication technique developed

for carrying out fabrication of the designed metamaterials structures, can be split into

two parts: The fabrication of the shadow masks by Excimer laser micromachining and

the fabrication of the metamaterial from shadow mask techniques.

2.2 The finite element method (FEM) and its implemen-

tation by COMSOL

Full wave three-dimension numerical simulations are carried out in this thesis to study

the electromagnetic properties of highly absorbing metamaterials. These simulations

are essentially performed using the commercial available software COMSOL Multi-

physics (version 3.5a) based on finite element method.

2.2.1 The Finite Element Method

The Finite Element Method (FEM) is a well-established technique in electromagnetic

calculation which are described trough a partial differential equations or can be formu-

lated as functional minimization. The term ’finite element’ stems from the procedure

in which a continuous physical structure is divided into small but finite size elements.

The endpoints or corner points of the element are called nodes. At these points the

unknown functions have to be determined. For a linear problem a system of linear

algebraic equations should is required to be solved. Values inside finite elements can

be recovered using nodal values. The Finite Element Method can handle complex

56 CHAPTER 2

geometries and materials3,4.

Two features of the FEM are worth to be mentioned:

1) Piece-wise approximation of physical fields on finite elements provides good

precision. The precision can be increased with simple approximating functions by

increasing the number of elements in the physical domain.

2) Locality of approximation leads to sparse equation systems for a discretized

problem. This helps to solve problems with very large number of nodal unknowns.

To summarize in general terms how the finite element method works, we list the

main steps of the finite element solution below.

1. The starting point for the finite element method is the partition of the physical

domain into small units of a simple shape called mesh elements. Each finite element

has a specific structural shape and is interconnected with the adjacent elements by

nodal points or nodes. At the nodes, degrees of freedom are located. A node is a

specific point in the finite element at which the value of the field variable is to be

explicitly calculated. Exterior nodes are located on the boundaries of the finite element

and may be used to connect an element to adjacent finite elements. Nodes that do

not lie on element boundaries are interior nodes and are not connected to any other

element. A physical domain of interest is represented as an assembly of these finite

elements. The process of subdividing a structure into a convenient number of smaller

components is known as discretization. The mesh generator discretizes the physical

domains (intervals) into smaller intervals (or mesh elements). If the boundary is curved,

these elements represent only an approximation of the original geometry. There are lots

of shapes the elements can have. Physical values at intervening points of the elements

are same and the field components can be estimated by interpolation. The description

of mesh consists of several arrays, many of which are nodal coordinates and element

connectivities.

2. We then select the kind of functions that will describe the variation of the


function φ inside each element (the trial function). This is equivalent to say, that we

select the basis set of functions that will describe our solution. Often polynomials, for

instance φ(x) = a0 +a1x (known as linear element) or φ(x) = a0 +a1x+a2x2, are selected as

interpolation functions. These interpolation functions are used to interpolate the field

variables over the elements. The accuracy of the results can be improved by increasing

the order of the polynomial. The degree of the polynomial depends on the number

of nodes assigned to the element. If we have n unknown coefficients a0, a1, ..., an − 1

we will need the element to have n nodes to be able to determine them. The most

convenient local approximation functions for these sub-areas are polynomials (linear,

quadratic or cubic). It worth mentioning here that the value of our trial function φ

for a given position x inside an element can be written as a function of the values

of φ at the N nodes the of element. For simplicity, let us assume a two-dimensional

case of a triangular element with a single field variable φ(x, y). The triangular element

described is said to have 3 degrees of freedom, as three nodal values of the field variable

are required to describe the field variable everywhere in the element (scalar).

φ(x, y) = N1φ1(x, y) + N2φ2(x, y) + N3φ3(x, y) (2.1)

In general, the number of degrees of freedom associated with a finite element is equal

to the product of the number of nodes and the number of values of the field variable

(and possibly its derivatives) that must be computed at each node. The matrix form of

58 CHAPTER 2

the above relations for n nodal points is as follows

φ = [N]· [φ] = [N1,N2.....Nn] ×

φ1

φ1

...

φn

.(2.2)

where φi’s are the values of the field variable at the nodes “i”, and Ni’s are the

interpolation functions, also known as shape functions or blending functions. In the

finite element approach, the nodal values of the field variable are treated as unknown

constants that are to be determined. The interpolation functions are most often polyno-

mial forms of the independent variables, derived to satisfy certain required conditions

at the nodes. The major point to be made here is that the interpolation functions are

predetermined, known functions of the independent variables; and these functions

describe the variation of the field variable within the finite element.

3. The matrix equation for the finite element should be established which relates the

nodal values of the unknown function to other parameters. Given the PDE we want to

solve, we must find a system of algebraic equations for each element “i”such that by

solving it we get the values of φ at the position of nodes of the element “i”([φ1, φ2, ...,

φN] ≡ φe ), i.e., we must find for each element "i" the matrix [N]i and the vector [f]i such

that,

[N]i[φi] = [ f ]i (2.3)

For this task different approaches can be used; the most convenient are: the variational

approach and the Galerkin method3.

4. Subsequently the equations for all the element are then assembled to find the

global equation system for the whole solution region. In other words we must combine


local element equations for all elements used for discretization. Element connectivities

are used for the assembly process. Before proceeding for the solution, boundary

conditions should be imposed appropriately.

5. Solve the global equation system. The finite element global equation system is

typically sparse, symmetric and positive definite. Different types of solvers can be used

to solve the problem. There are two fundamental classes of algorithms that are used to

solve for the system

[φi] = [ f ]i[Ni]−1 (2.4)

direct and iterative methods. The nodal values of the sought function are produced

by the solution. The more the number of nodes used, the better is the quality of the

solution.

6. Once we know the φ values, we can compute other magnitudes using the

values of φ. In many cases we need to calculate additional parameters after solution

of the global equation system. For instance if we have solved for electric field of

the Maxwell’s equation, magnetic field, Poynting vector representing the energy flow,

reflection, transmission etc. can be computed for the physical domain.

2.2.2 Implementing the FEM in COMSOL

The basic modelling steps for simulation in COMSOL multiphysics are listed below

1. Choose the right Application Mode

2. Draw the geometry

3. Physics: material parameters, boundary conditions, frequency, etc.

4. Mesh the geometry, and adjust settings as needed.

5. Check the Solver Parameters and solve the problem

6. Post-processing: plot the fields and compute the wanted parameters

Below are the basic steps to build the geometry, define the material parameters and

60 CHAPTER 2

specify the boundary conditions, and selecting the appropriate solver for the given

problem.

Options: This gives facilities like defining constants and expressions, there are two

type of the expressions local and global. Depending on the type of variable, use a

variable in a local or global context to simplify model definitions and for convenient

access to quantities related to the expression that defines the variable. It is practical

to have names for important model parameters like frequency, wavelength, plasma

frequency etc.

Draw: The first step to model a metamaterial in COMSOL is defining the structure.

The geometry is built in a drawing program, from elementary bodies like rectangle,

cylinder or ellipsoid, etc.. The geometry can also be extruded from the 2D drawing or

can be directly loaded from the CAD. The individual bodies can be composed to form

a single object by boolean operations (union, intersection, difference). The tri-layer

metamaterial structure consisting of a metallic disk on top of continuous metal film

separated by a dielectric film spacer was drawn in COMSOL. The tri-layer is placed on

top of a substrate as fabricated. Perfectly matched layers (PMLs) were placed at the top

of the air superstrate and the bottom of the fused silica substrate to absorb the excited

mode from the source port and any higher order modes generated by the metamaterial

structure. The complete geometry is shown in the figure below.

Physics: The next step, after the geometry is built, is to define the representative

partial differential equation (PDE) to see the underlying physical laws of a simulation.

The available analysis types for example, static, transient and harmonic in frequency

can be selected in the analysis column. Stationary analysis (harmonic propagation,

frequency domain) was selected in the analysis type while the simulation was run to

solve for the electric field. For the electromagnetic analysis of the system, COMSOL

solves the following Maxwell’s equations to find the solution in terms of either the

electric field E or the magnetic field H:


∇ × (µr−1∇ ×

~E(~r)) − k02εr

~E(~r) = 0 (2.5)

∇ × (εr−1∇ ×

~H(~r)) − k02µr

~E(~r) = 0 (2.6)

.

Sub domain Settings: Once the geometry has been built, the next step is to define

the sub domain settings. In the sub-domain settings we define the materials in each

domain. The materials properties like refractive index or permittivity can be defined

either from material library or can be specified by the user. In sub-domains setting

we also need to define the Perfectly Matched Layers (PMLs) in the top and bottom

domain in order to terminate any unwanted reflection from the exterior boundary that

could affects the source. PML formulation can be derived from Maxwell’s equations

by introducing a complex-valued coordinate transformation.

Boundary Settings: The analysis of a real structure is reduced to the study of

a periodic unit cell by applying periodic boundary conditions to mimic an infinite

periodic structure. The periodic boundary condition along the directions of periodicity

are imposed through Floquet’s theorem which relates phase shift between the tangential

field components. As applied, this condition states that the solution on one side of the

unit equals the solution on the other side multiplied by a complex-valued phase factor.

The phase shift between the boundaries is evaluated from the perpendicular component

of the wave vector. For exapmple, if the unit cell is periodic in y-direction, only the

x-component is required,

Edest = Esource· exp[−ik· (rdest − rsource)] (2.7)

Periodic boundary conditions must have compatible meshes.

62 CHAPTER 2

Figure 2.1: 3D finite element model for the tri-layer metamaterial structure unit cell.

Port conditions are used for specifying the incident wave and to compute transmis-

sion and reflection coefficients. Port boundary conditions are placed on the interior

boundaries of the PMLs, adjacent to the air domain on top and fused silica domain

at the bottom. The reflection and transmission characteristics can be automatically

determine the in terms of S-parameters from the port boundary conditions. The com-

puted electric field Ec on the port consists of the incident plus the reflected field. The

S-parameters are given by

S11 =

∫port1((Ec − Er).E∗r)dA1∫

port1(Er.E∗r)dA1(2.8)


and

S12 =

∫port2(Ec.E∗t)dA2∫port2(Et.E∗t)dA2

(2.9)

Where Er and Et are the electric patterns on ports 1 and 2.

At interfaces between sub-domains, we impose the tangential continuity condition.

Mesh: The triangle icon gives a mesh. The mesh can be controlled in some detail by

parameters under the menu Interactive Mesh. For high accuracy and small simulation

time we need to do the refinement of the mesh in individual sub-domains. The mesh

generator discretizes the domains into tetrahedral, hexahedral, prism, or pyramid

mesh elements. Selective meshing of the computational domain was carried out by

local refinement of the mesh. The accuracy was important near metal-dielectric-metal

tri-layer due to strong field enhancement, thus, a more refined mesh was implemented

within the tri-layer.

Solve: The generated equations are solved when we click the = icon. Under the

menu choice Solve >Solver Parameters icon there are various options offered. Choice of

solver can be very important for large (and non-linear) problems. We have used para-

metric solver to obtained wavelength dependent reflection and transmission coefficient.

Direct and iterative solver can used for the solving the problem. We have used direct

solver for our problem. The direct solvers used by COMSOL are the UNFMPACK,

PARDISO, and SPOOLES etc. All of the solvers are based on LU decomposition and

would lead to the same solution. We use the PARDISO, which is a high-performance,

robust, memory-efficient solver for solving large sparse symmetric and non symmetric

linear systems of equations.

2.2.3 A benchmark problem

We first test a benchmark problem proposed by Jiaming Hao et al.5. They reported

the design, characterization, and experimental demonstration of an ultra-thin, wide-

64 CHAPTER 2

1.3 1.4 1.5 1.6 1.7 1.8 1.9 2.00.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1.0

Absorba

nce

Wavelength ( m)

FEM

Figure 2.2: Schematic diagram of the simulated unit cell with geometrical parameters, ay = az= 310 nm, h = 50 nm, d = 10 nm. Right: Simulated absorbance as a function of wavelength.

angle, sub-wavelength high performance metamaterial absorber for optical frequencies.

Their experimental results show that an absorption peak of 88% was achieved at the

wavelength of 1.58 µm, though theoretical they obtained near perfect absorption.

We simulated the proposed and fabricated metamaterial design using COMSOL

Multiphysics and validated the accuracy of our model with the experimental obser-

vation. In our test, we consider a metamaterial with a square unit cell of a = 310 nm

consisting of square patches with sides of r = 170 nm separated from a continuous

film of gold thin film by a 10 nm thin film of Al2O3. PML was implemented at the

top and bottom of the metamaterial unit cell to avoid any residual reflection affecting

the source boundary. Floquet boundary condition were applied on both side of the

unit cell to realize an infinite 2D array of unit cell. Port boundary was used for wave

excitation with electric field parallel to the length of the silver rods. We plot absorption

spectra as a functions of wavelength calculated using the COMSOL Multiphysics. The

calculated absorbance shows similar trends as obtained from the experiment and FDTD

simulation5.

2.3. Fabrication of Metamaterials 65

2.3 Fabrication of Metamaterials

2.3.1 Excimer Laser Micromachining

Laser micromachining specifically refers to direct removal of material from its surface

with a intensive laser beam usually in the form of pulses or pulse trains with pulse

energy far exceeding the ablation threshold of the target material6–8. The ablation

threshold, however, is dependent on material properties as well as the interacting laser

characteristics such as laser wavelength and pulse width. Therefore, laser processes

are flexible and can be highly selective. Laser wavelengths have become available in

a wide spectrum range from the infrared to the ultraviolet using a variety of material

media and frequency mixing techniques. Since late 1990s, ultra short laser pulses from

picoseconds to femtosecond are intensively studied as to their interaction mechanism

with transparent materials. Although ultra short pulses within tens of picoseconds can

be achieved by advanced techniques like mode-locking, the pulse energy is reduced

by several orders of magnitude and the laser system is relatively bulky. Nanosecond

lasers with intermediate pulse width are still predominant in industry due to their

excellent flexibility and cost effectiveness. This section describes the experimental

work on laser micromachining and micro-patterning of polyamide sheets for shadow

mask fabrication and thin film ablation with nanosecond UV laser for the fabrication

of metamaterial devices that works at infrared wavelengths.

Excimer lasers are used for a variety of material modification, feature generation

and texturing purposes at the micro- and nanometric length scales9–11. The small wave-

lengths of these lasers (of the order of 100 nm) along with the short-time nanosecond

duration pulses allow the manufacture of micrometer-sized features with very small

heat affected zones12. The excimer laser has become a workhorse for machining of

unconventional materials like polymers13, insulators14, ceramics15 and nanostructured

materials like porous alumina16. The laser machining process depends on both the ma-

66 CHAPTER 2

Figure 2.3: Schematic diagram of the experimental setup for laser machining

terial and the laser characteristic such as wavelength, and pulse duration. Metals and

semiconductors typically undergo melt vaporization17, while polymers and insulators

can be ablated by bond breaking due to photo-dissociation, particularly when ultra-

violet lasers are used. Excimer laser has been popular for machining sharp features

with good aspect ratios on polymer materials18–20. The specific ablation mechanisms in

laser micromachining and the resulting morphology of the ablated region such as the

aspect ratio and side-wall roughness varies with material properties, laser wavelength,

power intensity as well as pulse duration. The relevant material properties are usually

the nature of bonds, the absorption coefficient, thermal conductivity, specific heat and

latent heats of melting and evaporation.

Laser micro-machining is usually carried out in two modes: (i) direct laser writing

by focusing and (ii) Mask projection with demagnification by a (usually homogenized)

laser beam21,22. Although mask projection techniques result in a high production rate as

well as feature fidelity, manufacture of the required mask having the requisite features

becomes a significant issue in limiting its use.


2.3.2 Experimental Procedures for Excimer laser micromachining

The experimental setup for laser machining using mask projection is shown in Fig. 2.3.

A KrF excimer laser (Coherent Variolas Compex Pro 205F)23, capable of producing

pulses of energy up to 750 mJ and of 20 ns pulse width at 248 nm wavelength, is used

for micromachining. The mask projection method essentially requires homogeneous

illumination at the mask plane. A pair of 8×8 fixed arrays of insect eye lenses is utilized

to create a square field of 20 mm×20 mm with a homogeneous top-hat beam profile.

Fig. 2.3 shows the schematic diagram of the experimental setup for laser machining

with the mask location24. The light transmitted across the mask is imaged on the work-

piece using an imaging lens with a typical demagnification of 10×. The intensity of the

laser pulses at the mask plane is measured with an energy meter (Coherent FieldMax

II). Binary masks with the required features, produced using techniques developed

in-house, were used for the laser micromachining. These masks contained features

machined in an area of 20 mm×20 mm on a 30 µm thick aluminum sheet. Typically,

the workpieces used consisted of Kapton (polyimide) sheets, boPET (biaxially oriented

polyethylene terephthalate) sheets and aluminum foils. Kapton and boPET sheets are

polymeric materials and serve to demonstrate the ability of excimer laser micromachin-

ing to make micro-channels and holes on the polymer sheets. The characterization of

the machined workpieces was primarily conducted by a (reflection and transmission)

microscope (Olympus BX51). Scanning electron microscopy (SEM), optical white light

profilometry (Wyko NT1100) and atomic force microscopy (Molecular Imaging Model:

PicoSPM II) were also utilized to characterize the surface topography and hole depths.

The length-scales of the transverse periodicities were also verified for periodic struc-

tures (holes) from the Fraunhofer diffraction patterns using a He-Ne laser. Experiments

were conducted to demonstrate the importance of establishing the image plane of the

imaging system, to measure the conformality of the features produced, to make high

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Figure 2.4: Top left panel shows the topography of the sample of arrays of 2 µm diameter holeswith a period of 4 µm machined on a Kapton sheet measured by AFM. Right panel: The SEMimage of an array of 1 µm holes with 2 µm period. These large scale arrays have a total arrayarea of 1 mm × 1 mm with excellent uniformity throughout. Bottom left panel shows opticalmicroscopic image of ablation in photoresist in the reflection mode. Bottom right panel showsthe SEM image of the 3µm disk on polymer film.

aspect ratio micrometer-sized features over large areas and to measure the material

removal rate (MRR).

2.3.3 Micro Machining of Single Micrometer Features

In order to achieve high quality machining of features down to 1 µm length scales,

proper location of the work piece is crucial. A micromachining three-axis translation

stage with a least count of 1.8 µm was utilized to locate the work piece at the image

plane of the laser beam. To illustrate the criticality of the placement of the work-piece

at the image plane, we moved the work-piece along the beam (z) axis and machined

patterns with single micrometer features at various planes above and below the image

plane, separated by distances of 10µm. The optical microscopic images of the machined


Figure 2.5: Schematic diagram showing the resolution of imaging two distinct spots about thefocal plane of two adjacent focused beams.

features are shown in Fig. 2.6 wherein the blurring of the machined structures as the

work-piece is moved few microns away from the image plane is apparent. It is clear

that unless the work-piece is located within 10 µm of the actual image plane, good

quality machining at 1 µm length scale will not be possible. We can understand the

above by analysing the diffraction of a confined laser beam. The figure shows two

beams (imagined to be coming from two holes in the mask) adjacent to each other such

that they are separated by a distance "a" at the image plane (a is described later in this

text)Fig. 2.6. The Rayleigh range associated with a Gaussian laser beam of waist size

w0 is

zR = π · w20/λ. (2.10)

We can identify each bright spot on the image plane as due to an independent laser

beam confined within a spot size a (here, a is the smallest feature size to be distinctly

produced on the work-piece). As per the definition of the Rayleigh range, this spot

size will grow to double its size (2a) at a distance of zR along the z axis. At this

distance, the electromagnetic fields in one spot start overlapping and interfering with

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the diffracted fields coming from the next bright spot which was at a distance a away on

the image plane. Neglecting the factor of "π" in Eq. (2.10) as we do not have a Gaussian

distribution here, and using λ = 0.248 µm, we conclude that the depth of focus, which

will be two times the Rayleigh range, i.e.

2zR = 2a2/0.248 ' 8 ∗ a2, (2.11)

where a is specified in micrometers. Using a = 1 µm (as we are working with 1µm

features), Eq. (2.11) gives a vertical range of about 8 µm for the placement of the

work-piece, which agrees well with our experimental observations in Fig. 2.6. This

analysis also yields a limit for the depth to width aspect ratio of the machined micro-

structures. Obviously for features having the characteristic size of the order of 10 µm,

the vertical range will be ≈ 8a2= 800 µm. Hence, larger features allow larger tolerance

in the positioning of the workpiece about the image plane of the imaging system.

Conversely, the larger the wavelength, the smaller the vertical range within which

the workpiece needs to be placed. It is shown by the above mentioned experiment

that while manufacturing features of the length scale of single micrometer using laser

micromachining, extreme care should be taken in positioning the workpiece at the

image plane of the imaging system or at the focal spot of the beam in the case of direct

writing. This will allow distinctly resolvable and sharp features to be produced on the

workpiece in a reproducible manner.

2.3.4 Laser micromachining of polyimide films

The physical phenomenon of machining of polyimide (also called KaptonTM by DuPont

company) by laser machining is by ablation. When a material (normally an organic

material) is irradiated by a short-wavelength (in UV range, such as excimer laser) and


Figure 2.6: Optical microscopic images of the micro machined structures on a Kapton sheetplaced at various planes above and below the focal plane.

Table 2.1: shows binding energies of polymer bonds.

Bond EnergyC-C, C-N 3 - 3.8 eVC-H, C-O 4.5 - 4.9 eVC=C, C=O 7 - 8 eV

short-pulse-length (shorter than the thermal relaxation time in microseconds) laser

beam, the molecular bonds in a very thin layer of the material surface can be broken

by the higher energy of shorter-wavelength photon with minimum thermal effect,

and this is also called ”cold-cutting". The photon energies between 3.60 and 4.29 eV

(in the wavelength between 344 and 288 nm are sufficient enough to break C-C and

C-H covalent bonds (with average binding energies of 347 kJ/mol and 414 kJ/mol,

respectively)8. Table 2.1 shows the typical binding energies of polymer bonds, and it is

clear that the KrF laser (248 nm) used in this study is able to break many types of bonds.

When large molecular chains with much shortened length occupy the same volume, the

increased degrees of freedom results in a large pressure and an explosive removal of the

material occurs. The machined spot is surrounded by a "Heat Affected Zone" (HAZ)12

due to heat conducted into the material which causes melting and re-solidification of

material in the HAZ leading to discoloration, change of physical / chemical properties,

cracks and voids due to thermal stress and material modification.

The maximum attainable aspect ratio (Rm) in laser micro drilling of polymers (for

features much greater in size than the wavelength of laser) is theoretically estimated

to be equal to F/Ft, where F and Ft are the fluence and the threshold fluence for the

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polymer22. A larger fluence gives a larger aspect ratio, attainable mostly by highly

focused beams. For a typical fluence F = 3 J/cm2 and Ft = 30 mJ/cm2, Rm = 100. For a

particular beam, this is dependent on the type of the polymer. It also depends on the

fluence at the beam waist and positioning of the top surface of the workpiece about

the beam waist. For features that are only slightly larger than the wavelength of the

laser being used, the focus-ability and Rayleigh range of the beam set the limits for the

aspect ratio. For 1 µm features, the Rayleigh range is 8 µm. Hence, aspect ratios of

order unity only can be achieved.

The possibility of making large length to width aspect ratio structures was examined.

Arrays of linear through slots upto 2 mm long and 10µm wide were machined on 30µm

thick Kapton sheets by using a suitable mask with linear through slots and translating

the workpiece lengthwise to draw the slots. The Kapton sheets were mounted properly

on a glass substrate. A special mention should be made of the observation that the

long thin strips of kapton in the machined sheet get tangled or deformed due to

electrostatic interactions when kept isolated in air after machining. But they can be

made to regain their machined shape by ultrasonification in water. This has potential

applications for microfluidic devices like peristaltic pumps for small discharges. We

could also machine arrays of 1 µm channels with very large aspect ratios on the surface

of a Kapton film, shown in Fig. 2.7, which have potential applications for small flow

reactors. The uniform profiles of these channels can be seen in the atomic force micro-

graph in Fig. 2.7. Large scale arrays of 2 µm and 1 µm diameter holes with a period of

4 µm and 2 µm, respectively, were also machined on Kapton sheets. The pulse energy

was about 340 µJ with a pulsed repetition rate of 2Hz. The arrays occupied an area

of 1 mm×1 mm and are shown in Fig. 2.7. These blind holes have depths of almost

a couple of micrometers which was measured by AFM. Optical microscope cannot be

used to measure the depths of holes with 1 µm diameter as the depths are very small

(1–2 µm) and change in increments of about 100 nm with increasing number of laser


Figure 2.7: Top left panel shows optical microscopic image of 2 µm wide lines in the reflectionmode. Right panel shows the AFM image of the fabricate long lines in polymer. Bottom leftpanel show SEM image of an array of 2 µm diameter square holes in polyimide film over 1 mmX 1 mm area. Bottom right panel show optical microscopic image of the 20µm square holes inthe polymer.

pulses. The pulse energy is about 340 µJ with a pulsed repetition rate of 2 Hz. The large

area uniformity of the periodic patterns has been judged by optical micrographs and

carrying out AFM and SEM scans over different machined areas (1 mm×1 mm areas).

The scans show almost identical patterning (see Fig. 2.7, right panel, for example) over

different areas. The set-up used by us is an experimental set-up and a conservative

estimate of the throughput of the patterning process is 40 mm2/s. By the use of industrial

grade equipments and automation this can be further enhanced. Hence, it has been

demonstrated that excimer lasers can be used to machine features with characteristic

sizes down to 1 µm accurately and rapidly.

2.3.5 Measurement of Material Removal Rate for Machining Holes

The material removal rate (depth per pulse) was examined by investigating the etch

depth as a function of the laser beam fluence and the number of pulses. The effect of

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D

epth

of

hole

( n

m )

800

1,000

1,200

1,400

1,600

1,800

2,000

2,200

Fluence at the substrate ( J/cm2 )1 1.2 1.4 1.6 1.8

5 pulses

10 pulses

15 pulses

Figure 2.8: Top left: Plot showing the depth of the holes in an array of 1 µm holes machined atvarious energies and with 5, 10, or 15 pulses. Top right: shows the machined hole-depths withrespect to the number of pulses at various pulse energies (The lines shown are only a guide tothe eye.). Bottom panel: shows the same data (top right) against the total energy = pulse energy× the number of pulses.

feature size on the machining parameters was investigated by considering 1 µm and 15

µm diameter hole arrays machined on a 30 µm thick Kapton sheet. The machining was

carried out at a very low laser pulse repetition rate of 1 Hz to avoid any cumulative

effects. Repetition rates of 2 and 3 Hz were not found to cause any change in the

feature shapes. For measuring the 1 µm hole features, an atomic force microscope was

used. For the 15 µm hole arrays machined using low energies and smaller number

of laser pulses, the hole depths, typically up to 5 µm, were measured by the optical

profilometer using white-light interferometry. The holes in the array with larger depths

were measured using an optical microscope. The machining rate was quantified by


measuring the depth of the holes as a function of the laser pulse energy, number of

pulses and total energy (= pulse energy×the number of pulses).

Fig. 2.8 shows the plot of depth versus fluence for 1 µm holes. The graph suggests

that the depth of the holes saturates at about 2 µm beyond a fluence of about 1.83 J/cm2

for sufficiently large number of pulses (10 and 15 pulses). Further, it is clear that less

number of higher energy pulses cause larger crater depths compared to more number

of lower energy pulses. For example, 5 pulses at the fluence of 1.83 J/cm2 (total energy =

9.15 J) generate a depth of about 1.5 µm which is greater than that created by 15 pulses

at a lower fluence of 1.1 J/cm2 (total energy = 16 J). As another example, 5 pulses at 1.1

J/cm2 result in hole depth of 0.9 µm. Subsequent sets of 5 pulses increase the hole depth

by only 300 nm and 200 nm, respectively. Thus, it appears that beyond some critical

depth the laser pulses are not able to effectively machine and remove material. The

depth of focus is clearly not a concern as it is about 8 µm in this case. The saturation of

the hole depth with number of pulses is a well known phenomenon in laser machining

at both micrometer and larger scales 25,26.

The ablation of polymers is photolitic in nature wherein a photon having energy

above a certain threshold (bond energy of carbon-carbon bond that is (∼3.5 eV) is

enough to break the carbon-carbon (C-C) bond. Low energy pulses do not break

enough number of C-C bonds and hence lead to small hole depths. Moderate energy

pulses are able to break enough number of C-C bonds that leads to efficient ablation

and comparatively greater hole depth. High energy pulses break a large number of

C-C bonds but over the same polymer mass (albeit into smaller polycarbon fragments

that explode out) leading to almost the same hole depth. Hence, beyond a particular

pulse energy the efficiency of ablative machining (depth per pulse) does not increase.

The plot of the MRR with number of laser pulses is almost linear initially and

indicates a hole-depth saturation with increasing depth, attributed to scattering and

wave-guiding effects by the hole shape as well as plasma shielding. During ablation by

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a laser pulse, the plasma generated by the initial portion of the pulse is confined within

the hole and tends to obstruct and absorb the remainder of the incoming laser pulse.

It thereby results in lower laser pulse energy reaching the ablation zone and lower

machining efficiencies. Additionally, ejection of molten material from a deeper hole

requires higher pressures and is difficult. Hence, significant re-deposition is observed

in deeper holes leading to a hole-depth saturation with increasing depth.

The depth for the 15 µm hole arrays as a function of the pulse energy and number

of pulses is shown in the Fig. 2.8. In Fig. 2.8, the variation of the depth of the holes

with the laser pulse energy is plotted and shows that the machined depth increases

with both the pulse energy as well as the number of pulses in an orderly manner. It is

obvious that control of the machined depth down to about 100 nm would be possible

by controlling the pulse energy accurately. In Fig. 2.8, the variation of the machined

depth of the holes with total energy is plotted. This plot shows that there are two

regimes of machining: the rate of machining (as indicated by the slope of the graph) for

the low energy pulses is much higher than that of the higher energy pulses, indicating

that low energy pulses machine more efficiently at this length scale for the same total

energy deposited at the work-piece.

The depth per pulse is observed to saturate above a certain pulse energy and

hence higher energy pulses yield no extra depth. This observation has important

consequences as it is well known that lower energy pulses above the ablation threshold

result in lower damage zone around the machined regions and our observation would

further encourage lower to moderate pulse energies from the viewpoint of machining

rates as well. Note that, however, this is contrary to the case of laser machining at

single micrometer length scales where higher energy pulses were found to machine

more efficiently. This is because scattering and diffraction by the machined structures

on the work-piece and obstruction of the incoming pulse by the plasma plume is less

important due to the larger sizes and the laser beam profile reaching the base of the


hole (made by previous laser pulses) is not substantially affected.

2.3.6 Laser micromachining of thin metallic films

As our work on metamaterials concerns patterned metal structures, we experimentally

investigated patterning of metallic thin films using Excimer laser micromachining. The

physical mechanism of laser ablation of metal surfaces occurs by simply heating the

material by absorption of laser energy, which is a thermal or pyrolytic process. When a

laser beam irradiates the workpiece surface, part of the laser beam energy is absorbed

by the work-piece surface due to the interaction between the electromagnetic radiation

and electrons of the work-piece materials. The removal of material from the surface

of the metal is due to melting and vaporization of the metal occurring at elevated

temperatures during and after the absorption of the concentrated large laser fluences.

The (ns) laser pulses create large enough concentration of energy and the material is

removed by melt expulsion driven by the vapour pressure and the recoil pressure. This

thermal mechanism, however, creates a large "Heat Affected Zone" (HAZ) surrounding

the laser spot on the metal surface. The energy transportation in the metal is governed

by heat conduction, and the thermal diffusion length is given by l = 2√

(kt), where k is the

thermal diffusion coefficient and t is the pulse duration. For 30 ns pulses, the thermal

diffusion length for Al is 3.03 µm. Thus, direct laser machining of micro-structures

with features of the order of the diffusion lengths or smaller becomes impossible as the

melt-vaporization process either ablates over or damages much larger areas.

The HAZ becomes the limiting feature for the laser micromachining process. One

way to reduce the HAZ would be to use intense picoseconds or femtosecond pulses,

but one is limited by the lack of deep UV laser sources as well as low pulse energies at

these shorter pulse durations in comparison to nanosecond excimer laser pulses.

Here, a novel technique for enhanced excimer laser micromachining of metallic

78 CHAPTER 2

thin films by first coating the metal film by a thin polymer film is developed. The

large photon energy at ultraviolet frequencies is very effective for photolytic ablation

of polymers. As most of the energy of the laser pulse is used up in the cutting of

chemical bonds in the polymer material, there is very little heat conduction into the

surrounding areas resulting in very small HAZ. The explosive removal of material

occurs due to the large pressure buildup in the irradiated area where the number of

degrees of freedom and pressure has increased tremendously due to the large number

of smaller polymer fragments. The method consists of coating the metal film (gold

or aluminum) with a thin film of a suitable polymer such as polyvinyl alcohol (PVA),

polyvinly pyroliddone (PVP), polymethyl methacrylate (PMMA) or commercial photo-

resists with large absorption coefficients at the laser wavelength used. This can be done

by spin coating or dip coating methods to form thin layers of the order of few tens of

nanometers to few hundreds of nanometers. The polymer film is essentially a sacrificial

layer. The gold film could be typically 20 to 200 nm thick. Upon irradiation with the

laser pulse, the polymer layer is machined photolytically and there is very localized

heating in the metal layer just beneath the polymer layer. This results in removing the

top portion of the metallic film along with the polymer layer for sufficient laser pulse

energy in the irradiated region only. The thickness of the gold film removed depends on

the laser pulse energy and can vary from few tens of nanometers to complete removal

of the metal film. The impact and momentum the imploding inner polymer regions

and the shock wave associated also probably play a role in the clean removal of the

gold film underneath. The polymer layer can now be removed by dissolving in a

suitable solvent like acetone for photo-resists and PMMA or water/alcohol for PVA and

PVP. There is very little heat diffusion in the transverse direction during the ablation of

material.

Fig. 2.9 shows the scanning electron microscope image of the patterned thin film

with circular holes of diameter 2 micron on a glass substrate. Fig. 2.9 shows the optical


Figure 2.9: Top left: SEM of an array of 3µm diameter holes in 40 nm thin gold film over 1mm×1 mm area (b) Right: The transmission optical microscope image of a 3 µm holes in 40 nmthin gold film. Bottom left: SEM image of an array of 10µm diameter holes in 40 nm thin goldfilm over 1 mm×1 mm area (b) Right: The transmission optical microscope image of a 10 µmholes in 40 nm thin gold film.

microscope transmission image of the micro-machined thin film showing complete

transmission of light from the holes. This demonstrates the complete removal of the

gold films in the machined areas. The 40 nm gold film is partially transmittive in

the reset of the regions. Note the complete absence of HAZ and the sharpness of the

features machined on the gold. Such arrays of 1 µm holes in conductive metal films

have important applications as frequency selective surfaces at IR frequencies.

2.3.7 Laser micromachining of ITO thin film

Indium tin oxide (ITO) is transparent conducting material which is most widely used

transparent conducting oxides because of its high electrical conductivity and optical

transparency at visible frequencies. In the infrared region of the spectrum it highly

reflective due to its metallic behaviour. Recent studies have demonstrated that tin-

80 CHAPTER 2

Figure 2.10: SEM image of the ITO disk arrays fabricated using laser micromachining of ITOthin film.

doped indium oxide (ITO) is good candidate as plasmonic materials in the near infrared

frequency range because they exhibit metallic behaviour and smaller losses compared

to those of silver and gold in the NIR. The direct laser machining of ITO films allows us

to fabricate high throughput infrared and Terahertz devices. The removal of material

from the surface of the ITO is due to melting and vaporization of the ITO occurring

at elevated temperatures during and after the absorption of the concentrated laser

fluences. We fabricated an array of 3 µm disks in 200 nm thick film over 1 mm square

area in a single pulse ablation. The energy of laser pulse used was measured to be 120

mJ at the mask plane.

2.3.8 Shadow lithography using a laser machined shadow mask

Shadow mask or stencil lithography is a resist-free patterning technique which can

be applied in patterning a broad range of materials deposited by various techniques,


and to a broad range of surfaces27–30. A typical shadow mask consists of a thin flat

substrate with open windows corresponding to the material patterns to be formed.

During the deposition process, evaporated materials can be selectively deposited on

the substrate through the open windows. The shadow mask is used as a hard mask,

protecting the covered regions of the substrate, while allowing the substrate to be

selectively deposited through the open windows. Conventional shadow masks made of

Si, Si3N4, TEMs grid are rigid and brittle, require complicated and expensive processing

steps involving lithography and etching31. Their mechanical stability and resolution

are generally not adequate for micron-size patterning, which limits their application

mainly to the creation of larger patterns (e.g. sub-millimeter). The deposited material

could be metallic, dielectric, and organic. Shadow mask technique can be an excellent

alternative technique for micro-patterning applications on flat and curved surfaces.

In this study, a new polymer shadow mask is fabricated on suspended polymeric

membrane using excimer laser machining, which is capable of simple and accurate

mask-substrate alignment and gap control. The fabricated shadow mask consists of 3

µm hole array machined through the thickness of the sheet on a free standing polyamide

sheet that can be handled robustly. It is worth noticing here that to make through holes

of just 2 or 3 µm across the whole thickness of few microns of the polyimide sheet

would nearly have been impossible with any other fabrication process. In this work,

advantage is taken of the fact that laser micromachining is capable of machining high

aspect ratio features on polymer films as discussed in the previous sections. Note that

micromachining in this approach only needs to be used for the shadow mask that can

be used repeatedly to produce the metamaterial arrays many times. This fabrication

technique is a single step dry process that has many advantages over the present day

common techniques to generate masks that involve lithography methods followed by

chemical etching.

Subsequently, the fabricated mask is placed in to intimate contact on a desired

82 CHAPTER 2

substrate, direct deposition of evaporated materials (such as noble metal) enables lift-

off free fabrication of micro-structure with high reliability and uniformity. Material is

only deposited on the areas of the substrate that are not shadowed from the particle

flux by the shadow mask. Isolated patterns of the deposited material are revealed

after the mechanical lift-off of the shadow mask. By physically masking the substrate

with this mask, it was possible to generate disk like patch arrays over large areas

(few mm2). Although the stencil was kept in physical contact with the substrate, a

small gap between stencil and substrate was unavoidable. The exact gap width was

not known but a gap <10 µm can be estimated. After the deposition, shadow mask

can be carefully peeled off from the substrate, cleaned and re-used it multiple times

without any difficulty. A drawback of the presence of the gap between the shadow

mask and the substrate is the loss of resolution due to blurring of the patterns called

broadening. Since, the dimensions of the features are large, one can reuse this mask

many times as the holes do not get clogged up and the micro-patterns can be formed in

a reproducible manner. Patterning of thin films by shadow mask technique is simple,

inexpensive, and does not require any resist processing and chemical or ion-etching.

This technique requires minimum steps and works well for many materials like metals,

their oxides and semiconductors even complex oxides that are not easily structured

by conventional techniques. The advantage of using shadow lithography is that one

can easily deposit multi layers of patches by successive depositions. This can be of

great use, for example, to generate multilayer metamaterials32. Suitable adhesive or

wetting layers like chromium or titanium can also be deposited through the shadow

masks. Important set-up parameters are: source width, source-stencil distance, stencil-

substrate separation, and the angle of the incoming material flux. The quality of

patterned formed in this process is best for an incoming flux of material along the

normal of the shadow mask with minimum gap present between shadow mask and

substrate.

2.4. Fourier Transform Infrared Spectroscopy (FTIR) 83

Figure 2.11: Schematic diagram of the shadow mask deposition technique, the yellow arrowsrepresent the incoming vapor flux.

Figure 2.12: Left: SEM image of shadow mask after the deposition, Right: Transmission opticalmicroscope image of an array of 3 µm diameter holes on a 8 µm square lattice.

2.4 Fourier Transform Infrared Spectroscopy (FTIR)

Reflection [R(λ)] and transmission [T(λ)] measurements of the fabricated metamaterial

samples over the wavelength 2.5 µm to 20 µm range were performed using a Fourier

84 CHAPTER 2

transform infrared spectrometer (Agilent, Model Cary 660) coupled to a IR microscope

and a cooled HgCdTe detector. The principle of working of this instrument is based on

interference of two beams. Most interferometers employ a beam splitter which takes

the incoming infrared beam and divides it into two optical beams. These two optical

beams are put into a Michelson interferometer, which has one of the two mirrors

fixed and the other moving back and forth very precisely, and changing the optical

path length. This change in optical path length creates interference fringe patterns

that vary with respect to the position of the mirror and the optical frequencies that

are present. This interference pattern, that is a function of the change in optical path

length, is known as an interferogram, and has peaks that correspond to the intensities of

different frequencies. The moving mirror produces an optical path difference between

the two arms of the interferometer. For path differences of (n + 1/2)λ, the two beams

interfere destructively in the case of the transmitted beam and constructively in the

case of the reflected beam. The FTIR measurements are based on measuring all of the

infrared frequencies, rather than individually, as in case of visible-UV spectroscopy

where a prism is used to disperse visible light into its colors. To find the reflection and

transmission, a Fast Fourier Transform is done on the interferogram to separated the

individual wavelengths of energy emitted from the infrared source, taking the collected

results that are a function of the mirror position and transforming them to a function

of wavelength.

All the reflection and transmission measurements were calibrated to that obtained

from a planar gold surface for reflection and with no sample loaded for transmission,

respectively, to compensate for variations due to atmospheric conditions and the lamp

spectrum. Reflection measurements were made with an angular aperture of the incident

beam averaged over an angular range of 140 due to the numerical aperture of the

microscope objective. The beam is reflected off the sample and then reflected by

another mirror to the receiver port of the instrument. The FTIR measurements for

2.4. Fourier Transform Infrared Spectroscopy (FTIR) 85

Figure 2.13: Schematic of the far-field characterization setup composed of a FTIR spectrometerequipped with a IR-microscope.

transmission were made at an incident angle 00 by mounting the sample and shining

infrared radiation from the source port of the instrument onto the fabricated structure,

and collecting the radiation from the back of the substrate and channelling it into the

receiver port of the instrument for measurement. All spectra are collected at a resolution

of 4 cm−1 and consist of 256 scans co-added with a scanner velocity of 40 kHz.

86 CHAPTER 2

2.5 References

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[3] G. P. Nikishkov, Introduction to the Finite Element Method, Lecture Notes. Universityof Aizu, 2004.

[4] J. E. Akin, Application and Implementation of Finite-element Methods (Academic Press,New York, 1982).

[5] J. M. Hao, J. Wang, X. L. Liu, W. J. Padilla, L. Zhou, and M. Qiu, "High performanceoptical absorber based on a plasmonic metamaterial,âAI Appl. Phys. Lett. 96,251104 (2010).

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[7] M. Gower and N. Rizvi, Applications of Laser Ablation to Microengineering,Exitech Limited, Oxford, 2002.

[8] M. Gower, Excimer Laser Microfabrication and Micromachining, Exitech Limited,Oxford, 2002.

[9] H. Helvajian, M. Meunier, A. Pique, Laser Precision Microfabrication, K.Sugioka,eds., Vol. 135 of Springer Series in Materials Science, Springer, Berlin, 1-34, 2010.

[10] Y. Kawamura, A. Kai, and K. Yoshii, "Various Kinds of Pulsed Ultraviolet LaserMicromachinings Using a Five Axis Microstage," J. Laser Micro/Nanoeng., 5, 163-168, 2010.

[11] J. Meijer, K. Du, A. Gillner, D. Hoffmann, V. S. Kovalenko, T. Masuzawa, A.Ostendorf, R. Poprawe and W. Schulz, "Laser Machining by Short and UltrashortPulses, State of the Art and New Opportunities in the Age of the Photons," CIRPAnn. Manuf. Technol., 5, 531-550, 2002.

[12] E. C. Harvey, P. T. Rumsby, M. C. Gower and J. L. Remnant, "Microstructuring byExcimer Laser" Micromach. Microfabr. Process Technol., 2639, 266-277, 1995.

[13] J. Ihlemann, H. Schmidt and B. Wolff-Rottke, "Excimer Laser Micromachining,"Adv. Mater. Opt. Electron., 2,87-92, 1993.

[14] T. C. Chen and R. B. Darling, "Parametric Studies on Pulsed Near UltravioletFrequency Tripled Nd:YAG Laser Micromachining of Sapphire and Silicon," J.Mater. Process. Technol., 169, 214-218, 2005.

2.5. References 87

[15] J. Zhang, K. Sugioka, S. Wada, H. Tashiro, K. Toyoda and K. Midorikawa, "PreciseMicrofabrication of Wide Band Gap Semiconductors (SiC and GaN) by VUV-UVMultiwavelength Laser Ablation," Appl. Surf. Sci., 127, 793-799, 1998.

[16] H. Jha, T. Kikuchi, M. Sakairi and H. Takahashi, "Laser Micromachining of PorousAnodic Alumina Film," Appl. Phys. A, 88, 617-622, 2007.

[17] X. Zhang, S. S. Chu, J. R. Ho and C. P. Grigoropoulos, "Excimer Laser Ablation ofThin Gold Films on a Quartz Crystal Microbalance at Various Argon BackgroundPressures" Appl. Phys. A, 64, 545-552, 1997.

[18] M. Jensen, "Laser Micromachining of Polymers," Ph.D. thesis, Technical Universityof Denmark, Denmark. 2004.

[19] D. Zhu, N. S. Qu, H. S. Li, Y. B. Zeng, D. L. Li and S. Q. Qian, "ElectrochemicalMicromachining of Microstructures of Micro Hole and Dimple Array," CIRP Ann.Manuf. Technol., 58, 177-180, 2009.

[20] M. P. Jahan, M. Rahman, Y. S. Wong and L. Fuhua, "On-Machine Fabrication ofHigh-Aspect-Ratio Micro-Electrodes and Application in Vibration-Assisted Micro-Electrodischarge Drilling of Tungsten Carbide" J. Eng. Manuf., 224, 795-814, 2010.

[21] J. P. H. Burt, A. D. Goater, C. J. Hayden and J. A.Tame, "Laser Micromachining ofBiofactory-on-a-Chip Devices," Proc. SPIE, 4637, 305-317, 2002.

[22] T. Terasawa, N. Hasegawa, T. Kurosaki and T. Tanaka, T., "0.3-Micron OpticalLithography Using a Phase-Shifting Mask" Proc. SPIE, 1088, 25-33, 1989.

[23] Coherent, Inc., "http://www.coherent.com/products/1043/VarioLas-Family", 2001.

[24] G. M. Whitesides, "The Origins and the Future of Microfluidics," Nature, 442,368-373, 2006.

[25] W. Zhang, Y. L. Yao and K. Chen, "Modelling and Analysis of UV Laser Microma-chining of Copper," Int. J. Adv. Manuf. Technol., 18, 323-331, 2001.

[26] C. Y. Jiang, W. S. Lau, T. M. Yue and L. Chiang, "On the Maximum Depth andProfile of Cut of Pulsed Nd-YAG Laser Machining" CIRP Ann. Manuf. Technol.,42, 223-226, 1993.

[27] F. Vroegindeweij, E.A. Speets, J.A.J. Steen, J. Brugger and D. H. A. Blank, "Exploringmicrostencils for sub-micron patterning using pulsed laser deposition" Appl. Phys.A 79, 743, 2004.

[28] E. A. Speets, B. J, Ravoo, F.J. G. Roesthuis, F. Vroegindeweij, D. H. A. Blankand D. N. Reinhoudt, "Fabrication of Arrays of Gold Islands on Self-AssembledMonolayers Using Pulsed Laser Deposition through Nanosieves" Nano. lett. 4,841, 2004.

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[29] E. A. Speets, P. M. te Riele, M. A. F. van den Boogaart, L. M. Doeswijk, B. J.Ravoo,A. J. H. M. Rijnders, J. Burger, D. Reinhoudt, Dave H. A. Blank, "Formation ofMetal Nano- and Micropatterns on Self-Assembled Monolayers by Pulsed LaserDeposition Through Nanostencils and Electroless Deposition," Adv. Funct. Mat.16, 1337, 2006.

[30] M. A. F. van den Boogaart, G. M. Kim, R. Pellens, J. P. van den Heuvel, J. Brugger,"Deep-ultraviolet-microelectromechanical systems stencils for high-throughputresistless patterning of mesoscopic structures" J. Vac. Sci. Technol. 22 , 3174, 2004.

[31] M. Kolbel, W. Tjerkstra, G. Kim, J. Brugger, C. J .M. van Rijn, W. Nijdam, J. Huskensand D.N. Reinhoudt, "Self-Assembled Monolayer Coatings on Nanostencils for theReduction of Materials Adhesion" Adv. Funct. Mater. 13, 219, 2003.

[32] X. M. Yan, S. M. Contreras, M. M. Koebel, J. A. Liddle and G. A. Somorjai, "ParallelFabrication of Sub-50-nm Uniformly Sized Nanoparticles by Deposition througha Patterned Silicon Nitride Nanostencil," Nano Lett. 5, 1129, 2005.

CHAPTER3Design of metamaterial absorbers forinfrared frequencies

3.1 Introduction

Since the first demonstration of a metamaterial perfect absorber at microwave fre-

quencies by Landy et. al. in 20081, metamaterials opened a new trend in the design

of absorbing materials. In fact, structured surfaces with absorption coefficient ap-

proaching unity have been demonstrated from microwave1 and terahertz2 through the

infrared3 almost into optical frequencies4. Among several configurations proposed

during the past few years, tri-layer designs formed by a sub-wavelength scale metallic

structure separated from a metallic film by a dielectric spacer layer appear the most

successful. The light trapping in metamaterial structure is based on simultaneous res-

onant excitation of an electric dipole and magnetic dipole in the tri-layer system. The

top layer on which radiation is incident is a structured metallic layer, separated from

the bottom continuous metallic layer by an intermediate dielectric layer of a suitable

material. Several designs have been given in the literature for the top structured layer

such as cross shaped resonators4, electric split-ring resonators3 and rectangular/square

patches2. Many of these structures are not truly in the homogenizable limit as their

unit cell sizes range from λ/2 to λ/64. As the absorption is derived from only a single

metamaterial layer, however, this has not been a very contentious issue.

In this chapter, we will provide simple designs for polarization independent, wide

89

90 CHAPTER 3

angle, highly absorbing ultra-thin metamaterial absorbers for infrared frequencies.

Numerical simulations have been carried out to model the metamaterial absorbers for

infrared frequencies. Our design consist of a tri-layer metal-dielectric-metal thin film

where the top layer consists of two-dimensional (2D) arrays of gold disks. The disk

array are optimal from the perspective of high-throughput experimental fabrication

e.g. laser micro-machining and photo-lithography. The optimization of absorbance

with respect to the ground plane thickness has been specifically studied by computer

simulations. In comparison to the existing literature on the perfectly absorbing meta-

materials, we investigated in detail the role of ground plane on electric and magnetic

resonances. We find that the ground plane can be made extremely thin and the min-

imum thickness primarily depends on the skin depth of the metallic film. This effect

is physically understood by the nature of the images charges formed in the ground

plane. We also find that it is not necessary to have a continuous ground plane, and

an array of three stacked disk of metal-dielectric-metal can also perform optimally as a

metamaterial absorber with a broader bandwidth.

3.1.1 Choice of the resonant absorption band

The structured units on the top layer act as electric dipole resonators, driven by the

electric field of the incident radiation, primarily control the dielectric response of the

tri-layer structure. A second resonance with an anti-parallel currents in the two metallic

layers, excited by the magnetic field component of the incident radiation, control the

magnetic response of the tri- layer composite medium. These two anti-parallel currents

along with the displacement field in the intervening dielectric act to form circulating

current loops with a confined magnetic field in between. This situation is very much

like the case of negative magnetic permeability in the fishnet structures11 and wire

pair structures12. The induced circulating currents result in a magnetic dipole moment

3.1. Introduction 91

Figure 3.1: Temperature dependent refractive index dispersion of zinc sulphide (ZnS) and zincselenide (ZnSe). Figure adopted from Ref.15

which can strongly interact with the magnetic field of the incident radiation13. If the

electric and the magnetic dipole resonances occur at same frequency, then a strong

localization of electromagnetic energy results in the metamaterial structure. Tuning

the electric and magnetic resonance frequencies and their relative strengths can give

rise to an optimal impedance matching for the incident radiation, thereby giving rise

to strong absorption of the radiation. The geometric details of the unit cell consisting

of metal-insulator-metal tri-layer patterned into a two dimensional periodic array: a

disk resonator at the top with a continuous ground plane at the bottom separated

by a continuous dielectric film are given in Fig. 3.2. The circular nature of the disks

is expected to give rise polarization independent excitation of the resonance. Gold

92 CHAPTER 3

is chosen to be the metallic element due to its chemical stability and low ohmic loss

while the dielectric layer is ZnSe, an excellent infrared material with good thermal

and mechanical properties. The electromagnetic properties of metamaterial absorber

structures were calculated using the COMSOL Multiphysics package based on the

finite element method. The dielectric permittivity of gold was modelled using the

Drude expression

ε(ω) = 1 −ω2

p

ω(ω + iγ), (3.1)

with a plasma frequency ωp/2π = 2176 THz and damping frequency γ/2π = 6.5 THz14.

The dielectric permittivity of ZnSe in the wavelength of interest is taken from well

known experimental results15 as shown in Fig. 3.1. The radiation was assumed to be

incident along the X-axis on the metamaterial layers parallel to the Y-Z plane. The

three dimensional unit cell was simulated using periodic boundary conditions along

the Y-Z directions so that structure can be regarded as an infinite two dimensional array.

The incident radiation is a transverse electromagnetic wave applied using wave-port

boundary conditions16. The frequency dependent reflectance [R(ω)] and transmit-

tance [T(ω)] were obtained from the S-parameters in the simulation package and the

absorbance was calculated as A(ω)= 1-R(ω)-T(ω).

In Fig. 3.2, we show the electromagnetic fields in the unit cell of an absorbing

metamaterial structure with 1 µm diameter gold disk of thickness 100 nm and dielectric

film thickness 60 nm. The incident wave is at the resonant wavelength 5.48 µm with an

intensity of 0.25 W/cm2. The electric field distribution in Fig. 3.2(a) clearly shows the

excitation of an electric dipole as well as a concentration of the electric field within the

capacitive film in the gap between disk and the ground plane shown. The magnetic

field distribution shown in Fig. 3.2(c) clearly indicates the localization of magnetic field


Figure 3.2: Electromagnetic quantities calculated for absorbing structures with h = 100 nm, t =150 nm, d = 60 nm, r = 1 µm and a = 2µm at the resonant wavelength 5.34 µm are shown (a)Electric field magnitude, (b) surface currents density, (c) Magnetic field magnitude, (d) powerflow given by Poynting vector, (e) resistive heating in the material.

94 CHAPTER 3

in the insulating layer which is caused by oppositely oriented current sheets on the

disk and the ground plane [Fig. 3.2(b)]. The currents in the two layers are slightly

unequal or slightly out of phase, a generic feature that has been recently pointed out17.

Thus, there is a simultaneous excitation of an electric as well as a magnetic resonance.

In Fig. 3.2(d), the Poynting vector associated with the radiation is depicted and the

electromagnetic energy clearly flows into the resonator formed by the tri-layer system.

The resistive heating in the metamaterial is defined as

Q =12ε0ωImε(ω)|E|2 +

12µ0ωImµ(ω)|H|2, (3.2)

and depicted by a color map in Fig. 3.2(e) shows that there is tremendous localized

absorption within the metallic regions. The absorption in the continuous gold film is

also in the regions near the disk only.

A change in the disk diameter will result in a shift of the electric resonance frequency,

and hence, result in a change of the effective dielectric permittivity [ε(ω)] of the system.

In comparison, a change in the dielectric layer thickness primarily affects the magnetic

resonance and will control the effective magnetic permeability [µ(ω)] of the system. The

capacitive coupling to the ground plane will also control the ε(ω), but to a lesser extent.

Thus, the combination of the diameter of disk and layer thickness can be optimized to

effectively match the impedance of the structure, Z=√µ(ω)/ε(ω), to vacuum, thereby

strongly coupling the incident radiation to the resonant structure.

We show in Fig. 3.3(a) that the peak absorption can be shifted to larger values by

reducing the dielectric layer thickness. The absorption in an optimized structure with 1

µm disks and various dielectric layer thicknesses, where the peak absorbance exceeds

99.9% is shown. These structures have continuous dielectric and gold films. A reduction

in the dielectric layer thickness results in a red shift of the resonance as well as an


Absorbance

0

0.2

0.4

0.6

0.8

1

Wavelength (µm)5 5.2 5.4 5.6 5.8 6

60 nm 70 nm 80 nm

(a)

Absorbance

0.9

0.92

0.94

0.96

0.98

1

Angle of incidance ( in degrees)-40 -20 0 20 40

TMTE

(b)

Absorbance

0

0.2

0.4

0.6

0.8

1

Wavelength (µm)5 5.2 5.4 5.6 5.8 6

200 nm 150 nm 100 nm 50 nm

(c)

Absorbance

0

0.2

0.4

0.6

0.8

1

Wavelength (µm)5.4 5.6 5.8 6 6.2 6.4 6.6

10 nm 20 nm 50 nm

(d)

Absorbance

0

0.2

0.4

0.6

0.8

1

Wavelength (µm)5 5.2 5.4 5.6 5.8 6

100 nm 50 nm

(e)

Figure 3.3: Simulated Absorbance spectra of the designed absorber structures for (a) differentthicknesses of dielectric film, (b) angle independence of the absorbance for different polariza-tion, (c) and (d) different thicknesses of ground plane and dielectric layer thickness of 60 nm,(e) different thickness of gold disk with dielectric layer 60 nm. (a) to (e) are for metamaterialstructure with continuous dielectric layer and gold ground plane.

optimization of the absorption. This can be understood by noting that the capacitance

of the resonator increases with the reducing thickness and the resonance frequency, ω0

= 1/√

LC where L is inductance and C is capacitance of the structure, reduces. Note

that when the dielectric layer thickness decreases although the inductance might also

appear to reduce, the frequencies are large enough that magnetic resonance frequency

no longer scales up with the reducing geometric inductance18.

The simulated absorbances as a function of the angle of incidence are presented in

Fig. 3.3(b) for both TE and TM waves with an oblique incident angle ranging from -45

to 45. It was observed from the figure that absorbance remains greater than 99% for

both TM and TE waves for incident angle ranging from -25 to 25 . The absorbance

96 CHAPTER 3

varies more weakly with incident angle for TE polarized radiation as the entire electric

field is parallel to the disk at all angles, while for TM polarization the electric field

component normal to disk decreases at larger angles as shown in Fig. 3.3(b).

In Fig. 3.3(c) the behavior of the absorption band with the ground plane thickness

is shown. In literature, this aspect has not been widely studied and it has been only

noted that the dependence is weak19. We begin by analyzing the role of ground

plane. Principally at these frequencies, gold behaves somewhat as a perfect conductor,

whereby mirror images of the charge distributions on the disk are formed on the

continuous gold film. This is consistent with the oppositely flowing currents in the

two metallic layers. We show in Fig. 3.3(d), the absorption in structures with varying

ground plane thicknesses while keeping the dielectric layer thickness and disk diameter

constant. It is seen that as long as ground plane thickness is a few times the skin

depth of the gold film (25 nm at 5.5 µm wavelength, see for example20), the peak

absorbance remains high(>99%). In complete agreement to our expectations, once

the ground plane thickness is smaller than the skin depth the absorbance reduces

and the reflectivity becomes large. For the ground plane thicknesses lesser than the

skin depth, image charges are not effectively formed and proper magnetic resonance

can not be established. This results in a dielectric dipole resonance without proper

impedance matching resulting in a substantial reflection. Note that the transmittance

through these resonant structures remains small (1% transmittance for 10 nm ground

plane) even when the ground plane thickness is very small. In Fig. 3.3(c) the spectral

absorbance for metamaterial, with disk thickness 100 nm and ground plane thicknesses

50 nm, 100 nm, 150 nm, 200 nm are shown. The dielectric layer thickness is the same

(60 nm) for all. It is seen that the peak absorption wavelength shifts to smaller values

by moderate amounts with increasing ground plane thickness. This is caused by the

reduced capacitance due to presence of more negative dielectric permittivity material

for increased ground plane thickness. We further show that as the ground plane


thickness approaches the skin depth, the peak absorbance keeps reducing, while red

shifting by significant amounts. Note that this effect can not be understood if one

considers the metal to be a perfect conductor. It is found that near unit absorption can

still be achieved by reducing the ground plane thickness as long as the ground plane

thickness is few times more than the skin depth. When the ground plane thickness

approaches or becomes smaller than the skin depth of gold, the peak absorbance starts

reducing from unity. Fig. 3.3(d) shows this reduction for ground plane thicknesses of

10 nm, 20 nm and 50 nm and a large red shift for the case of 10 nm ground plane.

The effect of the finite skin depth can be used to define the relative thickness of the

disk and ground plane. In Fig. 3.3(e), the effect of the gold disk thickness on absorbance

is shown. It is found that the absorption decreases from unity as the gold disk thickness

decreases. This effect arises because the charge distributions on the gold disk’s surface

can not be reflected properly in the ground plane due to the finite skin depth. This is

particularly true for the charges on the top surface of the gold disk.

We have also investigated the absorbance for square gold patch/ZnSe layer/Continuous

gold layer: top structured layer consist of an array of square gold patches of side 1 µm

and dielectric film thickness of 50 nm. The designed metamaterial structure has a peak

absorbance of over 97% at 6.5 µm as shown in Fig. 3.4. The electromagnetic resonances

giving rise to high absorption are similar to the resonance of MDM structure with top

structured layer consisting of circular disk array. Our study shows that square patches

don’t show any beneficial feature over the circular patch resonators. Instead making

the patch circular has several advantages as we would not want to bother about making

sharp corners which might be necessary with square and rectangular patches. These

sharp features and corners are a nightmare for any scientist involved in micro/nano

fabrication processes.

98 CHAPTER 3

6.0 6.2 6.4 6.6 6.8 7.0 7.2 7.4 7.6 7.8 8.00.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1.0

Absorba

nce

Wavelength ( m)

A

Figure 3.4: Left: Schematic diagram of the unit cell of a metamaterial absorber with geometricalparameters are, ay = az = 2 µm, h =200 nm, d = 150 nm, r =1 µm, t = 50 nm. Right: Calculatedabsorbance as a function of wavelength for normal incidence.

3.2 Design of dual-band absorbers

The bandwidth of a metamaterial absorber is an important aspect that greatly affects

the applications, particularly with respect to bolometric and energy harvesting applica-

tions. Aiming at the expansion of the absorption band as well as to having multi-band

absorption, one way has been to combine multiple non-degenerate resonant struc-

tures within a unit cell to give rise to multiple absorption bands corresponding to

each resonator in the sub-lattice21–24. Following this design strategy, broadband and

multiple-band metamaterial absorbers have been demonstrated at microwave, THz25,

and infrared frequencies24,25, respectively. Liu et al.25 theoretically and experimentally

demonstrated dual-band and wide-band near perfect absorbers at mid-wave infrared

frequencies with a multiplexed unit cell. However, this design strategy reduces the

filling factor considerably for each resonator by necessarily enlarging the unit cell size,

and hence the peak absorbance for each band is reduced. Moreover, when non degen-

erate resonators are very close to each other, their fields can often overlap resulting in

hybridized multipole resonances with different set of bands. Thus the simplicity of the

design is lost, and further attaining very high absorbance over 98% on multiple bands

3.2. Design of dual-band absorbers 99

4.0 4.5 5.0 5.5 6.0 6.5 7.0 7.5 8.0 8.5 9.00.0

0.2

0.4

0.6

0.8

1.0

Absorba

nce

Wavelength ( m)

ZnS & Ge ZnS & GaAs

Figure 3.5: Left: Schematic diagram of the unit cell of a dual band absorber with geometricalparameters are, ay = az = 2 µm, h =200 nm, d = 150 nm, r =1 µm, t1 = 80 nm, t2 = 50 nm, t3 =100 nm. Right: Calculated absorbance as a function of wavelength for normal incidence for thedielectric pair of spacers as ZnS and Ge (black), and ZnS and GaAs (red)

has been difficult.

In this section, we present designs for polarization independent, wide angle, meta-

material absorbers over multiple bands of infrared wavelengths from 3–10 µm. The

unit cell of a proposed dual band infrared metamaterial absorber is shown in Fig. 3.5

and consists of metal-dielectric-metal disks stacked alternately on top of stacked con-

tinuous dielectric and metallic films. The circular disks have been shown to give rise

to polarization independent excitation of the resonances. Different dielectric spacers

with very different dielectric permittivity have been chosen to give rise to resonances at

different frequencies. Using this approach, one can obtain resonances localized on dif-

ferent layers at different frequencies that are completely independent of each other. This

approach allows us to design absorbers with very high absorbance at pre-determined

frequencies. In comparison to using differently sized resonators arranged in the plane

resulting in a reduction of the filling fraction and corresponding decrease of the peak

absorbance, stacking the resonators with independent resonances in the third dimen-

sion accomplishes multi-band absorbance effectively with no reduction in the filling

100 CHAPTER 3

fraction or resonance strength. Further, this approach of stacking the resonators can

also be combined with the approach of having multi-band resonators in the planar unit

cell to obtain multi-band absorptivity to reduce the number of layers when too many

layers need to be stacked.

Consider the metamaterial shown in Fig. 3.5(Left panel), with a square lattice for the

array. For numerical simulations, the dielectric permittivity of gold was modelled using

the Drude expression ε(ω) = 1−[ω2p/ω(ω + iγ)], with a plasma frequency ofωp/2π= 2176

THz and damping frequency ofγ/2π= 6.5 THz14. The dielectric layers are zinc sulphide

(ZnS)29 and germanium (Ge)30 that are reasonably non absorptive at the wavelengths

of interest. The substrate was taken to be germanium (Ge). The wavelength dependent

reflectance [R(λ)] and transmittance [T(λ)] were obtained from the S-parameters in the

simulation package. The absorbance was calculated as A(ω) = 1 − R(ω) − T(ω).

Fig. 3.5 (right) shows the absorbance obtained for the designed structure shown in

Fig. 3.5 (left) with the dielectric pair of spacers as ZnS and Ge (black), and ZnS and

GaAs (red) respectively. For ZnS and Ge pair, two distinct peaks occur at 4.98 µm

and 8.5 µm with peak absorbance of 99% and 99.9%, respectively. For ZnS and GaAs

pair, two distinct peaks comparatively occur at 4.98 µm and 7 µm with similar peak

absorbance. As shown in Fig. 3.5, the separation between two peaks in the absorption

spectrum can be adjusted by replacing the lower dielectric spacer Ge with GaAs, which

has smaller dielectric permittivity as compared to Ge. We also observe that the two

resonances do not affect each other as the absorption peak at 4.98 µm corresponding to

fields localized in the ZnS remains same for both the cases. The stacked dielectric and

metal disks do not affect the resonance of the tri-layer resonator composed of metal

disk on top of the continuous dielectric-metal films. Transmission was found to be zero

for the entire range of wavelengths.

To understand the origin of the spectral characteristics, the simulated electric and

magnetic field distributions in the x-z plane of the two resonances (for ZnS and Ge

3.2. Design of dual-band absorbers 101

Figure 3.6: Electromagnetic quantities calculated for the absorbing structure as shown inFig. 3.5: (a) Electric field magnitude, (b) Magnetic field magnitude and (c) Poynting vectorat 4.98 µm; (d) Electric field magnitude, (e) Magnetic field magnitude and (f) Poynting vectorat 8.5 µm.

102 CHAPTER 3

dielectric spacers) are plotted in Fig. 3.6. The electric field distribution in Fig. 3.6(a)

shows the excitation of a dipole corresponding to positive charges at one edge and

negative charges at the other edge of the gold disks as well as a concentration of the

electric field within the capacitive film in the gap between the disks corresponding to

the first absorption peak at 4.98µm. The magnetic field distribution shown in Fig. 3.6(b)

clearly indicates the strong localization of the magnetic fields within the dielectric disk,

which is caused by oppositely oriented current sheets on the neighboring metallic disks.

The currents in the two layers are slightly unequal and out of phase. Thus, there is

simultaneous excitation of an electric as well as a magnetic resonance. In Fig. 3.6(c)

the Poynting vectors associated with the radiation is depicted and the electromagnetic

energy clearly flows into the resonator formed by metal-dielectric-metal disks. The

second peak at 8.5 µm in the absorbance spectra arises due to very similar excitation

of the electric and magnetic dipole resonances in the tri-layer system formed by the

bottom metal disk and continuous metallic plane separated by the continuous dielectric

film as shown in Fig. 3.6(d) and (e). The local electromagnetic power flow is enhanced

at the lower dielectric layer adjacent to the continuous metallic films shown in the

Poynting vector map of Fig. 3.6(f).

It should be stressed that the same size of the gold disk can act as a good dielectric

resonator at various wavelengths ranging from the near infra-red (NIR) to long wave

infra-red (LWIR) due to capacitive loading by the surrounding dielectric. For example,

we show in Fig. 3.7, the resonant reflectivity of an array of gold disks calculated

with various substrates (ZnS, GaAs and Ge). The peak reflectivity corresponding

to various dielectric substrate continuously shifts to larger wavelength with larger

dielectric permittivity of the substrate. This property allows us to generate dual/multi

band absorber with resonant absorption in widely spaced bands. Our example shown

in Fig. 3.5 has one band in MWIR and another in LWIR. One also notes that the profile

of the reflectivity becomes very broad with increasing substrate permittivity.

3.3. Design of multi-band absorbers 103

3 4 5 6 7 8 9 100.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

Reflectan

ce

Wavelength ( m)

Ge GaAs ZnS

Figure 3.7: Calculated reflectance of an array of gold disks of 1 µm diameter and 100 nm thick-ness in a square lattice of period 2 µm on various substrates as shown in legend. The dielectricpermittivity used for different substrate were εZnS=2.2, εGaAs=3.29 and εGe=4.0038.

The polarization insensitive performance of the metamaterial absorber is highly

desirable for many practical applications. We show the absorption spectra as a function

of incident angle for both TE and TM polarizations in Fig. 3.8. Our simple design shows

a wide band absorbance of more that 90% for both TE and TM waves with an oblique

incident angle ranging from almost -20 to 20. We note that the multi-layered disks

have reduced this angular range for resonant absorption in comparison to the single

band absorber where an angular range of -40 to 40 was obtained for both TE and TM

polarizations. It is observed from the figure that absorbance remains greater than 95%

for TM waves for incident angle ranging from almost -40 to 40 .

3.3 Design of multi-band absorbers

We further extend the multi-layered approach where alternating multiple metallic

and dielectric disks are stacked to the design of a four-band resonant metamaterial

absorber. By adjusting the dielectric spacer materials and thicknesses, one obtains

104 CHAPTER 3

-50 -40 -30 -20 -10 0 10 20 30 40 500.5

0.6

0.7

0.8

0.9

1.0

Absorba

nce

Angle of incidene (degree)

TE TM

-30 -20 -10 0 10 20 300.5

0.6

0.7

0.8

0.9

1.0

Absorba

nce

Angle of incidence (degree)

TE TM

Figure 3.8: Calculated absorbance for the dual band metamaterial absorber shown in Fig. 3.5 at4.98 µm (left) and at 8.5 µm (right) as a function of incidence angle for different polarizations,with ZnS as one dielectric and Ge as second dielectric layers. Black lines are meant to guide theeye only.

different resonances for the different sets of tri-layers. For example, four resonances are

observed at 4.4 µm, 6.06 µm, 6.64 µm and 8.53 µm wavelengths corresponding to the

four different dielectric materials used as ZnS, ZnTe, GaAs, and Ge, as shown in Fig. 3.9.

The electric and magnetic field distributions at the resonance frequencies are similar

to the field distributions shown in Fig. 3.6. The resonant fields in one tri-layer are not

affected by the presence of the other layers so long as the corresponding resonance

frequencies are spaced far apart. Thus, by just adding two layers of dielectric and

metal of optimal thicknesses, the performance of the absorber is doubled. However,

when the resonance peaks are close together, the resonances start affecting each other

(see the resonance at 6.06 µm in Fig. 3.9). There is certain amount of detuning of

the resonance due to the other resonant tri-layer resulting in a frequency shift and

impedance mismatch. Optimization routines based on genetic algorithms would be

very useful for optimizing resonant condition in such cases. This effect does not arise

from the relative placement of the corresponding tri-layers in the multi-layer stack.

In order to compare with the approach that uses unit cells containing different

structures that are tiled in the plane, we show another hybrid design for a multi-band

metamaterial consisting of an array with a sub-lattice of two stacked doubly resonant


4 5 6 7 8 90.0

0.2

0.4

0.6

0.8

1.0

Ref

lect

ance

(R) &

Abs

orba

nce

(A)

Wavelength ( m)

R A

Figure 3.9: Calculated absorbance and reflectance spectra for multi-band absorber for 1 µmdisks with dielectric layer thicknesses dZnS = 35 nm, dZnTe = 50 nm, dGaAs = 90 nm, and dGe =150 nm.

metal-dielectric-metal disks of diameter 0.8µm and 1µm respectively on the continuous

dielectric-metal film. The simulated absorption spectrum of the metamaterial structure

is shown in Fig. 3.10 has four absorbance bands peaked at 4.02 µm, 5.02 µm, 7.12

µm and 8.72 µm wavelengths respectively. The first two peaks in the absorbance

spectrum at 4 µm and 4.98 µm correspond to the simultaneous excitation of the electric

and magnetic dipoles in the metal-dielectric-metal disks of diameter 0.8 µm and 1 µm

respectively, while two peaks in the absorbance spectra at 7.12 µm and 8.72 µm occurs

due to simultaneous electric and magnetic resonance in the tri-layer system formed by

the bottom metal disks of diameter 0.8 µm and 1 µm and continuous metallic plane

separated by the continuous dielectric film respectively.

The additional peak with lower peak absorbance of 90 % occurring at 3.62 µm is

due to a multi-polar excitation in bottom disks of 1 µm as shown in Fig. 3.10. The

peak at 6.92 µm and 8.46 µm are due to the electric and the magnetic dipole moments

excited in two tri-layer system formed by the bottom disks of 1 µm diameter separated

by the continuous dielectric and metal films. Interestingly, the excited dipole moments

are perpendicular to each other due to the field interactions as a result of the spatial

106 CHAPTER 3

4 5 6 7 8 90.0

0.2

0.4

0.6

0.8

1.0R

efle

ctan

ce (R

) & A

bsor

banc

e (A

)

Wavelength ( m)

R A

Figure 3.10: Calculated absorptivity and reflectivity for the design shown in Fig. 3.10 with twogold disks of diameter 0.8 µm and 1 µm with ZnS as one dielectric layer material and Ge as thematerial for the second dielectric layer.

arrangement of unit cell (shown in Fig. 3.11). Comparatively, at the full peak (7.12 µm),

the two dipoles within the unit cell are oriented parallel to each other. This corresponds

to the metamaterial L-C resonance of the tri-layer system. Let us now dwell on the

comparative features of the two approaches. The commonly suggested approach of

enlarging the planar unit cell by tiling two or more non-degenerate resonant structures

and our approach of stacking the structures in the third dimension. It is clear that

the latter approach can have high filling fractions, particularly for larger number of

non-degenerate structures. The multi-layer approach preserves the simplicity of the

description as a metamaterial in terms of single scatterer resonance, while in the filled

sub-lattice approach, we see that the interactions between the disk resonators within

the plane can enormously complicate the understanding of the resonances and the


Figure 3.11: Schematic diagram of the sub-lattice design with same geometrical parametersare, a= 2.5 µm, r1 = 1 µm, r2 = 0.9 µm, and d= 100 nm and layer thicknesses same as shown inFig. 3.5; and Electric field magnitude at (a) 3.64 µm, (b) 6.92 µm and (c) 7.12 µm wavelengths.

performance of the metamaterial. It should be noted that the fabrication of layered

structures will involve a greater level of complexity than planar metamaterials. We

suggest shadow mask deposition where a stencil mask containing the desired pattern

can be used to fabricate the multi-layered structure by sequential deposition of physical

vapors through the mask as a rapid and simple method suitable for the fabrication of

the proposed multi-layered metamaterial.

108 CHAPTER 3

3.3.1 Metal/dielectric/metal disks stack based absorber

Next, we investigated the absorbance for a metamaterial structure consisting of two

metal disks of 100 nm with a dielectric disk of 60 nm thickness sandwiched in between

[see the inset in Fig. 3.12]. The diameter of all disks are 1 µm. We found a large peak

absorbance of more than 97% at 5.26 µm with an enhanced bandwidth as compared to

the metamaterial structure with a continuous dielectric and gold films. The broadband

absorption in these structures is due to a confined surface current in the bottom gold

disk in comparison to the continuous ground plane that result in a broadband electro-

magnetic resonances. As we have seen in the previous section the same size of the gold

disk can act as a good dielectric resonator over very broad wavelengths ranging from

the near infra-red (NIR) to long wave infra-red (LWIR) due to capacitive loading by

the surrounding dielectric. It is the magnetic resonance that is extremely sensitive to

dielectric layer thickness to form a strong magnetic resonance. Thus if one can have a

metamaterial which has a broad band magnetic resonance. The resultant design will

have a broadband absorption with a high peak absorbance. In order to investigate the

magnetic resonance in case of continuous and structured ground plane, we carried out

numerical simulation for metamaterial design with stack metal/dielectric/metal disks.

We note from our simulations that the surface currents in the ground plane disperse

out away from area of the disk at above and below resonance wavelengths (5.45 µm).

In comparison, in the case of stacked disks, the surface currents are physically confined

to the area of the disk at all frequencies above and below resonance Fig. 3.13. Hence a

broadband absorption of over 1 µm bandwidth, although the extent of absorbance is

reduced (90%) over this band due to imperfect impedance matching. The transmittance

in the area of the stacked disks is noted to be almost zero.

We have also evaluated absorption spectra for a dual-band design as discussed in

Fig. 3.5 with stacks of metal/dielectric/metal/dielectric/metal. The absorption spectrum

3.4. Conclusions 109

Figure 3.12: Left: shows the broadband absorbance for stacks of MDM disk with same geo-metrical parameters as shown in Fig. 3.2 Right: shows the broadband absorbance for stacks ofMDMDM disk with geometrical parameters as shown in Fig. 3.5.

of the metamaterial shows two broadened peaks at a wavelength at 4.95 µm and 7.65

µm with peak absorbances of 78% and 65% respectively. The lower peak absorbance are

due to the interference between two resonance in two metal/dielectric/metal tri-layers

and hence in order to achieve near perfect absorption, one needs to properly optimize

the dielectric layer thicknesses. It is important to note that the peak wavelength has

shifted from the 4.98 µm and 8.5 µm for the continuous metallic film to 4.98 µm and

7.75 µm for the discontinuous structured bottom metal disk array.

3.4 Conclusions

In conclusion, we have provided simple designs consisting of resonant disk-like metal-

lic particle coupled to continuous dielectric and metallic films for highly absorbing

metamaterial for mid-infrared wavelengths. These metamaterial structures exhibit

high absorption of over 99.9% over large angular ranges of incident wave. Further, the

absorption is reasonably polarization independent. We have investigated in detail the

role of the ground plane thickness and shown that the minimum ground plane thick-

ness is limited by the skin depth only. Another metamaterial absorber design consisting

110 CHAPTER 3

Figure 3.13: Top panels: surface current within the metal disk and continuous metalfilm for wavelengths 5 µm, 5.45 µm and 6 µm. Bottom panels: Surface currents formetal/dielectric/metal disks.

of stacked metal-dielectric-metal circular disk is shown to provide for broadband ab-

sorption (bandwidth~1 µm), but with a smaller peak absorbance of 97%. We further

extended our approach to designed multi-band metamaterial absorbers composed of

periodically patterned stacked metal/dielectric disk structures on top of a continuous

dielectric and metallic film at infrared wavelengths. Further, we showed that the

absorption peaks separation can be adjusted by appropriate choice of the dielectric

spacers. The absorption is reasonably independent of the incidence angle for both TE

and TM polarizations. It is shown that the metamaterial absorber consisting multiple

stacked non-degenerate resonators have certain advantage over the designs that tile

multiple non-degenerate resonant units in the plane within a unit cell, and it is more

straightforward to understand the resonant behaviour in the resonant multi-layered

absorber than a multi-band metamaterial absorber based on multi sub-lattice planar

designs. Polarization and angle independent peak absorbance (99%) can be obtained

across all the SWIR and MIR frequencies.

3.5. References 111

3.5 References

[1] N. I. Landy, S. Sajuyigbe, J. J. Mock, D. R. Smith, and W. J. Padilla, “Perfectmetamaterial absorber,” Phys. Rev. Lett. 100, 207402 (2008).

[2] H. Tao, N. I. Landy, C. M. Bingham, X. Zhang, R. D. Averitt, and W. J. Padilla, “Ametamaterial absorber for the terahertz regime: design, fabrication and character-ization,” Opt. Express 16, 7181-7188 (2008).

[3] X. Liu, T. Starr, A. F. Starr and W. J. Padilla, “Infrared spatial and frequency selectivemetamaterial with near-unity absorbance,” Phys. Rev. Lett. 104, 207403,(2010).

[4] J. Hao, J. Wang, X. Liu, W. J. Padilla, L. Zhou, and M. Qiu, “High performanceoptical absorber based on a plasmonic metamaterial,” Appl. Phys. Lett. 96, 251104(2010).

[5] N. Liu, M. Mesch, T. Weiss, M. Hentschel, and H. Giessen, “Infrared perfectabsorber and its application as plasmonic sensor,” Nano Lett. 10, 2342-2348 (2010).

[6] T. Maier and H. Brueckl, “Multispectral microbolometers for the mid infra-red,”Opt. Lett. 35, 3766-3768 (2010).

[7] C. Wu, B. Neuner, J. John, A. Milder, B. Zollars, S. Savoy and G. Shvets,“Metamaterial-based integrated plasmonic absorber/emitter for solar thermo-photovoltaic systems,” J. Opt.14, 024005 (2012).

[8] X. Chen, Y. Chen, M. Yan, and M. Qiu, “Nanosecond Photothermal Effects inPlasmonic Nanostructures,” ACS Nano 6, 2550-2557 (2012).

[9] H. T. Chen, J. Zhou, J. F. O’Hara, F. Chen, A. K. Azad, and A. J. Taylor, “Antire-flection Coating Using Metamaterials and Identification of Its Mechanism,” Phys.Rev. Lett. 105, 073901 (2010).

[10] J. Wang, Y. Chen, J. Hao, M. Yan, and M. Qiu, “Shape-dependent absorptioncharacteristics of three-layered metamaterial absorbers at near-infrared,” Appl.Phys. Lett. 109, 074510 (2011).

[11] S. Zhang, W. Fan, N. C. Panoiu, K. J. Malloy, R. M. Osgood,and S. R. J. Brueck,“Experimental Demonstration of Near-Infrared Negative-Index Metamaterials,”Phys. Rev. Lett. 95, 137404 (2005).

[12] U. K. Chettiar, A. V. Kildishev, T. A. Klar, and V. M. Shalaev, “Negative indexmetamaterial combining magnetic resonators with metal films,” Opt. Express 14,7872-7877 (2006).

[13] V. A. Podolskiy, A. K. Sarychev, E. E. Narimanov and V. M. Shalaev, “Resonantlight interaction with plasmonic nanowire systems,” J. Opt. A: Pure Appl. Opt. 7,S32-S37 (2005).

112 CHAPTER 3

[14] M. A. Ordal, L. L. Long, R. J. Bell, S. E. Bell, R. R. Bell, R. W. Alexander, Jr, and C.A. Ward, “Optical properties of the metals Al, Co, Cu, Au, Fe, Pb, Ni, Pd, Pt, Ag,Ti, and W in the infrared and far-infrared,” Appl. Opt.22, 1099-1119 (1983).

[15] G. Hawkins and R. Hunneman, “The temperature-dependent spectral propertiesof filter substrate materials in the far-infrared (6-40 µm),” Infrared Phys Techn 45,69-79 (2004).

[16] COMSOL Multiphysics RF Module 3.5a User’s Guide.

[17] Y. Zeng, H. T. Chen, and D. A. R. Dalvit, “A reinterpretation of the metamaterialperfect absorber,” arXiv:1201.5109v1, (2012).

[18] S. O’Brien and J. B. Pendry, “Magnetic activity at infrared frequencies in structuredmetallic photonic crystals,” J. Phys.: Condens. Matter 14, 6383-6394 (2002).

[19] J. Hao, J. Wang, X. Liu, W. J. Padilla, L. Zhou, and M. Qiu, “Supporting Informationfor High performance optical absorber based on a plasmonic metamaterial,” Appl.Phys. Lett. 96, (2010).

[20] R. Qiang, R. L. Chen and J. Chen, “Modeling Electrical Properties of Gold Films atInfrared Frequency Using FDTD Method,” Int. J. Infra Milli 25, 1263-1270 (2004).

[21] Q. Wen, H. Zhang, Y. Xie, Q. Yang and Y. Liu, Appl. Phys. Lett. 95, 241111 (2009).

[22] H.Tao, C. M. Bingham, D. Pilon, K. Fan, A. C. Strikwerda, D. Shrekenhamer, W. J.Padilla, X. Zhang and R. D. Averitt, J. Phys. D: Appl. Phys. 43, 225102 (2010).

[23] X. Liu, T. Tyler, T. Starr, A. F. Starr, N. M. Jokerst, and W. J. Padilla,“Infraredspatial and frequency selective metamaterial with near-unity absorbance,” Phys.Rev. Lett. 107, 045901, 2010.

[24] C. Wu and G. Shvets, "Design of metamaterial surfaces with broadband ab-sorbance" Opt. Lett. 37, 308, 2010.

[25] Y. H. Liu, S. Gu, C. R. Luo, and X. P. Zhao, Appl. Phys., A Mater. Sci. Process.(2012).

[26] J. Grant, Y. Ma, S. Saha, A. Khalid, and D. R. S. Cumming, "Polarization insensitive,broadband terahertz metamaterial absorber" Opt. Lett. 36, 3476, 2011.

[27] J. Hendrickson, J. P. Guo, B. Y. Zhang, W. Buchwald, and R. Soref, "Widebandperfect light absorber at midwave infrared using multiplexed metal structures"Opt. Lett. 37, 371, 2012.

[28] Q. Feng, M. Pu, C. Hu, and X. Luo1, "Engineering the dispersion of metamaterialsurface for broadband infrared absorption" Opt. Lett. 37, 2133, 2012.

3.5. References 113

[29] M Debenham, "Refractive indices of zinc sulfide in the 0.405-13 µm wavelengthrange" Appl. Opt. 23, 2238, 1984.

[30] M. Saito, S. Nakamura, and M. Miyagi, "Measurement of the refractive index andthickness for infrared optical films deposited on rough substrates," Appl. Opt. 31,61391, 1992.

CHAPTER4Fabrication of Metamaterial absorberswith multiband absorbance frommultipole resonances

4.1 Introduction

A detailed computational modeling carried out in previous chapter showed that a

tri-layer metamaterial structure, comprising of metallic circular micro-disks separated

from a metallic thin film by a dielectric zinc film, behaves as a near-perfect absorber

at infra-red wavelengths due to the excitation of strongly localized electromagnetic

resonances. In this chapter, we present the fabrication and characterization of such

polarization independent metamaterial absorbers.

In this thesis, the shadow mask deposition method has been chosen to define the

desired metallic patterns for high throughput dry fabrication of metamaterial structure

without any pre or post processing. It is mainly due to the fact that the shadow mask

can define pattern with reasonably high precision during deposition processes, like

thermal evaporation, by masking the target surface. The shadow masks were fabricated

using Excimer laser micromachining. Details of the shadow mask fabrication and its

implementation to form the required patterns are discussed in detail in chapter 2. We

also demonstrate in this chapter, an alternative manner of metamaterial fabrication that

is based on Excimer laser micromachining and glancing angle deposition methods. This

technique allows for the dry fabrication of metamaterial on flexible substrates including

115

116 CHAPTER 4

flexible polymer like sheets.

4.2 Fabrication of a perfect absorber by shadow mask

deposition

The optimized geometrical parameters for a metamaterial absorber at long wavelength

infra-red frequencies were computationally obtained for the design proposed by us

in the previous chapter and are shown in Fig. 4.1. We use pure fused quartz glass

substrates (Suprasil), which are polished to λ/6. The substrates have a thickness of

1 mm and an area of 4 cm2. After cleaning the substrates with standard cleaning

processes, thermal evaporation was used for the deposition of the conducting layer

of gold or aluminum as well as zinc sulfide, which was the dielectric spacer layer.

The vacuum pressure during the deposition was maintained at about 1.2×10−5 mbar.

Thermal vapor deposition was used for deposition of both dielectric and metallic

films. The deposition rate is controlled at 1Å/s for ZnS, 1Å/s for gold and 0.5Å/s for

aluminum and the thickness of the films were controlled by a well calibrated quartz

crystal thickness monitor. First, a uniform 60 nm thick gold film was deposited on a

fused silica substrate, followed by the deposition of a 280 nm thick uniform film of

ZnS. Following deposition of the continuous ZnS layer on the top of metallic ground

plane, the laser machined shadow mask containing hole array was employed on top of

ZnS/Au deposited substrate to pattern the metallic disks by direct deposition through

the holes in the membrane to produce the array of Au disks. A scanning electron

microscope (SEM) image of the fabricated structure (Au/ZnS/Au tri-layer) is shown in

Fig. 4.1 (Middle). We have also fabricated a metamaterial consists of an array of uniform

aluminum disks deposited with the same shadow mask used for the deposition of Au

disk. Al disk was found to have better adhesion as compared to the Au disk and hence

4.3. IR absorbing properties of the Metamaterials 117

a small diffusion of the Al disk as compared to the Au disk as shown in Fig 4.1. The

patterned Au disks were measured to have the following dimensions: diameter = 3.2

µm, period a = 8 µm and a disk height of 100 nm as measured with by atomic force

microscope (XE 70 Park Systems). The patterned area was 1mm2. In order to get good

quality pattern with shadow mask deposition, the gap between the shadow mask and

the substrate was ensure to be as minimum as possible as well as the evaporated flux

must reach to substrate as normal as possible. Any gap between the shadow mask

and the substrate will cause an diffusion of the evaporated flux coming. An example

of such deposition with an incoming flux coming at an angle to the substrate normal

is shown in Fig. 4.1 (Right), the optical image of the fabricated sample clearly shows

the diffusion of the evaluated material along the shadow mask misalignment direction.

Hence the highly selective deposition is achieved for an incoming flux of material

along the normal of the shadow mask with no gap present between shadow mask and

substrate.

4.3 IR absorbing properties of the Metamaterials

Transmission [T(ω)] and reflection [R(ω)] spectra were measured over the wavelengths

of 2.5 µm to 17 µm band using a Fourier transform IR spectrometer (Agilent, Model

Cary 660) combined with an infrared microscope (liquid-N2-cooled MCT detector, 15×

objective lens). The reflection measurements were normalized with the reflectance (≈ 1)

from a gold mirror. Due to the numerical aperture of the objective lens, the reflection

measurements are averaged over an angular range of 14. The measured absorption

spectrum [A(ω) = 1−R(ω)−T(ω)] of the metamaterial absorber (Au/ZnS/Au) is shown

in Fig. 4.2. The transmittance in our case is literally zero due to the optically thick

metallic ground plane at IR frequencies and the fused silica substrate which strongly

absorb the infrared radiation. We observed that in addition to the absorption band at the

118 CHAPTER 4

Figure 4.1: Top left: Schematic of unit cell of an absorbing metamaterial with t=100 nm, d=280nm, h=60 nm, disk diameter = 3.2 µm and periodicity in X-Y directions are 8 µm. Top middle:SEM image shows the top view of the of fabricated metamaterial structure (Au/ZnS/Au tri-layer). The bar indicator is 8 µm long. Top right: Optical microscope image of fabricated tri-layer structure in transmission mode. The 60 nm gold film allows for some transmission of lightand the Au disk on top appears dark. Bottom left: SEM image of the fabricated metamaterialstructure with Au disk on top. Bottom Middle: AFM image of the top Au disk. Bottom right:Measured profile of the disk and its data processing showing small diffusion of evaporatedflux.

long wavelength range (12.58 µm) associated with the fundamental resonance mode,

there exist other large resonant absorption bands at shorter wavelengths at 3.35 µm,

and 5.4 µm respectively. Additionally, there are some more resonant peak-like features

at 4.45 µm, 5.88 µm and 6.16 µm. The metamaterial absorber with Al disks on top was

observed to have the fundamental resonance at 13 µm with a peak absorbance of 96%

associated with the other large resonant absorption bands at shorter wavelengths at 3.4

µm and 5.4 µm respectively. The higher peak absorbance, in case of Al disk on top, for

all modes is due to a more strong coupling between top disk and bottom plane leading

to a better impedance matching of the tri-layer structure.

In literature, these higher order modes have not been widely studied and it has been

noted that the only fundamental modes are usually utilized for perfect absorption. The

4.3. IR absorbing properties of the Metamaterials 119

3 4 5 6 7 8 9 10 11 12 13 14 15 16 170

10

20

30

40

50

60

70

80

90

100

Abs

orpt

ion

(%)

Wavelength ( m)

Al-ZnS-Au Au-ZnS-Au

m=1m=3m=5

3 4 5 6 7 8 9 10 11 12 13 14 15 16 170

10

20

30

40

50

60

70

80

90

100

Abs

orpt

ion

(%)

Wavelength ( m)

Simulated

m=1

m=3m=5

Figure 4.2: Measured power absorption versus the wavelength from the fabricated metamate-rials absorber structures consisting of Au/Al disks separated from a 60 nm gold thin film by a280 nm ZnS film. Right: Simulated absorbance for the Au-ZnS-Au disk metamaterial structure.

higher order modes that could also lead to high absorption in association with the

fundamental mode occurs at shorter wavelengths. Principally at these wavelength,

metamaterial is not homogenizable. The broadening in the absorption band beyond

14 µm is due to the inherent absorption of radiation in the ZnS film. ZnS films are

commonly used in multi-spectral applications across the visible to infrared region from

0.4 µm–14 µm and become opaque thereafter2.

Fig. 4.3 shows the absorbance obtained from a metamaterial structures with a 5 µm

disk separated from a 100 nm continuous Al film by a 280 nm thick ZnS. We observed

an expected shift in the resonance peaks to higher wavelength due to a larger size of the

top metallic disk. The peak absorbance obtained from the fabricated structures are 55%,

65% and 55% at the resonance wavelength of 3.9 µm, 6.5 µm and 15 µm resistivity. The

lower values of absorbance at the resonance wavelengths are due to the unoptimized

film thickness of ZnS, which weaken the strength of magnetic resonance and overall

absorbance is reduced due to unoptimized impedance.

120 CHAPTER 4

3 4 5 6 7 8 9 10 11 12 13 14 15 16 170

10

20

30

40

50

60

70

80 5 m disk/ZnS/Al

Abs

orba

nce

(%)

Wavelength ( m)

Figure 4.3: Left: Optical microscopic image of fabricated metamaterial structure in reflectionmode. The bar indicator is 15 µm long. Right: Measured absorbance versus the wavelengthfrom the fabricated metamaterial with an array of Al disk diameter of 5 µm separated from a100 nm gold thin film by a 280 nm ZnS film.

4.4 Computer modeling and discussion of multiband ab-

sorption

To understand the multi-band absorption, numerical simulations of this structure was

performed using COMSOL Multiphysics. Details of the numerical simulations can

be found in chapter 2. Fig. 4.2 shows the simulated absorbance of the tri-layer meta-

material (Au-ZnS-Au). We begin by analyzing the electromagnetic resonance at peak

wavelengths in the absorption spectrum. The simulated absorption spectra are noted

to be in reasonably good agreement with the experimentally observed spectra. The

resonances are identified by the maxima in the absorption, and approximated by the

relation λnm = 2l√εr/m, where m is an integer that gives the resonance order, and l is

the disk diameter along the direction of the electric field polarization vector. The m = 1

resonance corresponds to the dipolar resonance and it is characterized by a low Q factor

(broad resonance) and a large extinction cross section. Multipolar resonances (m >1)

that also exhibit high absorption at shorter wavelength are narrower than the dipolar

resonance due to their weaker coupling to light3. The three major absorption bands at

13 µm, 5.5 µm, and 3.4 µm are clearly seen to have about 90% absorption, while the

4.4. Computer modeling and discussion of multiband absorption 121

Figure 4.4: Field distributions for the three modes at resonant wavelength 12.58 µm, 5.4 µm,and 3.35 µm for the normal incident angle. Fig. (a), (d), (g) represent the electric field in topdisk. Fig. (b), (e) and (h) represent the magnitude of the magnetic field in tri-layer. Fig. (c), (f)and (i) show the distribution of the electric field field in z-direction. Fig. (j), (k), (l) representthe multipolar nature of the electric field in the top disk at 6.16 µm, 5.88 µm and 4.45 µmrespectively.

122 CHAPTER 4

finer absorption peaks are also reproduced. The peak absorption level experimentally

observed for the fundamental mode at 13 µm is more than 96% and numerical simula-

tion of the fabricated structure shows of about 98%. We can numerically optimize the

structure by simulation to be close to 100%. The broadening of the peaks in the mea-

sured spectrum in Fig. 4.2 is possibly due to the inhomogeneous broadening caused

by the dispersion in the geometrical parameters of the disks due to limitations of the

fabrication process.

Each peak on the absorption curve corresponds to a specific electromagnetic reso-

nance of the disk embedded within the tri-layer structure. The calculated electric and

magnetic field distributions for the three resonances at the frequencies corresponding

to the peak absorption gives insight on the nature of the resonances and are plotted

in Fig. 4.4. The electric field distribution in Fig. 4.4(a) shows the excitation of the

fundamental dipole corresponding to opposite charges accumulating at the edges of

the gold disks. The excited dipole forms an oppositely oriented image dipole on the

ground plane giving rise to a concentration of the electric field within the spacer layer

between the disks and the ground plane as shown in Fig. 4.4(c). The magnetic field

distribution shown in Fig. 4.4(b) clearly indicates the excitation of the magnetic dipole

in the tri-layer, which is caused by oppositely oriented current sheets on the top disk

and ground plane. This simultaneous excitation of the electric and magnetic dipole

resonances of the structure give rise to the fundamental absorption peak at 12.58 µm.

The tri-layer structure, comprising of structured metallic patch separated from a

metallic thin film by a dielectric film, can be treated as a polarized object placed in

front of a conducting ground plane. Assuming the metallic patch to be a polarizable

dipole, an image dipole is induced in the bottom metallic film in response to the

presence of the metallic patch. The in-plane (parallel to the film) dipole moments of

the image are opposite to those of the metallic patch. The tri-layer structure supports

a series of cavity-like resonances analogous to a grounded patch antenna, in which


the electromagnetic field is localized within the gap between the ground plane and

the metallic patch element. Thus, the modes of excitation in the tri-layer structure are

dominated by the specific modes of charge distribution in the top disk that is polarized

by the incident electric field.

The higher order modes occur at MWIR wavelengths due to the fact that the disk

diameter is larger than a multiple of a half-wavelength of the modes. From the field

maps at 5.4 µm, we note that the electric field distribution shows excitation of multiple

half wavelength charge oscillations in the gold disk corresponding to the first higher

order mode as shown in Fig. 4.4(d). The charge distribution essentially results in

multiple current loops between the disk and metal film that gives rise to excitation

of three currents loops or magnetic dipoles in the tri-layer system. The simultaneous

excitation of higher order electric and magnetic resonances results in perfect impedance

matching to achieve near-unit absorption at a higher frequency or shorter wavelength.

Similarly, the third major peak at 3.35 µm in the absorbance spectrum arises due to

the next higher order excitation of multiple half-wavelength charge oscillations in the

top gold disk as shown in Fig. 4.4(g) and the corresponding magnetic field distribution

is shown in Fig. 4.4(h). Much like the fundamental dipole charge distribution [(+-)

in Fig. 4.4(a), the surface charges distributions for higher order mode n = 3 [(+-+-) in

Fig. 4.4(d)] and n = 5 [(+-+-+-) in Fig. 4.4(g)] possess a finite dipole moment for these

three modes.

The field distributions at the other resonant features at 6.16 µm, 5.88 µm, and

4.45 µm reveal interesting multipole excitations of the disk. We show in Fig. 4.4 (j),

(k) and (l), the resonant electric fields associated with the multipolar modes of the

disks within the dielectric spacer at the wavelengths of 6.16 µm, 5.88 µm, and 4.45

µm respectively. These fields are highly localized to the structures as well as highly

enhanced in comparison to fields at nearby wavelengths.

Similar resonant plasmonic modes have been recently reported for silver nano

124 CHAPTER 4

patches on a silver film at visible frequencies1. Multipole excitation for perfect absorp-

tion at microwave frequencies have also been proposed recently4. The metamaterial

structure is sub-wavelength in size (a ∼ 3µm) at the fundamental resonance band (12.58

µm) and the metamaterial would be homogenizable. At the resonance bands at lower

wavelengths, however, the metamaterial would not be described by homogeneous ef-

fective media parameters. The resonances are, however, extremely localized as well

as very strong, indicating that they would be reasonably independent of the period of

array. These absorption bands will also have different dispersion characteristics. Hao

et. al.5,6 proposed a metamaterial absorber where higher-order resonance modes can

be used to obtain absorbers at visible wavelengths. Simultaneous resonant absorption

at the different bands was not possible, however, due to the different optimal dielectric

thicknesses required for the different modes. In our case, it should be noted that sev-

eral multipole resonances can be reasonably impedance matched simultaneously with

a single dielectric spacer thickness.

The top disk that acts as a patch antenna placed on top of a ground plane separated

from a dielectric film and the resonances associated with the excitation of the funda-

mental and higher modes can be described by cavity resonances of classical antenna

theory. The characteristic length (l) of patch antenna is directly related to the wave-

length λnm = 2l√εr/√

n2 + m2, where n, m = 0, 1, 2, .. are integers with m2 + n2 , 0

and εr is the dielectric permittivity of the spacer material7. Since the polarization in the

patch antenna is mostly along the direction of electric field, one can assume m = 0. The

fundamental mode (n=1, m=0) of a metallic patch is a mode that presents no cut-off and

is always supported. However, higher harmonic modes of a metallic patch can only

be excited when the size of the patch can sustain the higher order Fabry-Perot cavity

like modes. Thus, moderately sized resonator can also exhibit in-plane multi-polar

resonances and these are located at shorter wavelengths compared those of the dipolar

resonance5. It is worth noticing here that odd order harmonics induces a net dipole


Figure 4.5: Schematic diagram showing charge distribution for different orders. All odd ordermodes possess a finite dipole for all the incident angles, however even order modes can onlypossess a net dipole for oblique angle.

moment in the disk that couple strongly to the incident field and can be excited at all

angles as explained in section 2. However, even-order resonances can not be excited at

normal incidence due to their symmetry, they can only be excited at oblique angles that

eventually break the symmetry. This results in surface charges distributions in such a

way that all the modes possess a finite dipole moment Fig. 4.5.

We note from the simulation spectra that multipolar resonances in the disk patch

could lead to an extremely narrow-band resonant peak. The simulated structure shows

narrow band high absorption at 6.16 µm, 5.88 µm, and 4.45 µm, which suggests that it

can be used as a highly directional thermal emitter. The field distribution shows that

narrow band peaks in absorption spectra arise due to multi-polar distribution of the

charge in the disk.

The different resonance frequency of the fabricated metamaterial structure with 3.2

µm disk on top of a 100 nm thin gold film separated by a 280 nm ZnS film are calculated

126 CHAPTER 4

Table 4.1: shows the calculated peak absorption wavelength for metamaterials structure fabri-cated using shadow mask deposition.

m n 2l√εr/√

n2 + m2

1 0 12.83 0 5.65 0 3.008

using λnm = 2ldisk√εZnS/

√

n2 + m2 and are listed in Table 4.1.

Next, we turn to the specific numerical investigation of the higher order modes

to ensure that diffraction effects do not considerably affect the absorbance/reflectance

even at these larger sizes, where the period of the unit cell is of the order of resonant

wavelength. For an incident angle of 14, the first orders of diffraction with wavelength

λ=5.4 µm will occur at 66 and -25. In Fig. 4.6, we plot the power flow (Poynting

vector map) for the case of an array of gold disks with and without a ground plane.

In the first case of the absorber, no transmittance is present and there is not much

evidence of scattered modes at large distance from the structure. In the case of a

disk array only, there is large transmittance and diffracted modes are strongly visible

from the power flow in both reflection and transmission. Note that the reflectance and

transmittance are calculated by integrating the power flow in the backward and forward

direction respectively and include the power flows due to the diffracted modes. We also

evaluated the angular dependence of the absorption for first higher order mode. From

Fig. 4.6, we note that absorption at the higher order resonance remains as high as 90%

for an angular rage of ±15 due to the strong localization of the resonance for both TE

and TM polarizations. These calculations strongly suggest that the diffraction does not

affect the absorption caused by the strongly localized resonances in the metamaterial

absorber.


-40 -30 -20 -10 0 10 20 30 400.50

0.55

0.60

0.65

0.70

0.75

0.80

0.85

0.90

0.95

Absorba

nce

Angle of incidence

TM TE

Figure 4.6: Top: Simulated power for Au/ZnS/Au structure (left) and for Au disk on the SiO2substrate (right). Bottom: Simulated absorbance versus the angle of incidence for the designedAu-ZnS-Au disk metamaterial absorber. The wavelength in the plot cases is 5µm, disk size =3.2µm and period of the array is 8µm.

128 CHAPTER 4

Figure 4.7: Schematic of fabrication process: (a) a polymer substrate (b) micro-pillars fabricatedusing laser micromachining (c) snowfall deposition of metal followed by ZnS on micro-pillarsas well as on side walls (d) schematic of GLAD deposition (e) metallic disk deposited on top ofmetal/dielectric coated pillars. Unit cell of an absorbing metamaterial with t=100 nm, d=280nm, h=50 nm, disk diameter = 3.8 µm and periodicity in X-Y directions are 8 µm. SEM imagesof fabricated metamaterial structure.

4.5 Fabrication and Characterization of Flexible meta-

materials

Most of the tri-layer structures were fabricated on top of a rigid substrate due to the

requirement of mechanical support for the fabrication process. However, for many

practical applications, metamaterials on the flexible substrate are in high demand so

that the metamaterial can be wrapped on a curved object without affecting the perfor-

mance9,10. Tao et al.11 have designed, fabricated and characterized thin flexible films of

metamaterial-based, resonant, near-unity absorbers which could be wrapped around

curved objects. While most of micro-nanofabrication techniques are limited to planar

dielectric substrates due to restriction imposed by the fabrication techniques, flexible

membrane based metamaterials have also been proposed and can be formed onto flex-

ible structures by layering them on a planar substrate, and subsequence by removing

them from the host substrate. Unlike other reports of metamaterials fabrication on

the flexible polyimide membranes, our membranes are fabricated directly on a 50 µm

thick polyimide sheet, which is thick enough to allow easy handling and mechanical

4.6. Excimer laser micromachining and Glancing angle deposition 129

manipulation and can be conformally wrapped around to various curved surfaces.

4.6 Excimer laser micromachining and Glancing angle de-

position

Excimer lasers micromachining is an efficient patterning method for polymers as the

small wavelengths of excimer lasers (KrF laser in this case has 248 nm) along with

the short-time nanosecond duration pulses have sufficiently high energy (4.9 eV for

the KrF) to directly break the polymer chain bonds and photo-ablate the material.

Extremely clean features with a high angle of cut can be obtained. The glancing angle

deposition technique is based on the oblique angle deposition, as shown in Fig. 4.7. The

principle of the GLAD is based on the self shadowing effect such that only the exposed

areas are coated by a directional incoming flux of material12 . The shadow effect can be

more precisely controlled on a pre-patterned substrate by the rotation (φ) of substrate

as the incident vapor flux is arriving at the substrate at an angle θ13. Fig. 4.8 shows the

scanning electron microscope image of the fabricated structures.

We first fabricated the disk arrays on a flexible polyimide sheet by using a excimer

laser micromachining and a mask consisting of circular opaque regions (metal coated)

on a fused silica substrate. The KrF excimer laser (Coherent Variolas Compex Pro

205F) with 15 puses of 40 mJ energy (at the mask) was used for micromachining. The

patterned polyimide sheet with 2D arrays of micro-pillars having hight of 3-4 µm

was used as the substrate for our tri-layer deposition. We first deposited a uniform

100 nm thin gold film followed by the deposition of a 300 nm thick uniform film of

ZnS at normal incidence. Thermal evaporation was used for the deposition of the

conducting layer of gold as well as zinc sulfide. This results in a uniform deposition of

metal/dielectric on the sides as well as on the micro pillars. Finally, in order to obtain a

130 CHAPTER 4

Figure 4.8: Top Left: SEM images of array of high aspect ratio disks after snowfall deposi-tion of gold thin film. Uniform deposition of metal on the sides as well as top of micro- andnano-pillars. (b) shows deposition of metal caps fabricated via oblique angle deposition. (c)Metal disk deposition on continuous gold/ZnS film by continuously rotating the pre patternedsubstrate at an oblique angle.Bottom Left: Optical microscopic image (5X) of the fabricatedmetamaterial wrapped around a pen. Right: higher magnification (50X) view of the left panel.

periodic array of gold disks on top metal/dielectric coated pillars, vapor deposition at

glancing angle deposition is carried out. The incidence angle (θ) between the incident

flux and substrate was chosen to be 17o and the substrate was made to rotate about

its central normal axis at an angular speed of 10 rpm such that it can precisely control

the locations of flux deposition. The patterned metamaterial disk has the following

dimensions: diameter = 3.8 µm, with a period a = 8 µm. The larger size of the disk is

due to the fact the rotation cycles during evaporation will cause evaporated metal to be

deposited on top of the micro-pillar as well as on the side walls. Most importantly, the

device was fabricated on a highly flexible polyimide substrate with a total thickness of

50 µm. This novel design enables its use in non-planar applications as it can be easily

4.6. Excimer laser micromachining and Glancing angle deposition 131

3 4 5 6 7 8 9 10 11 12 13 14

40

50

60

70

80

90

100

Abs

orba

nce

(%)

Wavelength ( m)

280 nm 300 nm

3 4 5 6 7 8 9 10 11 12 13 14 15 16 170

10

20

30

40

50

60

70

80

90

100

Abs

orba

nce

(%)

Wavelength ( m)

00

900

Figure 4.9: Left: Measured power absorption versus the wavelength from the fabricated meta-materials absorber structures consisting of Al disks separated from a 100 nm modulated goldthin film by a 280 and 300 nm ZnS film. Right: measured absorbance for the fabricated meta-material wrapped around a pen as shown in Fig. 4.7.

Table 4.2: shows the calculated peak absorption wavelength for metamaterials structure fabri-cated on Kaptop.

m n 2l√εr/√

n2 + m2

1 0 14.12 0 83 0 5.35 0 3.2

wrapped around objects. Similar structures have been fabricated using lithography on

SU8 for polymeric photo-voltaic cells made up of an array of sub-micron and nano-

pillars which not only increase the area of the light absorbing surface, but also improve

the carrier collection efficiency of bulk-heterojunction organic solar cells14.

The measured absorption spectrum [A(ω) = 1 − R(ω) − T(ω)] of the metamaterial

absorber is shown in Fig. 4.9. Note that the transmittance in our case is literally zero due

to metal layer and the fused silica substrate. We observed that non-degenerate meta-

material unit cell exhibit multiple absorption band in addition to the absorption band

at the long wavelength range (13.85 µm) associated with the fundamental resonance

mode and other highly resonant absorption bands at shorter wavelengths resonances

are at 3 µm and 5 µm respectively. The shifting of fundamental peak is due to the

larger size of the disk resulting from additional sidewise deposition during GLAD. The

132 CHAPTER 4

larger size of disk will need a more thick dielectric film for optimizing the absorption

resonances. As shown in Fig. 4.9, the peak absorbance are higher for 300 nm thin ZnS

film as compared to the 280 nm thin ZnS film. The origin of peaks at are attributed to

the fundamental and higher order modes i.e. n = 1, 3, 5. We observe an additional peak

in the absorbance spectrum is at 10.5 µm. This peak probably corresponds to the m =

2 mode. However, our simulation on the earlier structure of section 4.4 cannot confirm

this as the geometry here is considerably more complex. It is worth noting that, in

practice, the incident light beam is composed of a range of incident angles, which can

couple to the flexible substrate at the critical angle to excite even higher order modes

also in the absorption spectra. It can be seen clearly from Fig. 4.9 near-unit absorption

occurs for a critical thickness of the dielectric spacer which plays an important role

in capacitive coupling between gold disk and the continuous gold film to gives rise

strong magnetic resonance. As the dielectric layer thickness increases or decreases from

the optimum thickness, the coupling strength decreases. The optimized thicknesses

d corresponding to the perfect absorption peaks are obtained from the simulation as

shown in Fig. 4.9. In order to investigate the performance of the these metamaterial

wrapped on a realistic curved surface, we measured the reflectance spectra from the

flexible metamaterial absorber wrapped around a pen. The peak absorbance in the

measured spectrum, for the electric field polarization (0o) of the incident beam parallel

to disk, has reduced to 60%, 65% and 80% for three absorption band at 13.58 µm, 5 µm

and 3 µm respectevely as shown in Fig. 4.9. When the polarization of incident beam (0o)

such that the incident electric field makes an angle to disk, the second order resonance

in the absorbance peak can be observed.


4.7 Conclusions

In conclusion, we have experimentally demonstrated a multi-band perfect metamate-

rial absorber over the MWIR to LWIR infrared regime by utilizing multipolar electric

and magnetic resonances with the metamaterial unit cell comprising of a single struc-

ture (micro-disk) separated from a metallic thin film by a dielectric zinc sulphide (ZnS)

film. The metamaterial was fabricated by shadow mask deposition. The infrared ab-

sorption properties arising from the multipolar resonances could be understood from

detailed computer simulations. Both the experimental and the computer simulation

results show that the multiple absorption bands can be realized by a single particle

resonator by exciting fundamental and higher order moments of resonances. Here we

have numerically and experimentally shown that the same spacer thickness can give

rise to different absorption bands with absorption level exceeding 90% and close to

unity (<95%) on one band. We have also computationally verified that diffraction does

not affect the absorption due to these multipole or higher order resonances.

We have also fabricated highly flexible, wide angle of incidence infrared metama-

terial absorber on a polyamide substrate. These metamaterials with small changes

in the structural sizes can have the fundamental resonances in the 8-12 µm thermal

band which would be ideal for improving the sensitivity of night vision bolometric de-

vices. The multi-band nature would be useful for hyper spectral imaging applications.

We have also investigated the dielectric layer thicknesses as well as disk diameters

dependence on the multi-band absorbance of the metamaterial structures.

134 CHAPTER 4

4.8 References

[1] A. Moreau, C. Ciraci, J. J. Mock, R. T. Hill, Q. Wang, B. J. Wiley, A. Chilkoti, andD. R. Smith, "Controlled-reflectance surfaces with film-coupled colloidal nanoan-tennas," Nature 492, 86, 2012.

[2] A. Rogalski and K. Chrzanowski, "Infrared devices and technique," Opto Electron.Rev. 10, 111, 2000.

[3] V. Giannini, G. Vecchi, and J. GoÂt’mez Rivas, "Lighting Up Multipolar SurfacePlasmon Polaritons by Collective Resonances in Arrays of Nanoantennas," Phys.Rev. Lett. 105, 266801, 2010.

[4] A. Sellier, T. V. Teperik, and A. de Lustrac, "Resonant circuit model for efficientmetamaterial absorber," Optics Exp. 21 A997-A1006, 2013.

[5] J. Hao, L. Zhao and M. Qui, "Nearly total absorption of light and heat generationby plasmonic metamaterials," Phy. Rev. B. 83, 165107, 2011.

[6] T. Maier and H. Brueckl, "Multispectral microbolometers for the midinfrared,"Opt. Lett. 35, 3766, 2010.

[7] C. A. Balanis, Antenna Theory: Analysis and Designs (John Wiley & Sons, Inc.,Singapore, 2005).

[8] L. Novotny, "Effective Wavelength Scaling for Optical Antennas," Phys. Rev. Lett.98, 266802, 2007.

[9] R. Melik, E. Unal, N. K. Perkgoz, C. Puttlitz, and H. V. Demir, "Flexible metama-terials for wireless strain sensing," Appl. Phys. Lett. 95, 181105, 2009.

[10] A. D. Falco, M. Ploschner, and T. F. Krauss, "Flexible metamaterials at visiblewavelengths," New J. Phys. 12, 113006, 2010.

[11] H. Tao, C. M. Bingham, A. C. Strikwerda, D. Pilon, D. Shrekenhamer, N. I. Landy,K. Fan, X. Zhang, W. J. Padilla, and R. D. Averitt, "Highly flexible wide angle ofincidence terahertz metamaterial absorber: Design, fabrication, and characteriza-tion," Phys. Rev. B 78, 241103, 2008.

[12] A. Lakhtakia and R. Messier, Sculptured Thin Films: Nanoengineered Morphology andOptics (SPIE Press, 2005)

[13] J. Dutta, S. A. Ramakrishna and A. Lakhtakia, "Periodically patterned columnarthin films as blazed diffraction gratings," Appl. Phys. Lett. 102, 161116, 2013.

[14] S. Kassegne, K. Moon, P. Ramos, M. Majzoub, G. zturk, K. Desai, M. Parikh, B.Nguyen, A. Khosla and P. Posada, "Organic MEMS/NEMS-based high-efficiency3D ITO-less flexible photovoltaic cells" J. Micromech. Microeng. 22, 115015, 2012.

CHAPTER5Broadband infrared metamaterialabsorbers with visible transparencybased on ITO

5.1 Introduction

As discussed in the previous chapters, metamaterials perfect absorber (MPA) could

exhibit near 100% absorption at a specific designed wavelength. The key to a highly

absorbing medium is to design resonant structures that can simultaneously be driven by

both the electric and magnetic fields of radiation. In these structures, the top patterned

layer can support a plasmonic or antenna resonance at a specific wavelength which

allows light to couple in to the spacer between the top and bottom metal layer, where it

is efficiently absorbed. So far, only highly conducting metals like Ag, Au and Al have

been used as constituents in the metamaterials. The resonance of metal-insulator-metal

are strongly affected by changes in the permittivity of the active layers. These metals

have plasma frequencies at ultra-violet frequencies and highly dispersive plasma-like

permittivities at IR frequencies. AS a result of this the absorption band of MDM

structure is limited to few hundred nanometer at IR wavelengths. There are many

ways to enhance bandwidth of metamaterial as discussed in the previous chapters

3 and 4. The mechanism of obtaining multi-band absorption is based on combining

several MDM resonators in the vertical or the horizontal plane in the single unit cell as

described in chapter 3 or by utilizing multi-polar resonances of a single resonator as

135

136 CHAPTER 5

demonstrated in chapter 4. However, all of these designs rely on combining of multiple

resonator that leads to unnecessary fabrication complication. Another possible way to

increase the absorption band without increasing fabrication complication is to use a

less dispersive material which can sustain these electromagnetic resonances. Recently,

doped semiconductors such as indium tin oxide (ITO) and aluminum doped zinc oxide

have been used for NIR plasmonic applications1,2.

In this chapter, we present the design, fabrication and characterization of an ITO

based metamaterial that efficiently absorbs radiation over the 4 µm to 7 µm band and

allows visible radiation to transmit through. The design consists of an array of circular

conducting (aluminum or ITO) micro-disks separated by a thin film of ZnS from a

continuous ITO film that acts as a ground plane. The metamaterial is designed to be

impedance matched for higher order mode that allows the use of a larger resonant

structure, which can be conveniently fabricated using micro-fabrication methods. A

tri-layer structure with strong electric and magnetic resonances is formed, while the

ITO ground plane renders the structure transparent to visible light. This metamaterial

shows broadband absorption as compared to the usual design where the top and bottom

layers are both metallic.

5.2 Material and design considerations for a broadband

metamaterial

The MDM tri-layer structure resonance wavelengths are given byλnm = 2l√εr/√

n2 + m2,

where l is the geometric length of the top metallic patch, n, m are positive integers with

m2+n2 , 0 and εr is the permittivity of the dielectric spacer4. As the polarization in

the patch is mostly along the direction of electric field, one can assume m = 0. The

dipolar mode (n=1, m=0) is most often dominating. Moderate sized resonators can

5.2. Material and design considerations for a broadband metamaterial 137

also exhibit in-plane, multi-polar resonances at shorter wavelengths compared to the

dipolar resonance5. Thus, one can utilize higher-order resonances with moderate patch

sizes comparable to a wavelength. The larger sizes could ease the fabrication demands

and well established micro-fabrication techniques can be applied to make infrared

metamaterial absorbers.

ITO thin films are good infrared reflectors while transparent at visible wavelengths,

and well known for transparent electrodes in photo-voltaic applications. The optical

properties of doped semiconductors can be well described by the Drude free electron

model below the plasma frequency. Due to the lower charge carrier concentration

compared to plasmonic metals, the plasma frequency of ITO is much smaller and

the dispersion of the permittivity is comparatively very small at IR frequencies. The

plasmon frequency of ITO corresponds to λ ∼ 1.2µm for carrier densities of 1021 cm−3 10.

The Drude dielectric permittivity of Au, Al and ITO are plotted in Fig. 5.1. The

magnitude of the real part of the permittivity of metals and its rapid dispersion at IR

frequency makes it difficult to create simulations electric and magnetic resonances that

are necessary for impedance matching at several frequencies or over a larger bandwidth.

Even though the penetration depths are small due to the large magnitude of Re(ε), the

rapid dispersion changes the conditions for the resonances. Hence it becomes difficult

to impedance match the metamaterial for a given structure and the same dielectric

spacer material or thickness over multiple frequencies. The much smaller Re(ε) and

the slower dispersion of ITO at IR frequencies would allow for an easier control of the

resonances through the structure.

138 CHAPTER 5

Figure 5.1: Left panel: Drude dispersion of the real and imaginary parts of the dielectric per-mittivity of Au (ωp/2π = 2176 THz, εb = 5.7 and γ/2π = 6.5 THz), Al (ωp/2π = 3464 THz, εb =5.1 and γ/2π = 19.41 THz) and ITO (ωp/2π = 461 THz, εb = 3.9, γ/2π = 28.7 THz). The rightpanel shows dispersion for ITO in an expanded view.

.

5.3 Computational modeling of the metamaterial absorber

with the ITO ground plane

We first optimized the geometrical parameters for the structure to resonant at the first

higher order mode (m = 3) with a resonant wavelength of λnm = 2l√εr/3. For a disk

of 3 µm diameter, the resonance wavelength is for the m = 3) 4.6 µm. Numerical

simulations of the electromagnetic fields were performed using the commercial finite

element method based COMSOL Multiphysics software11. In the simulations, the

Drude free-electron model was used for the dielectric permittivities of Al and ITO as

ε(ω) = εb − [ω2p/ω(ω + iγ)] with ωp/2π = 3464 THz, εb = 5.1 and γ/2π = 19.41 THz

for Al12, and ωp/2π = 461 THz, εb = 3.9, γ/2π = 28.7 THz for ITO1. The dielectric

permittivity of ZnS was taken from experimental data in Ref. 13. More details of

the computer simulations can be found in the chapter on the methods of numerical

simulations.

The wavelength dependent reflectance [R(λ)] and transmittance [T(λ)] were ob-

tained by integrating the power flow (Poynting vector) normal to two planar surfaces

5.3. Computational modeling of the metamaterial absorber with the ITO ground plane 139

Figure 5.2: Left panel: Schematic of unit cell of an absorbing metamaterial with h = 200 nm, d= 380 nm, t = 100 nm, disk diameter = 3 µm and periodicity in X-Z directions are 8µm.

3 4 5 6 7 8 9 10 11 12 13 14 15 16 170.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1.0

Absorba

nce

Wavelength ( m)

ITO/ZnS/ITO Al/ZnS/ITO

3 4 5 6 7 8 9 10 11 12 13 14 15 16 170.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1.0

Abs

orba

nce

(A)/

Ref

lect

ance

(R)

Wavelength ( m)

A(Al/ZnS/ITO) R(ITO)

Figure 5.3: Left panel: Simulated absorption versus the wavelength for the metamaterials ab-sorber structures designed. Right panel: Measured absorption from the fabricated metamate-rials absorber structures and the reflectance of plane ITO film.

placed above and below the metamaterial structure respectively. The absorbance, cal-

culated as A(λ) = 1 − R(λ) − T(λ), is plotted in Fig. 5.3 for a ZnS layer thickness of 380

nm and shows peaks with absorbances exceeding 98% at 4.5 µm, 6.5 µm and 7 µm.

We also observe a lower peak absorbance of about 80% at 16 µm corresponding to the

fundamental dipole mode of the disk. The resonance peaks at 4–7 µm almost merge

and have a much wider net bandwidth of about 2.5 µm wavelengths compared to

Al/ZnS/Al perfect absorber structures in the mid-wave IR region discussed in chapter

140 CHAPTER 5

Figure 5.4: Left: Electric field magnitude, Right: Magnetic field magnitude in tri-layer ofAl/ZnS/ITO metamaterial at 4.6 µm wavelengths. The nature of the m = 3 mode is appar-ent with three current loops.

4. This significant increase of bandwidth is due to the small dispersion of the complex

permittivity of ITO (compared to aluminum or gold) that enables optimal impedance

matching of the structure for the same dielectric layer thickness at multiple peaks within

the given band. The overall dispersion of the metamaterial response is small and the

field enhancements within the structure occurs over a wider wavelength band.

The calculated electric and magnetic field distributions at the peak absorption wave-

length of 4.5 µm give insights on the nature of the resonances and are plotted in Fig. 5.4.

The field distributions confirm that the absorption properties of the metamaterial are

due to the electric and magnetic resonances excited in the tri-layer structure. The elec-

tric field distribution shows half-wavelength-like charge distributions excited in the

top disk and the corresponding image charge formation in the ITO film. This results

in strong localization of the electric field within the dielectric layer. The magnetic field

distribution clearly shows a magnetic resonance with a first higher order mode (n = 3)

of the tri-layer. There are three magnetic loops corresponding to anti-parallel currents

induced in the metallic disk and the ground plane. Simultaneous excitation of the

electric and magnetic resonances leads to a strong confinement of the electromagnetic

fields inside the tri-layer. Significant electric and magnetic fields penetrate into the

5.4. Fabrication and characterization of the metamaterial 141

Figure 5.5: Left: Electric field magnitude, Right: Magnetic field magnitude in tri-layer ofITO/ZnS/ITO metamaterial at 6.16 µm wavelengths. The field penetration inside ITO diskand ground plane can be seen.

lower ITO layer as compared to the Al disk, and can be clearly seen in Fig. 5.5. We

also evaluated the absorbance for the tri-layer design with the same geometric param-

eters as shown in Fig. 5.6, but with ITO disks and a ITO ground plane. The simulated

absorbance shows two distinct peaks at 4.25 µm and 7 µm with absorption exceeding

95% corresponding to the higher order modes with m = 3 and m = 5 respectively. The

absorption band corresponding to the fundamental dipole mode at long wavelengths,

cannot be effectively excited as the skin depth in ITO at MWIR and LWIR wavelengths

is very different for semi-conducting films as compared to the skin depth of metals.

Hence, the optimum layer thicknesses for effective excitation of the far spaced modes

becomes different.

5.4 Fabrication and characterization of the metamaterial

The optimal metamaterial design was fabricated using area-selective deposition through

shadow-mask lithography techniques. Thermal evaporation was used for the depo-

sition of aluminum as well as ZnS, which was the dielectric spacer material used. A

uniform 380 nm thick ZnS film was deposited on a commercially available ITO coated

142 CHAPTER 5

Figure 5.6: Left panel: SEM image of the fabricated structure with disk diameter = 3 µm andperiodicity in X-Z directions are 8µm. The bar indicator is 8 µm long. Inset: Diffraction of a He-Ne (632.8 nm) laser transmitted through the structure with a zeroth order transmittance of 45%.Right: The atomic force microscope scan shows a disk height of about 100 nm. Bottom: Opticalmicroscope image of fabricated metamaterial in transmission mode. The structure absorb theIR radiation and diffract through the visible radiation.

glass with an ITO film thickness of 200 nm and sheet resistance of 50 Ω/sq. Subsequent

to the deposition of the continuous ZnS layer, a shadow mask containing an array of

micro-holes was employed to form the Al disks on top by direct deposition of Al vapor

through the holes in the membrane. The shadow mask containing 3 µm holes in a

square array of period 8 µm over 1.5 mm2 area was fabricated using excimer laser mi-

cromachining. A scanning electron microscope (SEM) image of the structure is shown

in Fig. 5.6. The Al disks were measured to have average diameters of (3 ± 0.1) µm

and disk heights of 100 nm (see Fig. 5.6) with some side-wall slope by atomic force


microscope (XE 70, Park Systems).

Reflection and transmission measurements over the wavelength range 2.5 µm to 17

µm range were performed using a Fourier transform infrared spectrometer (Agilent,

Model Cary 660) coupled to a IR microscope (Agilent, Model Cary 600) and a cooled

HgCdTe detector. The measurements are averaged over an angular range of 14o due

to the numerical aperture of the 10× microscope objective. Reflection spectra were

taken with polarized light and normalized to that obtained from a smooth gold film.

The reflection from the plain ITO film was about 85% to 90% over the 3 µm to 14

µm wavelength band and is shown in Fig. 5.3. The reflection from the metamaterial

was reasonably polarization independent due to the circular symmetry of the disks.

The measured absorption spectrum [A(λ) = 1 − R(λ)] of the metamaterial absorber is

shown in Fig. 5.3. Broadband absorption with a peak absorbance of 97% at 5 µm was

measured and ascribed to the merged resonances corresponding to m = 3 and 5. The

measured spectra are in reasonable conformity with the predicted spectra with minor

differences that presumably arise from the inverted cup-like shapes of the disks (see

AFM scan in Fig. 5.6). Fabrication imperfections cause inhomogeneously broadened

peaks that merge and give rise to a broadband absorption greater than 70 % over the 4

µm – 7 µm band. We have only shown the data up to 17 µm as ZnS is transparent only

up to 14 µm and starts absorbing at wavelengths beyond. The peak in the absorption

due to fundamental (m = 1) resonance is clearly visible at about (17 µm) is imperfect

impedance matching and the peak absorbance is not very large.

5.5 Conclusions

Most metamaterial designs utilize an LC resonance or the fundamental dipole (m = 1)

mode for use as a sub-wavelength sized resonator. However, highly localized higher

order modes that need not to be in sub-wavelength limit, can also give rise to near-

144 CHAPTER 5

perfect absorption as shown here for the m = 3 mode. For a particular size of the

patch, the resonance wavelength of the higher order modes are at lower wavelengths

than for the fundamental mode. For a given band, the size of the resonator utilizing

a higher order mode will be larger. This leads to significant easing of the demands

on fabrication of the metamaterial at MWIR and NIR wavelengths. Note that using a

higher order mode with a larger unit cell comparable to the wavelength renders the

system not homogenzable as diffracted modes will also be present. The simulated

R(λ) and T(λ) include the power in the diffracted beams while only zeroth order

specular reflection is present in the experimental measurements. Very little power flow

in the diffracted modes in reflection and negligible overall transmission in noted in

simulations. The reasonably good agreement between simulated and measured data

indicates that diffraction effects do not considerably affect the absorbance/reflectance,

presumably due to the strength and localization of the resonances. The lowered plasma

frequency and conductivity of ITO allows the broadening of the resonances due to the

smaller quality of the resonances.

Use of ITO in the metamaterial has several advantages over previous designs and

allows for increased flexibility: e.g., the ITO ground plane can be configured in a CMOS

configuration to tune the absorption of the metamaterial via charge injection into the

ITO14. Another great advantage is the transparency at visible wavelengths that allows

such an IR absorbing metamaterial to interface with other applications that require

visible light. With rapid micro-patterning techniques, such metamaterials with ITO

disks can be used for smart window applications that need high visible transparency

and high absorptivity/emissivity at 8 µm to 12 µm wavelengths.

In summary, we have designed, fabricated, and experimentally demonstrated a

broadband infrared metamaterial absorber that is transparent at visible wavelengths.

A maximum absorption level of about 97% at 5 µm wavelength with 50% bandwidth

of over 3.5 µm is achieved in the simulations as well as in the fabricated structures.


The large bandwidth is due to the small dispersion in the dielectric permittivity of

ITO at IR wavelengths. Fabrication by shadow mask deposition techniques is rapid

and allows for direct fabrication of large structured areas. The fabricated absorber is

transparent to visible light and allows the flexibility of using visible radiation to control

the metamaterial or for other applications.

146 CHAPTER 5

5.6 References

[1] P. R. West, S. Ishii, G. V. Naik, N. K. Emani, V. M. Shalaev, and A. Boltasseva,“Searching for better plasmonic materials,” Laser Photon. Rev. 4, 795-808 (2010).

[2] S Law, C. Roberts, T. Kilpatrick, L. Yu, T. Ribaudo, E. A. Shaner, V.A. Podolskiy,D Wasserman, "All-Semiconductor Negative Indesx Plasmonic Absorbers," Phys.Rev. Lett., 112, 017401 (2014).

[3] C. M. Watts, X. Liu, and W. J. Padilla, “Metamaterial Electromagnetic Wave Ab-sorbers,” Adv. Materials 24, OP98-OP120 (2012).

[4] C. A. Balanis, Antenna Theory: Analysis and Designs (John Wiley & Sons, Inc.,Singapore, 2005).

[5] J. Hao, L. Zhao, and M. Qui,“Nearly total absorption of light and heat generationby plasmonic metamaterials,” Phy. Rev. B. 83, 165107 (2011).

[6] J. A. Bossard, L. Lin, S. Yun, L. Liu, D. H Werner, and T. S. Mayer, “Near IdealOptical Metamaterial Absorbers with Super Octave Bandwidth,” ACS Nano 8,1517-1524 (2014).

[7] B. Zhang, J. Hendrickson, and J. Guo, “Multispectral near perfect metamaterial ab-sorbers using spatially multiplexed plasmon resonance metal square structures,”J. Opt. Soc. Am. B 30, 660 (2013).

[8] E. Lier, D. H. Werner, C. P. Scarborough, Q. Wu, and J. A. Bossard, “An octave-bandwidth negligible-loss radio-frequency metamaterial,” Nature mat. 10, 216(2011).

[9] Q. Feng, M. Pu, C. Hu, and X. Luo, “Engineering the dispersion of metamaterialsurface for broadband infrared absorption ,” Opt. Lett. 37, 2133-2135 (2011).

[10] I. Hamberg and C. G. Granqvist, “Evaporated Sn-doped In2O3 films: basic opticalproperties and applications to energy efficient windows,” J. Appl. Phy. 60, R123-R159 (1986).


[12] M. A. Ordal, L. L. Long, R. J. Bell, S. E. Bell, R. R. Bell, R. W. Alexander, Jr, and C.A. Ward, “Optical properties of the metals Al, Co, Cu, Au, Fe, Pb, Ni, Pd, Pt, Ag,Ti, and W in the infrared and far-infrared,”Applied Optics, 22,, 1099-1119 (1983).

[13] H. H. Li, “Refractive Index of ZnS, ZnSe, and ZnTe and Its Wavelength andTemperature Derivatives,” J. Phys. Chem. Ref. Data 13, 103-151 (1984).

[14] V. J. Sorger, N. D. Lanzillotti-Kimura, Ren-Min Ma, and X. Zhang, “Ultra-compactsilicon nanophotonic modulator with broadband response,” Nanophoton. 1, 17-22(2012).

CHAPTER6Thermally switchable metamaterials

6.1 Introduction

The very resonant nature of metamaterials absorber that result in high absorption also

restrict their usable bandwidth in the resonance-frequency window, which is precisely

where many device operations are optimized. In most cases, this frequency window

is fixed at the time of fabrication and yields materials with a passive response over

a limited bandwidth. The ability to dynamically control the response of a fabricated

devices to electromagnetic radiation is a very powerful concept that has long been a

cherished goal of scientists. Various methods have been utilized to achieve amplitude

and frequency modulation including photo-doping1,2, electronic control3,4, tempera-

ture control5, and micro-electromechanical systems (MEMS)6. Similar type designs

have also shown the capability to modulate the electromagnetic phase7. Electronic

control is of particular interest to many because of the ability to integrate such devices

with electronics and for achieving high modulation speeds4.

As discussed in the previous chapter 3, the unit cell of the highly absorbing meta-

material structure typically consists of a tri-layer system with a top structured metallic

layer and a bottom continuous metal layer separated by a continuous dielectric layer.

The resulting structure forms independently electric and magnetic dipole resonators

that couple to the electromagnetic fields of incident radiation resulting in large disper-

sion of the dielectric permittivity (ε) and magnetic permeability (µ) of the medium.

147

148 CHAPTER 6

The reflectance of the medium can be reduced to zero by manipulating the electric and

magnetic resonances simultaneously such that ε ' µ, and perfect impedance matching

conditions are achieved with strong resonant coupling to the structures, resulting in

near perfect absorption8. As the electric and magnetic resonance frequencies of meta-

materials are determined by their geometry and the dielectric environment, they are

limited to a specific resonance frequency within a narrow operating bandwidth that

is predetermined by the fabricated dimensions. There are several ways to control the

electromagnetic response of metamaterials after their fabrication, e.g. by introducing a

material whose properties can be changed by external applied fields9,10.

The dielectric material placed in between the metal layers, plays an important role in

manipulating the resonance conditions for the perfect absorption through the effective

capacitance. Thus, by changing only the optical properties of the insulating layer, not

the geometry of the pattern arrays, the effective capacitance can be tuned. Undoped

vanadium dioxide (VO2) is a smart material that undergoes a ultrafast Mott insulator to

metal transition at 341K, and its conductivity changes dramatically across the transition

by three to four order of magnitude11. VO2 has been used for the dynamical control of

split ring resonator metamaterial12,13.

In this chapter, we discuss how an active phase change material like VO2 can be uti-

lized to control the properties of a metamaterial, when the active material is carefully

incorporated in to the structure of the metamaterial. In section (6.2), we computa-

tionally design a saturable absorber mirror where the metamaterial goes from a low

reflectance state to a high reflectivity state at high temperature. Such devices can have

useful applications as Q-switches in IR lasers. In section (6.3), we demonstrated ex-

perimentally a switchable, VO2 based metamaterial that behaves in a converse manner

by switching from a high reflectivity low temperature state to a low reflectivity (high

absorbance) high temperature state within the metamaterial resonance band.

6.2. Design of a metamaterial saturable absorber 149

6.2 Design of a metamaterial saturable absorber

The design of the proposed metamaterial unit cell consists of vanadium dioxide thin

film, a phase change material, sandwiched between two metallic layers. The top

layer consists of metallic circular disk array and an optically thin continuous metallic

film.(see Fig. 6.1). When VO2 in the low temperatures dielectric phase is used as the

dielectric spacer layer, the composite metamaterial behaves as a near-perfect absorber.

The absorbed radiation heats the metamaterial structure, and for sufficient intensity, the

temperature of the embedded VO2 will exceed the transition temperature of 341 K and

VO2 will transit to the metallic phase. At these temperatures, however, the metamaterial

with a metallic VO2 film behaves as a good reflector because the structured top layer

and the bottom continuous layer get shorted and the whole metamaterial structure

acts as a low impedance surface. For such devices, knowledge of the heat generation

and temperature variation within the metamaterial is very essential. Inhomogeneous

heat dissipation can give rise to inhomogeneities in the dielectric properties, thereby

modifying the photonic properties, which need to be quantified.

We simultaneously solved for the electromagnetic properties and the heat diffu-

sion within the metamaterials by the commercially available finite element method

based software COMSOL Multiphysics14. The electromagnetic properties of meta-

materials are first solved for both the phases of VO2. In the numerical simulations,

the dielectric permittivity of gold is described by the Drude expression for plasma,

ε(ω) = 1 − [ω2p/ω(ω + iγ)], with a plasma frequency ωp/2π = 2176 THz and damping

frequency γ/2π = 6.5 THz15. The dielectric permittivity of VO2 has been taken from

experimental data16. The three dimensional unit cell was simulated using periodic

boundary conditions along the Y-Z directions so that structure could be regarded as

an infinite two dimensional array. The incident radiation is a transverse electromag-

netic wave applied using wave port boundary conditions14. The frequency dependent

150 CHAPTER 6

Figure 6.1: Top left: Schematic of unit cell of an absorbing metamaterial with h = 100 nm, t =200 nm, d = 200 nm, disk diameter = 2 µm and periodicity in Y-Z directions are 4 µm. (A) showsthe absorbance and reflectance of the metamaterial for insulating and metallic VO2 phases, (B)shows the surface currents (arrow) and the magnetic fields (slice), and (C) power flow in thestructure for 10.22 µm. (D) and (E) shows the electric fields and magnetic fields for metallicVO2 phase respectively.

6.2. Design of a metamaterial saturable absorber 151

Figure 6.2: (a) Heat source in dielectric phase of VO2 (b) heat source in metallic phase of VO2,(c) temperature distribution for dielectric phase of VO2 , and (d) temperature distribution formetallic phase of VO2

reflectance[R(ω)] and transmittance[T(ω)] were obtained from the S-parameters in the

simulation package and the absorbance was calculated as A(ω) = 1 − R(ω) − T(ω).

As shown in Fig. 6.1 a magnetic resonance corresponding to the anti-parallel induced

currents on the two metal surfaces, is excited by the magnetic field component of the

incident radiation. Accumulation of the energy in the structure as indicated by the

power flow (Poynting vector map) shown in Fig. 6.1. Fig. 1 (A) shows the absorbance

and reflectance of the tri-layer with VO2 in the low and high temperature phases. When

VO2 is in dielectric phase, the metamaterial is in the absorptive state with absorbance

152 CHAPTER 6

exceeding even 99% at 10.22 µm with a FWHM of 800 nm. At high temperatures(341K),

the metamaterial with a conducting VO2 film shows, instead, high reflectivity with re-

flectance exceeding 95% over the band 9 µm to 11 µm.

The absorption of electromagnetic radiation in metamaterial is due to losses in the

dielectric material, and due to losses by ohmic heating in the metallic plate. Resis-

tive heating, typically, is dominant over the dielectric loss at optical & IR frequencies

and, is greatly enhanced at the resonance frequency. The heat generated within the

metamaterial is taken to be the source for the heat transfer problem. The thickness

dependent thermal conductivity of 100 nm and 200 nm thin gold films are taken to be

200 W m−1K−1 and 250 W m−1K−1 respectively17 and the thermal conductivity of VO2

for dielectric and metallic phase are taken to be 4 W m−1K−1 and 6 W m−1K−1 respec-

tively. Periodic boundary conditions were applied along Y-Z directions by setting the

heat flux to zero. The convective heat transfer coefficient of air, in the outward vector

normal to surface, is set to be h = 5 W m−1K−1. The ambient temperature is assumed to

be 300 K. The numerical simulation shows that the temperature within the VO2 layer is

a function of the incident radiation flux and can exceed the insulator to metal transition

temperature for a threshold incident radiant flux of 140 mW cm−2. The heat sources

within the metamaterial unit cell are depicted in Fig. 6.2 (a) and (b). Fig. 6.2 (a) shows

that for an absorptive metamaterial, there is strong enhancement of the heat generated

around the edges of the gold disk as well as on the continuous gold film near the disk

only. However, the temperature distribution within the metamaterials in steady state

is found to be uniformly distributed in the transverse plane due to the high thermal

conductivity of the continuous metallic gold film. This ensures the entire VO2 film

homogeneously undergoes the phase transition. It is a uniform film, either metallic or

dielectric.

In the high temperature reflecting state, almost all the radiation falling on the meta-

material structure is now reflected back (R ≈ 95%) and the metamaterial structure

6.3. Experimental demonstration of switchable metamaterials 153

begins to cool down. Eventually, the temperature will go below the transition temper-

ature and the metamaterial will return to its initial absorptive state. We have verified

that a bare film of VO2 in comparison can also transit between two reflective states with

about 35% difference in reflectivity18. The timescales of the phase transition in the VO2

are essentially about a hundred femtoseconds19, and are hence too short to affect the

switching process. There, however, will be a hysteresis in the behavior of the VO220,

which will cause the phase transition in the cooling cycle to be at a lower temperature

than the phase transition in the heating cycle.

We will now dwell on some potential applications of this metamaterial. Such a

saturable absorber mirror can be ideally utilized as a cavity mirror for Q-switching

of CO2 lasers, in a similar manner to a semiconductor absorber mirror (SeSAM) used

for near infrared lenses21. We also note that the saturation intensity can be changed

by simple means of the changing the thermal insulation. For example, placing the

metamaterial saturable absorber mirror in vacuum eliminates the heat transfer through

top surface and the saturation intensity goes down to about 25 mW cm−2. Thus there

can be great versatility in configuring the metamaterial for different applications.

6.3 Experimental demonstration of switchable metama-

terials

In this section, we present our preliminary experimental results on a tunable metama-

terial absorber in another adaptation where the bottom film of the tri-layer structure is a

phase-change material (VO2). In its insulating phase, the tri-layer is a metal-dielectric-

dielectric structure with a 60% absorption. However, when heated by external means

across the phase transition of the VO2, the tri-layer changes to a metal-dielectric-metal

structure with over 92% absorption within the metamaterial absorption band. The

154 CHAPTER 6

15 20 25 30 35 40 45 50 55 600

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ance

(%)

Frequency (THz)

VO2 at 400C

VO2 at 800C

15 20 25 30 35 40 45 50 55 600

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30

40

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60

70

Ref

lect

ance

(%)

Frequency (THz)

VO2 (at 400C) + ZnS

VO2 (at 800C) + ZnS

Figure 6.3: Left: shows the measured reflectance of the insulating and metallic VO2 thin filmson a SiO2 substrate at 400C and 800C respectively, Right: shows the measured reflectance fromthe 380 nm thin ZnS on top of VO2 thin film at 400C and 800C respectively.

metamaterial structure were fabricated by shadow mask deposition techniques. A

continuous film of VO2 deposited by spray pyrolysis technique on the quartz substrate

was supplied by our collaborators R. Bharthi & Prof. A. Umarji (IISc Banglore). Next, a

uniform 380 nm thick ZnS film was thermally evaporated on top of the deposited VO2

film. Following the deposition of the continuous ZnS layer, the shadow masks contain-

ing hole array was employed to form the aluminum disks on top by direct deposition

through the holes in the membrane to produce the array of Al disks.

The fabricated sample is characterized using an infrared microscope with a Fourier

transform infrared (FTIR) spectrometer. We characterize the reflectivity from the sam-

ple as a function of substrate temperature. All reflectance are referenced with respect

to the reflectivity of a plain gold mirror. A stage with temperature control was used

to heat the sample at increments of 50C, and we collected the reflection spectra at each

temperature. We first show the reflectance in Fig. 6.3 from the plain VO2 film. This film

switches from a low reflectance (10%) to a high reflectivity metallic state (70%). There is

a peak for reflectivity at about 32 THz for VO2 in the low temperature insulating phase.

This effect is expected to arise form destructive interference of multiple reflections from

multi-layer dielectric thin films22. The reflectivity in the two phases when a ZnS thin

6.3. Experimental demonstration of switchable metamaterials 155

film is deposited over the VO2 is shown in Fig. 6.3 (Right panel). The reflectivity of the

system when VO2 is in the metallic phase is considerably reduced. When the substrate

temperature is well below the phase transition temperature, the bottom VO2 film is in

the insulating phase and the electromagnetic response of the ZnS/VO2 can be under-

stood in terms of the multiple reflection occurring from the stack of dielectric films.

When the substrate temperature is above the phase transition temperature, the bottom

VO2 film changes to metallic phase and the electromagnetic response of the ZnS/VO2

is that of a dielectric film (ZnS) place on a metallic VO2 thin film as shown in Fig. 6.3

and the reflectivity of metamaterial goes to a higher value of 30 %.

We show the reflectivity of the metamaterial with the VO2 ground plane in Fig. 6.4.

Our experimental result shows two possible switching behaviors at 33 THz and 22.5

frequencies. The fabricated metamaterial shows first switching behavior from a high

reflection state at low temperature (at 400C (red curve)) to a low reflection state at

high temperature (at 800C (black curve)) at 32.5 THz as VO2 changes its phase form

insulating phase to metallic phase. It switches conversely from a high reflectivity at

low temperatures (400C) to a low reflectivity state at high temperature (800C) at 22.5

THz.

The second switching behavior of the fabricated metamaterial at 22.5 THz is due

to switching on or off the metamaterial absorber resonance. When the substrate tem-

perature is well below the phase transition temperature, the bottom VO2 film is in

the insulating phase and the electromagnetic response of the metamaterial is that of

circular metallic patches placed on top stacked dielectric films. In this configuration,

the reflectivity of metamaterial achieves a higher value of 60%, i.e., with low absorp-

tion. We find that the metamaterial shows very small change in the reflectivity until

the substrate temperature crosses the phase transition temperature of VO2, at which

VO2 changes its phase from insulating to metallic. When the substrate temperature is

increased above the phase transition temperature the bottom VO2 film became metallic

156 CHAPTER 6

15 20 25 30 35 40 45 50 55 600

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20

30

40

50

60

70

80 400C 800C

Ref

lect

ance

(%)

Frequency (THz)15 20 25 30 35 40 45

20

30

40

50

60

70

80

90

100

Ref

lect

ance

(%)

Frequency (THz)

Simulation

Figure 6.4: Top: Schematic of unit cell of an switchable metamaterial. Bottom left: shows themeasured reflectance of the metamaterial with insulating and metallic VO2 phases at 400C and800C respectively. Right: Simulated reflectance by assuming a metallic phase of VO2 in themetamaterial structure.

and the composite structure forms a metal-dielectric-metal metamaterial tri-layer. The

tri-layer structure gives rise to simultaneous resonant excitation of an electric dipole

and a magnetic dipole and the optimized impedance matching of the metamaterial is

established at the resonant frequency of 22.5 THz. The metamaterial absorption band

can be clearly delineated in Fig. 6.4. The reflectivity dramatically drops to a lesser that

8% at the peak of resonant absorption band. The reflectivity and transmittivity from

the metamaterial should almost be near zero values in the ideal case implying high

absorption. In our case, the VO2 microstructure clearly shows large grains which con-

siderably scatter the radiation. This causes the lower reflectivity in the high reflectance

state and the slightly lower levels of absorption than the ideal in the absorbing state.

We observe that the reflectivity of metamaterial structure at 400C (red curves in

Fig. 6.4) is relatively high with values around 50% to the reflectivity of metamaterial


structure at 800C with values around 10%.

Fig. 6.4 also displays the simulated reflectivity from the metamaterial for the metallic

phase of VO2. We find that simulations match reasonably well to the experimental

reflectivity with the VO2 considered in the metallic state. The thermal switching of

metamaterial structure from the metamaterial structure was found to be reversible over

many cycles. The modulation hysteresis of metamaterial is found to be similar to the

optical constant hysteresis behavior of VO2 thin films. It has been shown by Nagashima

et al.23 that the switching of the optical properties of VO2 thin films strongly depends

on the growth conditions of the VO2 film.

6.4 Conclusions

In conclusion, we have presented a simple design of a metamaterial that shows a satu-

ration of absorption due to the inclusion of a thin film of phase change material (VO2)

at mid-infrared wavelengths. The metamaterial structure exhibits high absorption of

over 99.9% over for the dielectric VO2 and low temperature and over 95% reflectance

at high temperature for metallic VO2. We have also investigated in detail the heat

generation and temperature distribution within the metamaterial which triggers the

insulator to metal phase transition in VO2 for sufficient incident radiation flux. The

saturation intensity of our design in the air is about 140 mW cm−2 and can be reduced

further by increasing the thermal insulation, e.g. by keeping the array in vacuum. We

have also demonstrated a thermally switchable metamaterial of infrared radiation in

the reflection configuration. Our primary result shows a modulation of the reflectivity

levels of 40% at a frequency of 22.5 THz and 20% at a frequency of 32.5 THz.

158 CHAPTER 6

6.5 References

[1] W. J. Padilla, A. J. Taylor, C. Highstrete, M. Lee, and R. D. Averitt, "DynamicalElectric and Magnetic Metamaterial Response at Terahertz Frequencies," Phys.Rev. Lett. 96, 107401, 2006.

[2] H. T. Chen, J. F. O’Hara, A. K. Azad, A. J. Taylor, R. D. Averitt, D. B. Shrekenhamer,and W. J. Padilla, "Experimental demonstration of frequency-agile terahertz meta-materials," Nature Photonics 2, 295, 2008.

[3] H. T. Chen, W. J. Padilla, J. M. O. Zide, A. C. Gossard, A. J. Taylor, and R. D. Averitt,"Active terahertz metamaterial devices," Nature 444, 597, 2006.

[4] H. T. Chen, S. Palit, T. Tyler, C. M. Bingham, J. M. O. Zide, J. F. OHara, D. R. Smith,A. C. Gossard, R. D. Averitt, and W. J. Padilla, "Hybrid metamaterials enable fastelectrical modulation of freely propagating terahertz waves," Appl. Phys. Lett. 93,091117, 2008.

[5] D. Shrekenhamer, S. Rout, A. C. Strikwerda, C. Bingham, R. D. Averitt, S.Sonkusale, and W. J. Padilla, "High speed terahertz modulation from metama-terials with embedded high electron mobility transistors," Opt. Express 19, 9968,2011.

[6] T. Driscoll, S. Palit, M. M. Qazilbash, M. Brehm, F. Keilmann, B. G. Chae, S. J.Yun, H. T. Kim, S. Cho, and N. M. Jokerst, "Dynamic tuning of an infrared hybrid-metamaterial resonance using vanadium dioxide" Appl. Phys. Lett. 93, 024101,2008.

[7] H. Tao, A. Strikwerda, K. Fan, W. Padilla, X. Zhang, and R. Averitt, "ReconfigurableTerahertz Metamaterials" Phys. Rev. Lett. 103, 147401, 2009.

[8] G. Dayal and S. A. Ramakrishna, “Design of highly absorbing metamaterials forInfrared frequencies,” Opt. Express 20, 17503, 2012.

[9] M. J. Dicken, K. Aydin, I. M. Pryce, L. A. Sweatlock, E. M. Boyd, S. Walavalkar, J.Ma, and H. A. Atwater, “Frequency tunable near-infrared metamaterials based onVO2 phase transition,” Opt. Express 17, 18330, 2009.

[10] S. Chakrabarti, S. A. Ramakrishna, and H. Wanare, “Coherently Controlling meta-materials,” Opt. Express 16, 19504, 2008.

[11] Z. Yang, C. Ko, and S. Ramanathan, “Oxide Electronics Utilizing Ultrafast Metal-Insulator Transitions,” Annu. Rev. Mater. Res. 41, 337, 2011.

[12] T. Driscoll, H. T. Kim, B. G. Chae, B. J. Kim, Y. W. Lee, N. M. Jokerst, S. Palit, D.R. Smith, M. Di Ventra, and D. N. Basov1, “Oxide Electronics Utilizing UltrafastMetal-Insulator Transitions,” Science 325, 1518, 2010.

6.5. References 159

[13] M. D. Goldflam, T. Driscoll, B. Chapler, O. Khatib, N. M. Jokerst, S. Palit, D. R.Smith, B. J. Kim, G. Seo, H. T. Kim, M. Di Ventra, and D. N. Basov, “MemoryMetamaterials,” Appl. Phys. Lett. 99, 044103, 2011.


[15] M. A. Ordal, L. L. Long, R. J. Bell, S. E. Bell, R. R. Bell, R. W. Alexander, Jr, and C.A. Ward,“Optical properties of the metals Al, Co, Cu, Au, Fe, Pb, Ni, Pd, Pt, Ag,Ti, and W in the infrared and far-infrared,” Appl. Opt. 22, 1099, 1983.

[16] O. P. Mikheeva and A. I. Sidorov, “Absorption and Scattering of Infrared Radiationby Vanadium Dioxide Nanoparticles with a Metallic Shell,” Technical Physics 48,602, 2002.

[17] G. Chen and P. Hui, “Thermal conductivities of evaporated gold films on siliconand glass,” Appl. Phys. Lett. 74, 2942, 1999.

[18] S. A. Pollack, D. B. Chang, F. A. Chudnovky, and I. A. Khakhaev, “Passive Q-switching and mode locking of Er:glass lasing using VO2 mirrors,” J. Appl. Phys.78, 3592, 1995.

[19] M. Rini, A. Cavalleri, R. W. Schoenlein, R. Lopez, L. C. Feldman, R. F. Haglund Jr., L.A. Boatner and T. E. Haynes, “Photoinduced phase transition in VO2 nanocrystals:ultrafast control of surface-plasmon resonance,” Opt. Lett. 30, 558, 2005.

[20] J. Nag and R. F. Haglund Jr., “Synthesis of vanadium dioxide thin films andnanoparticles,” J. Phys.: Condens. Matter 20, 264016, 2008.

[21] D. J. H. C. Maas, A. R. Bellancourt, M. Hoffmann, B. Rudin, Y. Barbarin, M. Golling,T. Sdmeyer, and U. Keller, “Growth parameter optimization for fast quantum dotSESAMs,” Opt. Express 16, 1886, 2008.

[22] M. A. Kats, D. Sharma, J. Lin, P. Genevet, R. Blanchard, Z. Yang, M. M. Qazilbash, D.N. Basov, S. Ramanathan, and F. Capasso "Ultra-thin perfect absorber employinga tunable phase change material" Appl. Phys. Lett. 101, 221101, 2012.

[23] M. Nagashima, H. Wada, "Near infrared optical properties of laser ablated VO2

thin films by ellipsometry" Thin Solid Films 312, 61, 1998.

CHAPTER7Future DirectionsInfrared perfect absorbers have the potential to facilitate the development of new and

novel optical devices such as thermal imager, selective thermal emitters, sensors, spatial

light modulators, IR camouflage, use in thermophotovoltaics, and wireless communi-

cation. In particular, perfect absorbers have the potential to significantly improve the

function of micr-bolometer focal-plane arrays used for imaging and sensing applica-

tions. These micro-bolometer arrays are typically broadband detectors. Individual

micro-bolometer pixels absorb light across the entire infrared region, generating a

thermal imaging. However, currently available broadband uncooled micro-bolometer

arrays are generally not sensitive enough to perform low-concentration chemical detec-

tion. Metamaterial perfect absorber based micro-bolometer arrays hold the potential

for significantly improving the thermal imaging, night vision, chemical and biological

sensing capabilities.

The designs of perfect absorber proposed and demonstrated in this thesis, with

multi-band spectral responses and significant enhancement of the local near-field inten-

sity, opens possibilities for infrared spectroscopy, e.g., infrared absorption spectroscopy

enables direct access to the vibrational fingerprints of a molecular structure. Simple de-

signs consisting of micro-disk arrays separated for a continuous optically thick metallic

plane by dielectric spacer, which are easy to fabricate, can be used to enhance absorp-

tion at multi-spectral wavelength through the excitation of fundamental and higher

order multipolar resonances in the metamaterial arrays. The resonant frequency of

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162 CHAPTER 7

the metamaterial elements could be tuned throughout some range of frequencies en-

abling hyper-spectral imaging. The ability to tailor the electromagnetic wave of the

metamaterials would expand the sensitivity and multiplex capabilities into the area

of biochemical interactions and would encourage the emergence of surface-enhanced

molecular spectroscopies. This thesis presents a new viewpoint on perfectly absorbing

metamaterial absorber, namely, that they can be considered as an array of resonantly

patch antennas that are impedance matched optimally.

Metamaterial perfect absorber design with Vanadium dioxide (VO2) inclusions, act-

ing as a phase change material within the metamaterial, causes the metamaterial to

switch from an absorptive to a highly reflective state (>95%) for a specific threshold

intensity of the incident radiation corresponding to the phase transition of VO2, result-

ing in the saturation of absorption in the metamaterial. The proposed designed can be

used as saturable absorber mirror for the lasing cavity of a CO2 laser or any IR laser

that permits the rapid Q-switching of the cavity. The wavelength of operation and

threshold levels for switching can be chosen by appropriate design of the metamaterial

and these metamaterials can be made by standard micro-fabrication processes. The

design results in a robust Q-switching mirror that has broadband activity over a large

bandwidth of CO2 laser emission, is switchable in short time scales of few nanoseconds,

and is based on robust inorganic materials.

In other applications such as solar energy harvesting and photonic detection, the

bandwidth of light absorbers is required to be quite broad. We proposed and demon-

strated a metamaterial that have broadband absorption at MIR frequencies using a

semi-conducting Indium Tin Oxide (ITO) film as ground plane. The metamaterial ab-

sorber consists of an array of uniform aluminum disks separated by a Zinc Sulphide

(ZnS) dielectric spacer layer from the ITO ground plane. Compared to noble metals,

semi-conducting ITO thin films have a low dispersion in the dielectric permittivity

which would result in small variation in effective permittivity of the metamaterial and

163

broadband in nature. The plasma frequency of ITO can be tuned in CMOS configuration

which would enable the metamaterial device to be controllable .

The structure dependent properties of metamaterial that engender many exceptional

phenomena also demand suitable fabrication method for their demonstration and to

enable their integration in photonic devices. The shadow mask fabrication method

developed in this thesis hold promises to a high throughput process for producing large

areas of deposited patterns including high aspect ratio structures on mechanically rigid

as well as flexible surfaces and can further be improved for fabricated on pre-patterned

surfaces of existing devices to enable multi-functional performance of the devices.

165

Publications of Govind Dayal

1. Design of highly absorbing metamaterials for Infrared frequencies,Govind Dayal and S. A. Ramakrishna, Opt. Express 20, 17503-17508 (2012).

2. Metamaterial Saturable Absorber Mirror,Govind Dayal and S. A. Ramakrishna, Opt. Lett. 38, 272-274 (2013).

3. Design of multi-band Metamaterial Perfect Absorbers with stacked metal-dielectricdisks.Govind Dayal and S. A. Ramakrishna, J. Opt. (IOP, UK) 15, 055106 (2013).

4. Excimer laser micromachining using binary mask projection for large area pat-terning with single micron features,Govind Dayal, S. A. Ramakrishna, Syed Nadeem Akhtar and J. Ramkumar,Journal of Micro and Nano manufacturing 1, 031002 (2013).

5. Broadband infrared metamaterial absorber with visible transparency using ITOas ground plane,Govind Dayal and S. A. Ramakrishna, Opt. Express 22, 15104-15110 (2014).

6. Multipolar Localized Resonances for Multi-band Metamaterial Perfect Absorbers,Govind Dayal and S. A. Ramakrishna, J. Opt. (IOP, UK) 16, 094016 (2014).

7. Thermally Switchable Metamaterials with VO2 ground plane,Naorem Rameshwari, Govind Dayal, S. A. Ramakrishna, Bharathi Rajeswaran,A.M. Umarji, Submitted.

8. Flexible Metamaterial Absorbers with multi-band infrared response,Govind Dayal and S. A. Ramakrishna, Submitted.

9. Microfeature edge quality enhancement in excimer laser micromachining of metalfilms by coating with a sacrificial polymer layer,S. Nadeem Akhtar, Shashank Sharma, Govind Dayal, S.A. Ramakrishna and J.Ramkumar, Submitted.

166 CHAPTER 7

Patents

1. Dry Processing Method for the Fabrication of Binary Masks with Arbitrary Shapesfor Ultra-Violet Laser Micromachining.Govind Dayal, S. A. Ramakrishna and J. Ramkumar, WO/2013/190444.

2. A green process for binary masks with isolated features for laser micromachiningand photo-lithography.Govind Dayal, S. A. Ramakrishna and J. Ramkumar, WO/2014/108772A1.

3. Saturable metamaterial absorber mirror for Q-switching applications in carbondioxide lasers.Govind Dayal and S. A. Ramakrishna, WO/2014/087256A1.

4. A dry process for rapid fabrication of large area shadow mask.Govind Dayal and S. A. Ramakrishna, U S Patent (In the process of filing), Indianpatent no. 1685/DEL/2014..

metamaterials for multi-spectral infrared absorbers govind dayal

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