Theoretical investigations on Theoretical investigations on

Optical MetamaterialsOptical Metamaterials

Jianji YangSupervisor : Christophe Sauvan

Nanophotonics and Electromagnetism Group

Laboratoire Charles Fabry de l’Institut d’Optique

Collaborators: Stéphane Collin, Jean Luc Pelouard

Laboratoire de Photonique et de Nanostructures (LPN)

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Metamaterials (MMs)

MMs:

Engineered materials possessing properties that are not available in nature, especially negative permeability and negative refractive index.

Potential applications : Imaging, Invisibility Cloaking, Sensors , Photon Management, Nonlinear Optics, Antennas, Wave Absorber…

Example:Negative Index “Perfect” Lens

J. Pendry, " Negative Refraction Makes a Perfect Lens ", Phys. Rev. Lett. 85, 3966 (2000).

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Concept of Effective Parameters

homogenization

Effective Parameters: It is a significant challenge to homogenize metamaterials, i.e. to determine the effective material parameters. Crucial Parameters:effective refractive index neff , effective permittivity ɛeff and effective permittivity µeff …

metamaterial

r

t

r

t

neff, ɛeff , µeff

ɛeff <0, µeff <0 neff <0

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Negative index in the microwaves

Magnetic Response

H

Split Ring Resonator

(SRR)Collection of SRR forms effective magnetic medium.

Electric Response

Metallic Wires

εm<0Collection of conducting wires forms an effective metal with a controllable plasma frequency.

Pendry, J. B., et al., 47, 2075, IEEE Trans. Microw. Theory Tech. (1999)Pendry, J. B., et al., 76, 4773 , Phys. Rev. Lett. (1996)

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eff 2 20

Fωμ = 1 -

ω - ω + iωΓ

2P

eff 2

ω= 1 -

ω

Γ: dissipation factor F: fractional factor ωP: controllable plasma frequency

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Split-ring resonators (SRRs) based metamaterial, functioning in microwave spectrum. R. A. Shelby et al., Vol. 292, pp. 77 - 79, Science (2001).

5mm

Negative index in the microwaves

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Moving to Optical Spectrum

Fishnet metamaterials, functioning in near-infrared spectrum.

J. Valentine et al., 455, 376-379, Nature (2008).

Fishnet Metamaterial

Conceptual Difficulties: high dissipation of metals, saturation of magnetic resonance…Fabrication Difficulties: difficulty of scaling-down and stacking-up…

Current Loop

1m

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Fishnet: important fundamental mode

Measurement agrees well with calculated fundamental Bloch mode.J. Valentine et al., 455, 376-379, Nature (2008).

measurement

fundamental Bloch mode

Quartz

FishnetPrism

Air

Incident Beam

Output Beam

n<0α

Prism Measurement

8J. Yang et al., Appl. Phys. Lett. 97, 061102 (2010)

Fishnet: important fundamental mode

Single Bloch Mode Approximation

(SBMA)

fundamental Bloch mode mediates the light transport in fishnet metamaterials.

SBMA

Rigorous

TT0.8

0.6

0.4

0.2

0

λ (μm)

RR

1.4 1.8 2.2

0.8

0.6

0.4

0.2

0

t

Fishnet

r air

neff

Fundamental Bloch Mode

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Microscopic Model: basic waveguide modes

TE01 : least attenuated mode of a rectangular hole

gap-SPP : least attenuated mode of a planar SPP waveguide

gap-SPP

TE01

Metal layer

Dielectriclayer

J. Yang et al., (submitted)

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Elementary Scattering Coefficients

ρ

gap-SPP

αα

τ

Incident TE01

H.T. Liu and P. Lalanne, 452, 728-731, Nature (2008)

α

αtsp

rsp

TE01

gap-SPP

Incidentgap-SPP

ρ , τ : reflectivity and transmissivity of TE01

rsp , tsp : reflectivity and transmissivity of gap-SPP

α : coupling coefficient between gap-SPP and TE01

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Coupled Mode Formalism

Analytical ModelAnalytical Model eff

2 2

0 z ( ) ( ) 1

cos (k a )n2( )

Dispersion relation

Am = τAm+1 + ρBm + αCn + αDn+1

Bm = τBm-1 + ρAm s+ αCn + αDn+1

Cn = tspCn+1 + rspDn + αBm+1 + αAm

Dn = tspDn+1 + rspCn + αBm+1 + αAmAm+1 Bm+1

Am Bm

Cn+1

Dn+1

Cn

Dn

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Microscopic Model

Microscopic modelFishnet mode (exact)

Am+1 Bm+1

Am Bm

Cn+1

Dn+1

Cn

Dn

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Resonance of gap-SPP

Current Loop

Gap-SPP mode shows resonance around 2m, via the coupling with TE01 mode, this resonance influences the light transport significantly.

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Conclusion:

We have studied the optical fishnet metamaterials theoretically. In particular we investigate the important fundamental Bloch mode of fishnet structure, and we also formulate the construction of this mode from a relatively microscopic point of view.

In the future, we will investigate other types of plasmonic structures, especially some potentially applicable designs.

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Thank you !