Nanooptics

The birth of Sant Eligio - patron saint of the goldsmiths.Niccolo da Varallo, 1480-1486

Courtesy of the Fabbrica del Duomo di Milano, Italy.

The glass has been stained by gold and silver nanoparticles that get their bright colors from localized surface plasmons!

Mikael Käll Applied Physics, Chalmers Univ. of Techn., Göteborg

e-mail: kall@chalmers.se

What is nanooptics?1.  Nanoscopy: microscopy with resolution well below the diffraction limit

1.  Near-field Scanning Optical Microscopy (NSOM) 2.  ”Computer assisted” nanoscopy, such as STORM, PALM etc 3.  Non-linear fluorescence imaging, such as STED

2.  Optical properties of nanoscale (1-100 nm) structures 1.  Metal nanostructures = nanoplasmonics 2.  Semiconducting nanostructures, e.g. quantum dots 3.  Carbon nanotubes, etc

3.  Single molecule optical imaging and spectroscopy 1.  Fluorescence correlation spectoscopy (FCS) 2.  Fluorescence resonance energy transfer (FRET) 3.  …

However, there are no strict limits, and many subfields incorporate components from 1-3 Example: TERS (tip-enhanced Raman spectroscopy), based on NSOM with nanoplasmonic metal tip that can be used to record vibration spectra from single molecules

I will focus on red parts!

Ernst Abbe (1840-1905)Ø  Developed image theory Ø  Developed methods for aberration corrections Ø  Leading technician at Carl Zeiss

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d = 0.61λNA

NA = nsinθ

Resolution limit of optical imaging (Abbe criterion)

NA is the numerical aperture of the lens used for imaging, α is half the opening angle

The reason for the finite resolution is diffraction in the optical instrument

A point source is imaged as a so-called Airy pattern. The radius of the central bright spot (the Airy disk) is:

€

d = 0.61λNA

NA = nsinθ

State-of the art diffraction-limited optical microscopy – the confocal fluorescence microscope

The image is created by raster-scanning a laser beam through the specimen and simultaneously recording emission from fluorescent molecules using a small “confocal” aperture (with a radius that equals the Airy disk) in front of the detector.

Main use in cell biology Cost ~1-5 MSkr Resolution ~300 nm at best Frame rate up to video rate

Nanoscopy: to circumvent the diffraction limitNSOM - Near-field Scanning Optical Microscopy Concept formulated by Synge in 1928; experimental realization in the 1990’s

NSOM imaging of “hot spots” between gold nanoparticles Rainer Hillenbrand, MPI Martinsried

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λ = 632 nm

Raster-scan a tiny subwavelength hole above the sample surface using AFM feedback and record light that is transmitted/reflected/emitted gives simultaneous optical and topographic images with resolution given approximately by the size of the hole.

What could be the pros and cons of NSOM?

PALM & STORMPhoto-activated localization microscopy & Stochastic image reconstruction microscopy

BASIC IDEA: if you know that you look at isolated point-sources, then you can use a measured or calculated Airy pattern (called the “point spread function” = PSF in 3D) to “deconvolute” the image to obtain the precise location of the point sources with nm resolution! To know that you have isolated point sources = molecules, you typically look at molecules that can be switched between a fluorescent and a non-fluorescent state, for example using UV light.

Photo  switching  and  image  forma2on  

Example: Photo-activable Green Fluorescent Protein – PA-GFP

A small fraction of the molecules in a sample are switched, then imaged, then bleached. Another (random) subset of molecules are switched, imaged and bleached. After many such cycles, one can build up a complete image of the sample by deconvoluting each separate image and then overlaying them

What could be the pros and cons of this technique?

STED  –  s2mulated  emission  deple2on  

Background: stimulated emission

www.mpibpc.mpg.de/groups/hell/

Basis for “Light Amplification by Stimulated Emission of Radiation” = LASER

STED  microscopy  

Two laser beams of slightly different wavelength: One Gaussian beam for “ordinary” fluorescence excitation. One “donut shaped” beam for stimulated emission in peripheral area of Gaussian beam. Only central subwavelength spot yield fluorescence.

What can be the pros and cons of STED?

Nanoplasmonics  

APPLICATIONS •  Bio/chemo sensing •  Surface-enhanced spectroscopy (SERS, SEF, SEIRA,..) •  Near-field optical microscopy/spectroscopy •  Nanoscale photonics applications / optical circuits •  Metamaterials, e.g. for negative refraction •  Contrast agents for bioimaging / photodynamic therapy •  etc.

Result of ISI Web of Science search for “plasmon” Feb 2009

Chalmers University of Technology

Key features of nanoplasmonic structures

Dimer of ~90 nm Ag particles for single molecule SERS measured by aperture-less NSOM

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d = 0.61λNA

Field confinement By using electron resonances (plasmons) in metal nanostructures, light can be focused down to molecular dimensions! Field enhancement The resonant optical fields can be enhanced by orders-of-magnitude near metal nanostructures Tunability The enhancement effects can be tuned in space and wavelength through the shape, size and material that defines the nanostructure

”Rayleigh limit”

The optical properties of nanoparticles are described by their induced dipole moments

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p(ω, t) =α0ω02

ω02 −ω 2 − iωγ

E0 cos(ωt) =α(ω)E(t)

The proportionality constant between p and E is called the polarizability α

The polarizability function is called a Lorentzian. The strength of the polarizability α0 is proportional to the number of charges in the nanoparticle. The resonance frequency depends on the “spring constant” acting on the charges when they are displaced by E.

What does p do?

The induced dipole absorb electromagnetic energy

The induced dipole scatter the electromagnetic field

Absorption is proportional to

Scattering is proportional to

ω Im[α(ω)]

ω 4 α(ω) 2

(the ω4 dependence of scattering is what makes the sky blue and the sun red at sunset!)

Polarizability of nanosphere

α(ω) = a3εsphere(ω)−εmediumεsphere(ω)+ 2εmedium

This is called the “Clausius-Mosotti polarizability” and is obtained by solving Poissons eq. in spherical coordinates with appropriate boundary conditions

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a is the radius of the sphereεsphere (ω) is the frequency dependent dielectric function of the sphereεmedium is the dielectric constant of the surrounding medium

ε = n2, n = refractive index

The polarizability becomes very large if if the material is such that:

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εsphere (ω) = −2εmedium at some particular frequency ω

Dielectric function of silver in the UV-NIR wavelength range

The Drude dielectric functiondescribes the electromagnetic response of a free-electron metal

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ε(ω) = n 2 (ω) = 1−ω p

2

ω 2 + iωτ, ω p ≡

N freee2

ε0me

Real and imaginary part of the dielectric function of gold compared to the Drude model based on the actual free-electron density of gold. The structure above ~2 eV is due to bound electrons (so-called inter-band transitions)

The Localized Surface Plasmon Resonance

-50

-40

-30

-20

-10

0

1 1.5 2 2.5 3 3.5 4

SILVER

GOLD

die

lect

ric

con

stan

t (r

eal

part

)

energy [eV]

UVVISNIR

SPR

-2εair

-2εdielectric

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α(ω) = a 3ε sphere (ω) −εmediumε sphere (ω) + 2εmedium

= a 3(1−ω p

2

ω 2 + iωΓ) − n2

(1−ω p2

ω 2 + iωΓ) + 2n 2≈ a 3 ωLSP

2

ωLSP2 −ω 2 − iωΓ

ωLSPsphere =

ω p

1+ 2n2

Resonance condition for sphere

The color of gold and silver

Plasmon engineering through nanolithography(electron beam lithography, colloidal lithography, focused ion-beam milling etc.)

L. Gunnarsson et al., J. Phys. Chem B 109, 1079 (2005). E.M. Hicks et al. Nano Letters 5, 1065 (2005). P. Hanarp et al., J. Phys. Chem. B 107, 5768 (2003). J. Aizpurua et al. Phys. Rev. Lett. 90, 057401 (2003). C. Haynes et al., J. Phys. Chem. B 107, 7337 (2003). L. Gunnarsson et al, Appl. Phys. Lett. 78, 802 (2001). L. Gunnarsson et al., NanoStructured Materials 12, 783 (1999)

1 cm

Tuning of optical response through particle shape, size and interactions.

Computational plasmonics■  Solve Maxwell’s equations in arbitrary geometries using; the

Finite Difference Time Domain method (FDTD); the Discrete Dipole Approximation (DDA); Green’s tensor methods (GT) or Mie theory.

■  Yields spatial and spectral information on field-enhancement and other near- and far-field properties

Plasmon shift due to change in refractive index of surounding medium

Air Im.oil

Single particle in air and immersion oil

An increasing refractive index of the surrounding medium reduce the restoring force in the charge displacement, causing a LSPR red-shift

n>≈1 n≈1.52

What does the E-field from an oscillating dipole look like?

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Er =p cosθ4πε0ε

⋅exp(ikr)

rk 2 2

k 2r 2−2ikr

'

( ) *

+ ,

Eθ =p sinθ4πε0ε

⋅exp(ikr)

rk 2 1

k 2r 2−ikr−1

'

( ) *

+ ,

r p

E

Θ

€

k =ω /c = 2π /λ wave vectorε0ε dielectric constant of medium

Protein A/G

Human IgG

Gt-α-h-IgG

Srdjan Acimovic unpublished results

Multiplexed LSPR sensing in active microfluidic networks by hyperspectral imaging

Field-enhancement near an induced dipole

Let’s look at the near-field for Θ = 0 p

z

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Einduced =p

2πε0ε⋅1r 3

=α(ω)E02πε0ε

⋅1r 3

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Etotal = Einduced + E0 =α(ω)2πε0ε

⋅1r 3

+1'

( )

*

+ , ⋅E0

The total field is the sum of the induced field and the incident field

We can then define a field-enhancement factor M or an intensity-enhancement factor M2 from:

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M =EtotalE0

=EinducedE0

+1 This factor can be >>1 if the polarizability is high and the distance to the dipole is small!

Raman scatteringν10 ν19

ν4

•  molecular “fingerprints” from vibrational structure

Sir C.V. Raman

Example: Hemoglobin

Unfortunately, Raman scattering is a too weak effect for many practical applications

aggregation

1 Hb per ~3 Ag

Single molecule SERSself-assembly of particle pairs through heme-protein binding

Eα

H.X. Xu et al., Phys. Rev. Lett. 83, p. 4357 (1999); E.J. Berneld et al., Single Molecules 1, 239-245 (2000); E.J. Bjerneld et. al., J.Phys.Chem. B 106, p. 1213 (2002); H.X. Xu et al., ChemPhysChem 4, 1001 (2003).; E.J. Bjerneld et al., J. Phys. Chem. A 108, 4187 (2004).

• SPECTRAL FLUCTUATIONS

• ENHANCEMENT FACTORS ~1010

• POLARIZATION DEPENDENCE

Simple model of Raman scatteringAssume that the molecule is vibrating! This means that the polarizability will fluctuate in time:

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αmol (t) =αmol0 +

∂αmol

∂QQ0 cos(ωvibt)

Amplitude of vibration Vibration frequency

“electron-vibration coupling constant”

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µ(t) =αmol (t)E0(t) = αmol0 +

∂αmol

∂QQ0 cos(ωvibt)

%

& '

(

) * E0 cos(ω lasert) = ...

The induced molecular dipole moment then varies with time as:

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... =αmol0 E0 cos(ω lasert) + 1

2∂αmol

∂QQ0E0 cos (ω laser +ωvib)t[ ] + cos (ω laser −ωvib)t[ ]( )

Remember from cos x cos formulas from math!

Rayleigh component, results in elastic scattering

Raman components, Results in inelastic scattering

Stokes part anti-Stokes part

Raman intensity

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I ∝∂µ∂t

2

⇒ I Stokes ∝ (ω laser −ωvib)4 ∂αmol

∂Q

2

E02

“blue sky” effect

applied intensity

degree of Raman activity

I StokesI AntiStokes =

(ωlaser −ωvib )4

(ωlaser +ωvib )4 exp

ωvibkBT

"#$

%&'

From quantum mechanics:

Boltzmann factor determines probability of thermally excited vibrations

The “antenna picture”

E0, local E0, far

Near field Far

field

ER, local ER, far

Near field

Far field

Reciprocity theorem

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σ Raman ∝ M (ω laser)2

M (ω laser ±ωvib)2∝ M 4

Ingoing field Outgoing field

MIN=MOUT

Dipole-dipole coupling between a molecule and a nanoparticle

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µ =αmol (E0 + Ap)p =α part(E0 + Aµ)

The coupled dipole equation (CDA)

Induced field from particle at location of molecule

Induced field from molecule at location of particle Applied field

Solve to get new effective polarizabilities:

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µ =αmol

1+ Aα part

1− A2α partαmol

E0 = $ α molE0

p =α part1+ Aαmol

1− A2α partαmol

E0 = $ α partE0

Simple derivation of SERSBecause of the coupling, we have now introduced a vibrational modulation of the particle polarizability, which is much much larger than the molecular polarizability!

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p(Q) = " α part (Q)E0 =α part1+ Aαmol (Q)

1− A2α partαmol (Q)E0

This yields:

€

I SERS

I Raman=

∂ # α part

∂Q

2

∂αmol∂Q

2=

Aα part + A2α part2

(1− A2α partαmol )2

&

' ( (

)

* + +

2

≈ Aα part( )4

=ApE0

&

' (

)

* +

4

≈ M 4

FOURTH POWER OF FIELD ENHANCEMENT FACTOR!

Dimers-on-mirror with attogram sensitivity

Hakonen et al., Nanoscale 7, 9405-9410 (2015)

100nm

100nm 500nm

cm2 areas of aligned Au-nanodisk dimers made by hole-mask colloidal lithography

Gold-on-Si nanopillars (Boisen group, DTU)

Antenna arrays for enhanced Raman spectroscopy

Nerve gas detection by SERS and a handheld Raman instrument

Aron Hakonen et al. Nanoscale, to appear (2015) Collaboration with Swedish Defence Academy & Boisen group, DTU

Quantity (mol) Quantity (mol)

TABUN VX

Nanoplasmonic structures from colloidal lithography

•  Nanosdisks, Nanoholes, Nanorings •  Dimers, trimers, tetramers •  Heterostructures •  Nanoandwiches

•  Short-range lateral order •  Weak near-field interactions between structural elements

Applications in •  Plasmonic sensing •  Surface-enhanced spectroscopy •  Solar harvesting •  …

Interference between •  Nanoparticle array •  Reflection from ”bare” dielectric boundary Leads to: •  Strongly dispersive spectral features •  Asymmetric Line-Shapes

Fano Interference between Localized Plasmons and Interface Reflections

Svedendahl and Käll, ACS Nano 2012. 6(8): p. 7533-7539

Totally destructive Fano interference = Complete Light Annihiliation

Tm = ΔT + T0 ΔT = k A(θi) cos(θi)

k ∝  thermal conductivities of surrounding materials A(θi) = Absorption T0 = ambient temperature ~22 °C

Surface of unit cell: •  T is material independent

Illuminating a circle homogeneously •  Maximum temperature in centre •  Mean T in square relates to

measured data •  Maximum in centre estimates

the maximum T of our samples

Laser diode: 658 nm, 50mW Optics: Focus ~80 µm, s-pol, varying θi Heat Camera: 𝜖=0.92

Photon Spin Selective Plasmonic MetasurfacesNear-complete absorption/reflection of right-handed/left-handed circularly polarized light in an ultrathin layer of aligned gold nanorods

Mikael Svedendahl, Robin Ogier, Yurui Fang et al., Phys. Rev. X 2015

Optical forcesp = k Light carries linear momentum.

Conservation of linear momentum forces an object to move

RADIATION PRESSURE Due to absorbed and reflected

photons

GRADIENT FORCE Due to refracted photons

OPTICAL BINDING BETWEEN

PARTICLES Due to mutually induced fields

Example: a spherical object in a laser beam with a Gaussian intensity profile.

Circular polarized photons carry angular momentum: L=σħ, σ=±1 for left/right

Rota2on  of  silver  nanowires  by  mechanically  rota2ng  a  half-­‐wave  plate  

L. Tong et al, Nano Letters 10, 268 (2010)

Spinning of Ag nanowire due to absorption of photon spin angular momentum in circular

polarized light

L. Tong et al, Nano Letters 10, 268 (2010)

Highest reported rotation frequency in water to date ~360 Hz for 300mW power and 1 micron thick calcite crystal

H. Rubenstein-Dunlop and co-workers, Nature 394, 348 (1998).

10 mW laser

The worlds smallest and fastest propellersSpinning Au nanorods in water by resonant light scattering

Lei Shao, et al. ACS Nano 2015

42 kHz, 2.5×106 r.p.m

Equation of motion and equilibrium rotation frequency

Moment of inertia

External torque (photon spin

transfer)

Friction / drag (Stokes

equation)

Stochastic torque (time average = 0)

steady state

Equilibrium rotation

frequency

LSPR-dependent rotational dynamics

830-nm laser

Diameter 65 nm; Length: 130 nm - > 170 nm

Lei Shao, et al. ACS Nano 2015

Spinning for hours with moderate temperature rise

5 mW @ 830 nm

Detecting local viscosity changes and molecular attachment

mPEG-SH 7.5 µM

Lei Shao, et al. ACS Nano 2015

Laser heating

Heating

Inserting realistic values results in a temperature of the order of the critical temperature of water Tc ≈ 650 K for the highest laser powers used! But no vapor formation observed… Increased temperature also leads to a decreased viscosity