fundamentals & applications of lecture 2/2 · pdf fileplasmonics svetlana v. boriskina...

Fundamentals & applications of plasmonics

Svetlana V. Boriskina

Lecture 2/2

S.V. Boriskina, 2012

Overview: lecture 2 • Recap of Lecture 1

• Refractive index sensing

• SP-induced nanoscale optical forces

– Optical trapping & manipulation of nano-objects

• Fluorescence & Raman spectroscopy

• Plasmonics for photovoltaics

• Hydrodynamic design of plasmonic components

• Magnetic effects

• Thermal effects:

– Plasmonic heating

– Near-field heat transfer via SPP waves

• Plasmonic photosensitization of materials

• Further reading & software packages

• Omitted topics


Drude-Lorentz-Sommerfeld theory

Image credit: Wikipedia

Collision

frequency

electron

velocity

mean free

path

lv 1

)(1)(

2

2

i

pDrude permittivity function:

ep mne 0

22 Plasma

frequency


Recap of Lecture 1: Propagating waves

Frequency (Quasi) particle

Dispersion equation

Plane wave

transverse photon

Bulk plasmon longitu-

dinal

plasmon metals:

semicond.:

Surface plasmon

TM: E=(Ex,0,Ez)

polariton = photon + plasmon

21

dm

dmx

ck

dxc

k

21221px

ck

e

pm

ne

0

2

d

p

1

eV10p

eV5.0p

ω

kx(ω)

p

dp 1

p

dp 1

p

High DOS, high localization


Recap of Lecture 1: Localized plasmons Scattering response

Schematic dipoles Near-field patterns

Plasmonic atom

Plasmonic molecules

Plasmonic antenna

array

High

DO

S, high

localizatio

n

Movie: http://juluribk.com

E

+++

- - -

Lowest-energy modes

λ

quadrupole

dipole

dimer heptamer


Plasmons interactions with matter • Optical

– Extreme light focusing/localization (sub-resolution imaging, photovoltaics)

– Strong sensitivity to environmental changes (sensing)

– Amplification of weak molecular signals (fluorescence, Raman scattering, absorption, circular dichroism)

• Electronic

– Enhancement of catalytic reactions

– Plasmonic photosensitization of materials

• Mechanical

– Mechanical manipulation of nanoobjects

• Thermal

– Selective heating of nanoscale areas

– Enhanced near-field heat transfer


SP-enhanced sensing

nFoM

Resonance linewidth

Sensitivity

Sensor figure of merit (FoM):

http://www.bio-sensors.net

SPP sensors

McFarland, A.D. & R.P. Van Duyne, Nano Lett. 2003. 3(8): p. 1057-1062.

LSP sensors

Requirements: • High sensitivity • High spectral resolution • Compact design


FOM enhancement & miniaturization • Fano resonances in plasmonic molecules

Mirin, N.A., K. Bao, & P. Nordlander, J. Phys. Chem. A, 2009. 113(16): p. 4028-4034.


Towards single-molecule sensitivity Hybrid modes in optoplasmonic molecules:

Santiago-Cordoba, M.A. et al, Appl. Phys. Lett., 2011. 99: p. 073701. Also: Boriskina, S.V. & B.M. Reinhard, Opt. Express, 2011. 19(22): 22305-22315; Ahn, W. et al, ACS Nano, 2012. 6(1): 951-960.


Rayleigh

ground

excited

virtual (induced dipole)

hν0

Raman spectroscopy Rayleigh scattering

Raman scattering

hν0 hν0

h(ν0 ± νm) hν0

νm - molecular fingerprint

Stokes Raman

vibrat. hνm

Raman – Nobel Prize in 1930

)cos( 00 tE

Dipole moment induced by light:

polarizability tensor

qqq 0)( vibrational coordinate

)cos(0 tqq m

t

tEq

qtE

m

m

)(cos

)(cos)cos(

0

0

0000

Rayleigh Raman (Stokes & anti-Stokes)

4

6

R ~

dI

particle size

R

3

Ram 10~ II

a very weak effect!

http://en.wikipedia.org/wiki/File:Symmetrical_stretching.gif


Surface enhanced Raman spectroscopy (SERS)

Fleischman M,et al Chem. Phys. Lett. 1974; 26: 123. Jeanmaire DL, Duyne RPV. J. Electroanal. Chem. 1977; 84: 1.

0Ram ~ EggE R

Review: Moskovits, M., J. Raman Spectr., 2005. 36(6-7): p. 485-496 +references therein

E-field enhancement @ ν0 E-field enhancement @ (ν0 –νm)

High field localization enables SERS fingerprinting of single molecules

Nie, S. & S.R. Emory, Science, 1997. 275(5303): 1102-1106.

R6G molecules on Ag nanoparticles

@ the molecule position!


Single molecule delivery to the SP hot spot

De Angelis, F., et al. Nat Photon. 5(11): p. 682-687.

• super-hydrophobic delivery:


Single molecule delivery to the SP hot spot

• Optical trapping:

Review: Juan, M.L. et al, Nat Photon, 2011. 5(6): p. 349-356

)"'(0

0 GGc

nIFU D kF

Gradient force

Dissipative force

Intensity enhancement

P r,U( ) µP0 r( )exp - U(r) kBT{ }

The probability to find a molecule @ r :

Optical potential

L. Novotny, et al, Phys. Rev. Lett. 79 (4), 645 (1997); H. Xu and M. Käll, Phys. Rev. Lett. 89 (24), 246802 (2002).

10)( TkU Br

Stable trapping:


SP-enhanced fluorescence Fluorescence

Fluorescence rate of a dipole with moment μ:

)( nrrrexcf hνexc hνf

non-radiative rate (resistive

heating) radiative rate

excitation rate

2),( excmexc rEμ

Excitation rate:

),(3

2)(

2

0

fmnrr

rμ

Fermi’s golden rule:

Local density of states

Spacer is needed to avoid quenching

The emission intensity affected by both the excitation & emission modification

Anger, P., P. Bharadwaj & L. Novotny, Phys. Rev. Lett., 2006. 96(11): p. 113002


SP-enhanced fluorescence

Russell, K.J., et al., Nat Photon, 2012. advance online publication.

),(3

2)(

2

0

fmnrr

rμ

Emission spectrum shaping by the high-LDOS nanoparticle resonances

Kinkhabwala, A., et al. Nature Photon., 2009. 3(11): p. 654-657.

Single-molecule fluorescence

See also a review: Ming, T., et al., J. Phys. Chem. Lett. 3(2): p. 191-202 (2012).


optical absorption

H. Atwater & A. Polman, Nature Mater. 2010

Plasmonic solar cells

charge carrier diffusion

c-Si: 250 - 700 μm

a-Si: 0.1 – 0.3 μm

Electronic/photonic lengths mismatch


Efficient nanoscale light trapping increase of the local density of optical states in a certain frequency range

Callahan et al, Nano Lett. 2012

Atwater & Polman, Nature Mater. 2010

scattering field enhancement waveguiding


extinction cross-section

How can a particle absorb more than the light incident upon it? C.F. Bohren, Am J. Phys. 1983, 51(4), p.326

HES Re21 Poynting vector determines electromagnetic power flow

powerflow saddle point

W. Ahn, S.V. Boriskina, et al, Nano Lett. 12, 219-227 (2012)


Optical energy flows in the direction of the phase change phase saddle

flow saddle

phase vortex

flow vortex

Local topological features (sources, saddle points, vortices & sinks) define phase landscape that governs optical power flow vortex nanogear transmission

W. Ahn, et al, Nano Lett. 12, 219-227 (2012)

kv g group velocity


Reconfigurable vortex transmissions

S.V. Boriskina & B.M. Reinhard, Nanoscale, 4, 76-90, 2012


‘… the title is straight out of Enterprise's engineering room’

NextBigFuture.com SciTech forum

Reconfigurable vortex transmissions: vortex nanogates

Physical picture behind vortex nanogate


Hydrodynamic design of SP components Electromagnetics

? Maxwell’s equations:

t

t

ΕJH

HE

H

E

0

Gauss’ law

Gauss’ law for magnetism

Faraday’s law

Ampere’s law

+ boundary conditions

Continuity (mass conservation) equation

Momentum conservation equation

Navier-Stokes equations:

0)( v t

fT

vvv

p

t )(

fluid density flow velocity

Fluid dynamics


Hydrodynamic form of Maxwell’s equations

2|)(|)()( rUrr I

)(rv

‘Photon fluid’ density:

‘Photon fluid’ velocity:

))((exp)(),( tit rrUrE

Madelung transformation:


convective term

)()()()( rrrvr

)()()()( rrrvrv QV

‘mass’ conservation:

momentum conservation:

)(12)( 2

0 rr kV

external potential created by the nanostructure

)()( 20 rr k

material loss or gain

• steady state flow • local convective acceleration possible • fluid flux (the momentum density):

)()()2(1 0 rvrS


Hydrodynamic form of Maxwell’s equations

)()()()( rrrvrv QV

Vortex generates a velocity field:



Energy flows in plasmonic nanostructures

Surface plasmon polariton wave:

Stockman’s nanolens:

Li, K., M.I. Stockman, & D.J. Bergman, Phys. Rev. Lett., 2003. 91(22): p. 227402.

S.V. Boriskina & Reinhard, Nanoscale, 4, 76-90, 2012

http://www.youtube.com/watch?feature=player_embedded&v=yJ8enHiq0H4


Magnetic SP effects

t HE

Plasmonic nanostructures built from nonmagnetic materials can exhibit effective magnetic permeability

Image: http://www.ndt-ed.org/

coil magnet

rotating currents in the rings induce magnetic flux

effective permeability

Split-ring resonator:

Pendry, J.B. et al, IEEE Trans. Microw. Theory Tech., 47(11), p.2075, 1999

double-negative metamaterials

Shelby, R.A., et al Science, 2001. 292(5514): p. 77-79.


Magnetic SP effects in nanoparticle clusters t HE

Liu, N., et al., Nano Letters, 2011. 12(1): p. 364-369.

charge density:

induced magnetic moments:

Anti-ferromagnetic response:

dy

yz

x

dx

2r

Ag

E

k

dy

yz

x

yz

x

dx

2r

Ag

E

k

E

kElectric field intensity:

Magnetic field distribution: S.V. Boriskina, in Plasmonics in metal nanostructures: Theory & applications ( Shahbazyan & Stockman eds.) Springer, 2012

Magnetic dipole

Fan, J.A., et al. Science, 2010. 328(5982): p. 1135-1138.


Thermal SP effects

Electric field to heat:

),(),(~ tttT rErj

dissipation of optical energy

temperature

nanopatterning

Atanasov, P.A., et al., Int. J. Nanopart. 2010. 3(3): p. 206-219.

cancer treatment

Chen, J., et al. Small, 2010. 6(7): p. 811-817.

Govorov A.O. & Richardson, Nano Today, 2007. 2(1) 30-38


Thermal SP effects Heat to electric field:

V

dGi '),'(),',(),( 0 xxjxxrE

fluctuating currents

~ DOS

Near-field heat transfer:

e.g., Narayanaswamy, A. & G. Chen, Appl. Phys. Lett. 2003. 82(20): p. 3544-3546; Fu, C.J. & W.C. Tan, J. Quant. Spectr. Radiat. Transf. 2009. 110(12): p. 1027-1036; Rousseau, E., et al. Nat Photon, 2009. 3(9): p. 514-517; Volokitin, A.I. & B.N.J. Persson. Rev. Mod. Phys., 2007. 79(4): p. 1291-1329

(cold, T2)

(hot, T1)

High SPP-induced DOS results in the near-field coherence

d


Plasmonic photosensitization of semiconductors

• hot electrons can tunnel from metal nanoantennas into semiconductor

• photon detection at energies below the semiconductor band gap

Knight, M.W., et al., Science. 332(6030): p. 702-704.

Theoretical prediction: Shalaev, V.M., et al., Phys. Rev. B, 1996. 53(17): p. 11388-11402.


Plasmonic enhancement of photocurrent

Mubeen, S., et al., Nano Letters. 11(12): p. 5548-5552.

Xu, G., et al (2012), Adv. Mater., 24: OP71–OP76

Echtermeyer, T.J., et al. 2012,

Nature Commun. 2: p. 458.

in silicon:

in graphene:


Books & review articles on plasmonics:

• Lal, S., S. Link, and N.J. Halas, Nano-optics from sensing to waveguiding. Nat Photon, 2007. 1(11): p. 641-648

• Halas, N.J., et al., Plasmons in strongly coupled metallic nanostructures. Chem. Rev., 2011. 111(6): p. 3913-3961

• Schuller, J.A., et al., Plasmonics for extreme light concentration and manipulation. Nature Mater., 2010. 9(3): p. 193-204

• Stockman, M.I., Nanoplasmonics: past, present, and glimpse into future. Opt. Express. 2011, 19(22): p. 22029-22106

• Maier, SA, Plasmonics: Fundamentals and Applications, Springer, NY, 2007

• Novotny, L., and B. Hecht. Principles of Nano-Optics, Cambridge University Press, 2006

This list is by no means complete …


Commercial & free software

• Lumerical FDTD Solutions

http://www.lumerical.com/tcad-products/fdtd/

• COMSOL Multiphysics® (FEM)

http://www.comsol.com/products/multiphysics/

• MEEP (FDTD)

http://ab-initio.mit.edu/wiki/index.php/Meep

• DDSCAT (discrete dipole approximation)

http://www.astro.princeton.edu/~draine/DDSCAT.html

• A collection of free software (including Mie theory methods)

http://www.scattport.org/index.php/light-scattering-software


Topics I had to omit due to the lack of time

Plasmonic cloaking: New Journal of Physics, Focus Issue on 'Cloaking and Transformation Optics', Guest Editors: Ulf Leonhardt and David R. Smith, Vol. 10, Nov 2008.

Non-local response: A.D. Boardman, Electromagnetic Surface Modes, Ch. Hydrodynamic Theory of Plasmon–polaritons on Plane Surfaces, John Wiley & Sons Ltd., 1982.

Resonant energy transfer & ‘dark’ plasmonic nanocircuits: Andrew, P. and W.L. Barnes, Energy Transfer Across a Metal Film Mediated by Surface Plasmon Polaritons. Science, 2004. 306(5698): p. 1002-1005

Akimov, A.V., et al., Generation of single optical plasmons in metallic nanowires coupled to quantum dots. Nature, 2007. 450(7168): p. 402-406.

Boriskina, S.V. and B.M. Reinhard, Spectrally and spatially configurable superlenses for optoplasmonic nanocircuits. Proc. Natl. Acad. Sci. USA, 2011. 108(8): p. 3147-3151.

Spasers: Stockman, M.I., Spasers explained. Nat Photon, 2008. 2(6): p. 327-329.

Plasmonic particles on demand: Luther, J.M., et al., Localized surface plasmon resonances arising from free carriers in doped quantum dots. Nat Mater, 2011. 10(5): p. 361-366.

finally, Metamaterials is a huge area in itself – could be a separate class

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