Plasmons in metallodielectric nanostructures

Peter NordlanderDepartment of Physics and Rice Quantum Institute

Rice University, Houston TX, USA

Work supported by the Army Research Office (MURI), NSF, TATP and the Robert A. Welch

Foundation

OutlineIntroductionFDTD simulationsTDLDA calculationsPlasmon hybridization

NanoshellsNanoparticle dimersNanoparticle on surface

Conclusions and references

RICELaboratory forLaboratory forNanophotonicsNanophotonics

LANPLANP

Surface Enhanced Raman Scattering (SERS)

By placing a molecule on a metal surface, the Raman intensity can be increased by ~106

Surface plasmons are responsible for the electric field enhancements! (R. P. Van Duyne et Al, 1977)

An incident photon is inelastically scattered leaving the molecule in a vibrationally excited state

Ground state vibrational manifold

Virtual or real level

anti-Stokes Stokes

Probability for Raman scattering is proportional to the fourth power of the electric fields across the molecule,i.e., E2(hν )*E2(hν ± hν’)

hν ± hν’

S

NH2

hν

Metal SurfaceS

NH2

S

NH2

S

NH2

Using nanoparticles and nanoparticle aggregate plasmons, one can get enhancements >1014

enabling single molecule spectroscopy (1996-1999)

Single molecule spectroscopies and microscopy

The electromagnetic field enhancements on nanoparticlesurfaces are caused by the excitation of plasmons.

The plasmons induce a large E&M near-field of a frequencyequal to the plasmon energy. This field enhances cross sections!

Ultraefficient chemical, biological sensing and microscopy

Theoretical Challenges

1) To identify which microscopic properties of nanostructures determine their plasmon energies! Different molecules require different excitation frequencies! How do we design plasmonicnanostructures with specific plasmon energies?

2) To identify which properties influence EM field enhancements.

Physical mechanism

Plasmons

A plasmon is an incompressible self oscillation of the conduction electrons

Bulk plasmon: The rigid displacement of the electronsinduces a dipole moment and an electricfield opposing the displacement.

)(4)()( 222

2

tentenEtdtdnme δπδ −=−= => H.O.

eB m

ne24πω =

------

++++++

δ(t)E(t)Electron density Newton’s equation for δ(t):

Metal = ions + electron gaselectron gas

Since all electrons of the nanoparticle is involved in oscillation, plasmons can interact strongly with light of the right frequency.

Electron density at the surface of the nanoparticle can induce largelocal electric fields of frequency ωB

FDTD Simulations of the E&M properties of nanostructures

Before( )Ω,kS

Incoming Plane WaveAfter

++

++

+-

+++

+

----

- -

--

Plasmons

Induced Fields

• The Finite Difference Time Domain method is a time marching algorithm which solves Maxwell’s equations in time and space for arbitrarynanostructures.

• Fully retarded • FDTD provides a “one size fits all” solution for studying the electromagnetic

responses of complex systems ranging in sizes from nanoshells toautomobiles.

• The Rice FDTD code is fully parallelized

Parallelizability• Local nature of FDTD

allows for easy distributed memory parallelization

– Job Specs• 100+ Gigabytes• 100+ Nodes• Run time from 1 to 4 days• Grid Sizes up to 10003 (to fit in 100 GB)• 97% parallelized

Single nanosphere in CW E&M field

Finite Difference Time Domain (FDTD) simulations

Instantaneous EZ component of E-field

Large electric field enhancement near the poles of the sphere!This is caused by the excitation of the dipolar plasmonFocusing into region much smaller than the wavelength of the light!

E

Bz

k

Incident plane wave with wavelength λ=475nm tuned to the dipolar plasmon energy

Au sphere withD=60nm

Nanosphere dimer in CW E&M field

E field is enormously enhanced in the junctionbetween the two nanospheres.

Instantaneous EZ component of E-field

E

Bz

k

Incident plane wave with wavelength λ=475nm. Diameter of the Au spheres D=60nm and separation DD=3nm

Spectral dependence

Spectral resolution is obtained by studying the responseto a a pulse containing many frequencies

When the pulse hits the dimer, many different dimerplasmons are excited!

Near and Far-field responseis obtained using FFT

Au (42,60)nm DD=2nm

E

Bz

k

Instantaneous EZ component of E-field

Extinction X-section (Scaled)

Enhancement at

Nanoshell Near Field Enhancement

Broad Tail

Ag(39,48)nmEnhancement at 542.2 nm

k

E

Pulse Polarization

lenanopartic without field Electriclenanopartic of presence in the field ElectrictEnhancemen =

Dimer Near Field Enhancement

Electric field enhancementsAg(39,48) dimer, DD=1.5nm at 718nm

Extinction X-section (Scaled)

Enhancement in center of dimer

Broad tail

k

E

Pulse Polarization

Single Shell EnhancementAverage enhancement of ~

250 over a 34 nm3 region between the shells!

Large enhancement over wide range of wavelengths!

Symmetric dimer plasmon

The plasmon energies of a nanoparticle depend on its shape!

eB m

ne24πω =

2B

surfωω =

12, +=

ll

BlS ωω

Surface:

Sphere:

Bulk:

Nanoshell:

a

b

Cavity:12

1, +

+=

ll

BlC ωω

Plasmon energies of a nanoshell can be

tuned!!!

++

+±= +

±12

22 )1(41

1211

2lB

l xlll

ωω

bax =

The plasmon energies of a nanoshelldepends on the aspect ratio x

Geometry is denoted (a,b)

Synthesis of Silica core-Gold shell Nanoshells30 nm

NanoshellsNanoparticle consisting of a metallic shell (Au, Ag, Ni..)

around a dielectric core

(N.J. Halas, Rice University 1997)

Nanoshells can be fabricated with differentdielectric cores and different metallic shells.

The core radius and the shell thicknesscan be controlled within a few percent

Experimentally realizable size ranges:core sizes: 5-500 nm

shell thickness: 1-100 nm

visibleUV near infrared mid infrared far infrared

Spectral Range of Nanoshells

cosmetics& pigments

solar energy applications

biotechnology

night vision, surveillance

photonics & telecom

environmentalsensing

Comparing Nanoshells to Quantum Dots:Comparing Nanoshells to Quantum Dots:

Quantum Dots:tunable excitonic nanoparticles

~1-10 nm diameterQuantum efficiencies ~ 0.1-0.5

Spectral range (emission): 400-2000 nmCross sections:

~10-19 m2

NanoshellsNanoshells:tunable tunable plasmonic nanoparticlesnanoparticles

~10-300 nm diameterQuantum efficienciesQuantum efficiencies ~10-4

Spectral range (extinction):Spectral range (extinction):500(Ag)-9000 nmCross sectionsCross sections:

~10~10--1313 mm22

Nanoshells (Halas Group)

Photo by Corey Radloff

Photo by Colleen Nehl(Hafner Group)

50 nm

Halas Group (photo by Corey Radloff)

Anti-symmetric plasmon “Cavity plasmon like”

= +3B

Sωω = BC ωω

32

=a

b

Symmetric plasmon “Sphere plasmon like”

++

++

--

-

+

+

-

+

- +

-+- -

Physical origin of the tunability of nanoshell plasmons

-+

+

--

+

- +

-+- -

++

Hybridization between the cavity and sphere plasmons

|C>

|S>

|N+>

|N->

Incompressible fluid model

η∇=),( trv 02 =∇ η

Plasmons are incompressible irrotational deformations of the electron liquid

In a spherical shell with inner radius a and outer radius b, thescalar potential takes the form

The deformation fields can be written in terms of a scalar potential

where

)()(11)(1

),,( 121

12

Ω

+

+=Ω ∑ ++

+

lmlm

llmlllm

l

YrtSlbr

tClatrη

Cavity plasmon Sphere plasmon

The kinetic and Coulomb energy can be expressed in terms of η

Plasmon Lagrangian

][2

22,

2

1

0lmlSlm

l

eS SSmnL ω−= ∑

∞

=

][2

22,

0

20lmlC

llm

eC CCmnL ω−= ∑

∞

= 121

, ++

=l

lBlC ωω

2b

2a

12, +=

ll

BlS ωω

++

+±= +

±12

22 )1(41

1211

2lB

l xlll

ωω

For each l and m, the interaction results in two plasmon modes

N- and N+ with energies:

])[1( 212

,,,

012

lmlm

l

lSlCml

eSCl

NS SCxmnLLxL+

+ ∑++−= ωω

The Lagrangian for the plasmons can be written in terms of C and S

SlmClm

x=a/b

lmlmllmlm CosSSinCN ξξ −=+

lmlmllmlm SinSCosCN ξξ +=−

212

2,

2,,tan

+

+ −=

l

lCl

lSlCl x

ωωωω

ξ

(Antiparallel alignment of multipoles)

(Parallel alignment of multipoles)

Interaction term

The interacting plasmon modes can be expressed as:

Tunability of Nanoshells

Thick shell => weak interaction:

=±→ →

±S

CBx

ωωωω

311

20

1

Thin shell => strong interaction:

∆−== 1bax

Sω

+ω

Cω

−ωThe ω- plasmon can be tuned

from far IR to UV

∆→ →∆±

32

01

B

B

ω

ωω

Sω

+ω

−ω

Cω

where

Analogy with molecular orbital theory provides simpleand intuitive understanding of plasmons in composite nanoparticles.

The coupling to light is proportional to the admixture of the |S> plasmon

TDLDA originally introduced for the calculation of optical properties of atoms (Zangwill & Soven 1980)

Many successful applications to atoms, molecules, clusters, nanoparticles, surfaces and solids

Method consists of:

1) Calculation of the electronic structure using the Local Density Approximation (LDA)

2) Calculation of the frequency dependent dielectric function using the Random Phase Approximation (RPA)

Time Dependent Local Density Approximation TDLDA

Efficient implementation on beowulf cluster allows system with morethan a million electrons to be modeled

The jellium model (# of electrons: ~106) Excellent description of conduction electrons in solids

aa/2

VB

The jellium is specified by: VB (Background potential) and

rS (Wigner Seitz radius) where

Electron-electron potential is calculated self-consistently.

1nπr34 3

s =

rW=5.4 eV

a b

rs=3 (a.u.)

VB

VC

Dielectric backgrounds can be introduced, i.e. dielectric core εC, d-electrons in the metallic shell ε(∞),and dielectric embedding medium εE.

.

2 0 4 0 6 0 8 0 1 0 0

0 . 0

0 . 4

0 . 8

1 . 2

r ( a . u . )0 2 0 4 0 6 0

0

4

8

1 2

Elec

tron

dens

ity (1

0-3 a

.u.)

r ( a . u . )

0 2 0 4 0 6 0- 0 . 5

- 0 . 4

- 0 . 3

- 0 . 2

- 0 . 1

0 . 0

0 . 1

V eff (H

artre

e)

r ( a . u . )2 0 4 0 6 0 8 0 1 0 0

- 0 . 5

- 0 . 4

- 0 . 3

- 0 . 2

- 0 . 1

0 . 0

0 . 1

r ( a . u . )

(20,40)a.u.

(40,80)a.u.

Calculated electron density distribution

Friedel oscillations at the surfaces of the nanoshellThese will influence the optical response!!!

(40,80)a.u.

(20,40)a.u.

Calculated electron potential V(r)

Density of states

- 0 .4 - 0 .3 - 0 .2 - 0 .1 0 .00

1 x 1 0 5

2 x 1 0 5

3 x 1 0 5

DO

S

E n e r g y ( H )

Shell: (55,95)a.u.

εF

Nanoshell DOS (0.007Ha)Bulk DOS (rS=3)

- 0 . 4 - 0 . 3 - 0 . 2 - 0 . 10

2 0

4 0

6 0

8 0

1 0 0

1 2 0

1 4 0

1 6 0

DO

S

E n e r g y ( H a r t r e e )- 0 . 4 - 0 . 3 - 0 . 2 - 0 . 10

5 0

1 0 0

1 5 0

2 0 0

2 5 0

3 0 0

E n e r g y ( H a r t r e e )

Quantum size effects!

(20,40) a.u. (40,80) a.u.

DOS is bulk-like!

Size effects

0 2 4 6 8 1 01 0 2

1 0 3

1 0 4

1 0 5

1 0 6

1 0 7

1 0 8

(76.5,127.5)a.u.

(51,85)a.u.

(25.5,42.5)a.u.

x=a/b=0.6

Mie scattering predicts no size dependence for small nanoshells with same aspect ratio

TDLDA calculation reveals a size dependent redshift of ω+ and ω-

This could be caused by a size dependent electron density profile at the nanoshell surfaces.

Electron spillout lowers the “effective” density and plasmon energy

1−∝∆ RSω

Im[α

(ω)]

0 2 4 6 8 1 01 0 3

1 0 4

1 0 5

1 0 6

1 0 7

1 0 8

Im α

(a.u

.)

h ν (e V )

1 2 3

Plasmon lineshapes and lifetimesElectronic structure relatively unaffected by dielectric media

Energy of plasmon resonances depend strongly on dielectric media

When the plasmon energy becomes resonant with single particle excitations => Broadening and splitting of the plasmon absorption peak

(77,96)a.u

Quantum effects: Strong sensitivity of plasmon widths to the environmentcaused by plasmon- electron hole pair (exciton) coupling

εC=1, εE=1εC=5.4, εE=1εC=5.4, εE=1.7

εC=5.4, εE=3.0

Structural tunability of nanoshells

0 2 4 6 8 10

Pol

ariz

abilit

y

Photon energy (eV)

0.6 0.7 0.8 0.9 1.00

2

4

6

8

10

Plasmon hybridizationTDLDA

Ro

Ri

Pla

smon

Ene

rgy

(eV

)

ω-

ω+

Ri/ R

o

(a,b) a.u.

(323,340)(210,227)(153,170)(96,113)(68,85)(51,68)(41,58)(32,49)(26,43) Tunability

Excellent agreement between TDLDA and plasmon hybridization

for ω+ and ω- modes

Single particleexcitations

ω+ω-

ωB

The structures aroundωB are caused by theFriedel oscillations atthe nanoshell surfaces

400 500 600 700 800 900 1000 1100

0.0

0.4

0.8

1.2

1.6Ab

sorb

ance

λ (nm)

0.0

0.4

0.8

1.2

0.0

0.4

0.8

Comparison with experiment: Gold nanoshell with Au2S core in water

8)(,7.1,4.5 =∞== εεε ECAveritt et al. PRL78(1997)4217

(4.1,5.1)nm

(8.6,9.9)nm

(13.1,14.8)nm

Experiment

Solid gold colloid

TDLDA

Calculated energies of the Plasmon resonances in excellentagreement with the experiments!=> rs =3 is a good choice

Calculated widths smallerthan the experimental data!Inhomogeneous size distribution?

Snapshots of optical absorptionof Au2S nanoshells during growth

400 500 600 700 800 900 1000

0.0

0.2

0.4

0.6

0.8

Abs

orba

nce

Abs

orba

nce

λ (nm)

0.0

0.2

0.4

0.6

0.8

1.0(a,b)=(4.1,5.1)nm(a,1.0275b)(a,1.055b)(a,1.0825b)(a,1.11b)

Comparison with experiment: Effect of size distribution

( ))()I(

22 2/1ωω

σ

X

XIedX

−−

∫∝

11.0=σ

Solid: Experimental dataRed: Size averaged spectrum

Widths in good agreementwith experimental data

Quantum effects introducea strong size dependenceof the plasmon peak

Size averaging: (a,X*b)

Averitt, Sarkar and Halas, PRL78(1997)4217

ω-

Plasmon Hybridization with dielectric media present

The plasmon energies are strongly influenced by dielectric screening when BOTH a dielectric core

and embedding medium are present.

a A qualitative understanding of the effectsof dielectrics on the plasmon resonancescan be obtained from ωC(εC) and ωS(εE)

1)1(1)(, ++

+=

CBClC l

lε

ωεω2a

)1()(, ++=

lll

EBElS ε

ωεω

Dielectric core εCinfluences ωC

Dielectric embedding medium εEinfluences ωS

2b

Physical understanding of the effects of dielectric background media

Dielectric core Embedding medium

0

2

4

6

8TDDFTTDDFT

Im α

(107 a

.u.)

0

1

2

3

Strongest influence on Spectral weight increases with dielectric constant

Strongest influence on Spectral weight increases with dielectric constant

+ω −ω

+ω

sω

Cω

−ω

Sω

Cω+ω

−ω

3

1

=

=

ε 2

=

4=ε

ε

ε

4 6 8hν (eV)

4 6 8hν (eV)

TDLDA TDLDA

Effect of polarizability of d-electronsThe d-electron of the metal ion cores contribute to the polarizabilityof the positive background, 1)()()( −+= −− ωεωεωε eldelcAu

In the frequency interval of interest for Au 8)()( =∞==− εωε consteld

The background dielectric will redshift the plasmon energies

)()1(1,

)()1( ∞+++

=∞++

=εε

ωωεε

ωωlll

lll

CBC

EBS

The effect of the d-electronsare strongest for |C>

Redshift

|S>

|C>|+>

|->2 3 4 5 6 7 8 9

0.0

0.4

0.8

1.2

1.6

εC=1, εE=1, εC=1, εE=1,

Abs

orba

nce

hν (eV)

ε(∞)=1ε(∞)=8

(60,90) a.uTDLDA

Nanoshell defects: Single Bump and crater

Very small change in the FAR FIELDextinction spectra

Increased field enhancements

FDTD Calculations

Near Field of a nanoshell with bump and crater defects

k

E

Pulse Polarization

Nanoshell defects: bumps and cratersSmall bumps: Minimal change

Large bumps:Red shift from hybridization of bump and nanoshell plasmons. Blue shift from shell thickening=> small shift

Large craters:Monotonous strong red shift from hybridization AND shell thinning

NSω defectω

Near Field of a bumpy Nanoshell

Maximum field enhancements on top of the bumbs ~150

The aspect ratio of the nanoshelldetermines the plasmon energy

The defects enhances the electricfields from the nanoshell plasmon

Near Field of a Nanoshell with deep craters

(92,128) Gold Nanoshell at 907 nm

82% of Gold Etched away

Maximum field enhancementat the edges of the craters ~250

Nanoshell defects: Ellipsoidal Shells

• Shift depends on polarization• Blueshift along short axis• Redshift along long axis• Mixture of 12.5% ellipsoids

would broaden peak by 20%

Ellipsoidal Near Field

k

E

Pulse Polarization

a) Ellipsoid perpendicular to fieldMaximum Enhancement 9

b) Ellipsoid aligned with fieldMaximum Enhancement 14

Nanoshell defects: Offset Cores

• Simple model of a nanoshellwith nonuniform shell thickness

• Lack of symmetry causes coupling of cavity and sphere plasmons of different angular momentum

• Many plasmons will be dipole active.

Near Field of a nanoshell with offset core

k

E

Pulse Polarization

1.5 nm 4.5 nm 7.5 nm

Maximum Enhancements• 9• 20• 50

Concentric nanoshells (Nanomatrushkas)

−+ω

+−ω

Plasmon Hamiltonian can be written in terms of individual nanoshell plasmons

|C1>

|C2>

|S1> |S2>

|Ν1+ >

|Ν1− > |Ν2

− >

|Ν2+ >

1 2

−−ω

The “bonding-bonding” plasmon can be shifted far into the IR−−ω

++ω

Plasmon hybridization for a nanomatrushka

212

12

2

12,1,

122

1210

21

)1)(1( lmlm

l

CSll

lmeInt

IntNSNSNM

CSabxxmnV

VLLL+

++

−−=

−+=

∑ ωω

The interaction term is written in terms of the individual nanoshell plasmons N+ and N-

))(( 2222111121 ξξξξ CosNSinNSinNCosNCS −+−+ ++−=

The plasmons on each shell interact with both plasmonson the other shell

The Lagrangian:

(Antiparallel alignment)

(Parallel alignment)

Energy levels Optical absorption

Nanomatrushka: Experiment-Theory comparison

(80,107), (135,157)nmStrong interaction: Thin spacer andω1

- similar to ω2-

(77,102), (141,145)nmWeak interaction: thicker spacer and ω1

- different from ω2-

(396,418), (654,693)nmVery weak interaction: Thick spacer andω1

- different from ω2-

Experiment

Theory

Plasmon Lagrangian for dimer

][2

22,

2

,lmlSlm

ml

eS SSnmL ω−= ∑

∞

)(21 DVLLL IntSSDimer ++=

∑ Ω=Ωml

lmlm YtSRlent

,30 )()(),(σ

12, +=

ll

BlS ωω

The Lagrangian for the plasmons in an individual sphere is

For two interacting spheres:

∫ ∫ −ΩΩ

ΩΩ=||

)()()(21

212

221

21 rr

dRdRDV Int σσ

∑

−−=

jiji

mji

Bijiii

em SSDVSSmnL,

)(,

22220)( )(

4)(

2 πωδω

∫ ++

+= )(

)()12())((

4)( 112)(

, jm

lj

lii

jim

ljjj

liji

mji CosP

XlCosP

SindRRllDVji

ii θθ

θθθθπ

Coulomb interaction:

The surface charge of each plasmon mode:

Plasmons with different m do not interact.

Interaction only between plasmons on different particles

Solid sphere dimers

12 +=

ll

Bl ωω

Plasmon hybridization

l=1

l=2

Au(10nm) m=0

l=1

l=2

l=1

l=2 l=2

l=1

l=3 l=3

D

Z-axis

For small D, plasmons with different l start to mix resulting in extra redshift of

the low l plasmons

Au(10nm) m=1

Bright

Dark

Dark

Bright

weaker interactions for m=1The mixing with higher l modesresults in strong increase ofEM field enhancement

Extinction spectra of homo dimer as a function of D

The mixing between thedifferent angular momentum modesresults in l=1 presence in all dimermodes

For a small dimer, only dipole-active modes can be excited

Dark lines: FDTD (Drude with broadening)Red symbols: Plasmon hybridization

Only bright plasmons have finite dipolemoment

Excellent agreement between FDTD andThe plasmon hybridization approach

Dimer plasmon energiesExtinction spectra forD indicated by arrows

Au(10nm)

Solid sphere heterodimers

12 +=

ll

Bl ωω

Plasmon hybridizationl=1l=2

Au(10-9nm) m=0

l=1

l=2 l=2

l=1

l=3 l=3

D

Z-axis

For heterodimers, there are avoided crossings. Both the symmetric and

antisymmetric plasmon modes have dipole moment at small D

Au(10-7nm) m=0

l=1

l=2

Extinction spectra of heterodimer as a function of D

Dark lines: FDTD (Drude with broadening)Red symbols: Plasmon hybridization

Only dipole active modes can be seenfor the present small dimer

The mixing between the different angular momentum modes results in l=1 presence in all dimer modes

For a heterodimer, all modes have a finite dipole moment

Excellent agreement between FDTD andThe plasmon hybridization approach

Dimer plasmon energiesExtinction spectra forD indicated by arrows

Nanoshell dimers

++

+±= +

±12

22 )1(41

1211

2lB

l xlll

ωω

dd

Au(8,10)nm m=0

At small separation hybridization with larger l plasmons results in redshift

l=1

l=1

l=2

l=2

l=1

l=1

l=3l=2

l=2l=3

Au(8,10)nm m=1

Plasmon Lagrangian for nanoparticle on a semi infinite surface

L=LNP+Lsurf-VI

[ ]∑ ⋅=k

ksurf kzkitP

Atr ]exp[exp)(1),( ρη

[ ]2

,|)(||)(|12

2220 Bsp

kkspk

esurf tPtPkA

mnL ωωω =−= ∑

12],[

2 ,22

,2

1

0

+=−= ∑

∞

= llSSmnL BlSlmlSlm

l

eNP ωωω

)()(2 ΩΦΩΩ= ∫∑∑ klmlmk

I dRV σ

∑ Ω=ml

lml

lmNP YrtStr

,)()(),(η

Z

2R

Solid sphere on surface

Z

D

The surface induces hybridization of nanosphere plasmons of different l

(Dark)

(Bright)

D=10nm

Strong redshiftof the dipolarplasmon with decreasing Z

31

1, BS ωω =

2B

Surfωω =

52

2, BS ωω =

Classical Image model (infinite ωsurf)

Plasmon hybridization (finite ωsurf)

A classical image model does not provide correctdescription of the plasmons of a nanoparticle interacting with a realistic metallic surface

Conclusions

• Simple conceptual approach for understanding plasmon resonances in complex nanoparticles and nanostructures

• Results from plasmon hybridization in perfect agreement with classical Mie theory and FDTD and TDLDA

Plasmon hybridization

FDTD• Efficient parallizable code for the calculation of EM properties of

nanostructures of arbitrary symmetry

ReferencesE. Prodan and P. Nordlander, CPL 349(2001)153, CPL 352(2002)140,

Nano Letters 4(2003)543-547E. Prodan, A. Lee, P. Nordlander, CPL 360(2002)325

P. Nordlander and E. Prodan, Proc. SPIE 4810(2002)94, SPIE5221(2003)151-164E. Prodan, P. Nordlander and N.J. Halas, CPL 368(2002)94,

Nano Letters 4(2003)1411-1415E. Prodan, C. Radloff, N.J. Halas and P. Nordlander, Science 302(2003)419-422

C. Oubre and P. Nordlander, Proc. SPIE 5221(2003)133-143E. Prodan and P. Nordlander JCP 120(2004) 5444-5454

P. Nordlander et Al., Nano Letters 4(2004)899-903

Plasmons can be used to manipulate E&M field on nm length scales