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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
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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)
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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
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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
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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
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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
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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
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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
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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
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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 =
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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
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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)
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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
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visibleUV near infrared mid infrared far infrared
Spectral Range of Nanoshells
cosmetics& pigments
solar energy applications
biotechnology
night vision, surveillance
photonics & telecom
environmentalsensing
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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)
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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->
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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
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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:
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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
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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
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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.
.
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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)
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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!
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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)]
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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
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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
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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
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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-
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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
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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
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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
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Nanoshell defects: Single Bump and crater
Very small change in the FAR FIELDextinction spectra
Increased field enhancements
FDTD Calculations
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Near Field of a nanoshell with bump and crater defects
k
E
Pulse Polarization
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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
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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
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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
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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%
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Ellipsoidal Near Field
k
E
Pulse Polarization
a) Ellipsoid perpendicular to fieldMaximum Enhancement 9
b) Ellipsoid aligned with fieldMaximum Enhancement 14
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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.
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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
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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
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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
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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
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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
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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
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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)
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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
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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
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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
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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
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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
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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