05SurfacePlasmons.ppt

Surface plasmons: outline
1. Time-line of major discoveries
2. Surface plasmons - surface mode of
electromagnetic waves on a metal
surface
3. Spectroscopy of SPs in nanostructures:
(a) Nanoparticles
(b) Gratings, nanostructures
4. Applications: sensors, nanophotonics,
surface enhanced Raman spectroscopy
(SERS)
Surface plasmons, A. Kolomenski, S. Peng, 9/24/2012

Time line
Excitation of SPs with a
prism: Raether, Kretschmann
1941
1907
Rayleigh’s explanation (angle-
diffraction orders)
1993-
Fano: role of surface
waves, surface plasmons
1968
1991
1902 Wood anomalies: reflection
on gratings (two types)
Nanoplasmonics, extraordinary
transmission, etc.
First biosensor on SPs
SPs allow to localize and guide
EM waves!!!
1974 Surface Enhaced Raman Spectroscopy

Maxwell’s equations (SI units) in a material,
differential form
density of charges
density of current
f

f
J

Wave equation
2 2
( ) ( )
B B B B
   
          
2
2 2 2
1 1
( ) ( ) ( )
B
E E B
t t t t
c c t

  
    
        
    

2
2
2 2
1
0
B
B
c t

 
  

2
2
2 2
1
0
E
E
c t

 
  

0
Double vector product rule is used
a x b x c = (ac) b - (ab) c

Plane waves
0 [ ( )]
B B Exp i k r t

   
  
)]
(
[
0 t
r
k
i
Exp
E
E 







B i k B
  
  
E i k E
  
  
is parallel to
is parallel to B
E

Thus, we seek the
solutions of the form:
From Maxwell’s equations
one can see that k

B

E


Incident light
Simple system of a metal bordering a
dielectric with incident plane wave
Dielectric, refractive index
is dielectric permittivity
Metal (gold)
2
n 

2

1 r im
i
  
 
Reflected light
Transmitted light
Surface plasmons, A. Kolomenski, S. Peng,
9/24/2012

Waves at the interface
Assume that incident light is p-polarized, which means that the E-vector is
parallel to the incidence plane
)]
(
[
)
,
0
,
( 1
1
1
1
1 t
z
k
x
k
i
Exp
E
E
E z
x
z
x 




1 1 1 1
(0, ,0) [ ( )]
y x z
B B Exp i k x k z t


  
Then the vector of the magnetic field is perpendicular to the incidence plane and
has the form
In medium 1, z<0,
2
1
2
2
1
2
1
c
k
k z
x



In medium 2, z>0, 2
2
2
2
2
2
2
c
k
k z
x



2 2 2 2
(0, ,0) [ ( )]
y x z
B B Exp i k x k z t


  
)]
(
[
)
,
0
,
( 2
2
2
2
2 t
z
k
x
k
i
Exp
E
E
E z
x
z
x 




x
y
z
1
E

x
1x
E
1z
E
9/24/2012

Boundary conditions
x
x E
E 2
1 
1 1 2 2 1 2
/ / , . .
y y y y
B B i e H H
 
 
1 1 2 2
z z
E E
 

1 1 1 2 2 2 1 1 1 2 2
1 2
( / ) / / ( / / ) ( / ) 0
t y y t
l l
E
B dl B dl B dl l B B B ds ds
t
      

        
    

1 1 2 1 1 1 2 2
1 2
( ) ( ) 0
z z
S S S V
Eds E ds E ds S E E E dv
    
       
   
1 1 2 2 1 1 2
1 2
( ) 0
i
x x i
l l
B
Edl E dl E dl l E E Eds ds
t

         
    

Gauss’s theorem
Stokes's theorem
Stokes's theorem
x
y
z dl
0
s 
0
s 
0
V  
9/24/2012

Relations in an E-M wave
 the curl operator
ˆ ˆ ˆ
x y z
x y z
A
x y z
A A A
   
 
  
( ) ( ) ( )
x y z x
Exp ikr Exp ik x ik y ik z ik Exp ikr
x x
 
   
 
[ ]
i k E i B

  
[ / ]
i k B i E
 
   
1 1
[ / ] ( )
z y
x x y z z y
k B
E k B k B k B

  
      
9/24/2012

Derivation of the dispersion equation
x
x E
E 2
1 
From the other condition =>
1 2
1 2
1 2
z z
y y
k k
H H
 

y
y H
H 2
1 
One boundary condition is
Therefore we have a system of 2 homogeneous equations and
a nontrivial solution is possible only if the determinant of this
system is equal to 0.
0
1
1
2
2
1
1
2
2
1
1
0 









z
z
z
z
k
k
k
k
D
0
0
2
2
2
1
1
1
2
1




y
z
y
z
y
y
H
k
H
k
H
H


Assume no external currents or free charges, magnetic permeability.
1 2 0
  
 
9/24/2012

Surface plasmon dispersion equation
1 2
1 2
z z
k k
 

)
(
)
( 2
1
2
2
2
2
2
2
2
2
2
1 k
c
k
c


 





We square both sides
2
1
2
1
2
2
2







c
k
We introduce , wavenumber of the surface plasmon, then we obtain
x
k
k 
2
2 2 2 2 2
2 1 2 1 1 2 2
( ) ( )
k
c

     
   

Dispersion equation and properties of
surface plasmons
We would like to have a solution which is localized to the surface, i.e. it
decays with distance from on both sides from the interface.
0
]
[ 1 
 
 

z
z z
ik
Exp
0
]
[ 2 
 
 

z
z z
ik
Exp
This is possible, if
0
, 1
1
2
2
2
2
1 



 q
iq
k
c
k z 

0
, 2
2
2
1
2
2
2 


 q
iq
k
c
k z 

1 1 1
[ ] [ ( )] [ ] 0
z
z
Exp ik z Exp i iq z Exp q z

   

Indeed, then we have waves localized near the interface
2 1 1
[ ] [ ( )] [ ] 0
z
z
Exp ik z Exp i iq z Exp q z

   


Dispersion equation analysis
1 2
1 2
z z
k k
 
  1 2
1 2
1 2
, 0
q q
and q q
 

 
This is only possible, if 1 2
0 0
or
 
  
2
1
2
1
2
2
2







c
k
If we look again at the dispersion equation
,k must be real (propagating wave!), then with
negative, we see that the condition for surface waves to exist is
1 2
0 0
or
 
 
1 2
0 0 ( )
and dielectric
 
 
1 2 1 2
0, . .
i e
   
   

Relation of Plasmonics to SOME other fields
Metamaterials
Plasmonics
Nanotechnology
Optics
Biotechnology
SERS
High harmonics generator
coherent control
imaging
Electronics
Opto-electronics
molecular interactions
nano-sensors
proteomics
nanostructures
nanophotonics
nanoantennas

The Growth of the Field of Surface Plasmons
PIETER G. KIK and MARK L. BRONGERSMA SURFACE PLASMON NANOPHOTONICS, (2007)
illustrated by the
number of scientific
articles published
annually containing
the phrase “surface
plasmon” in either
the title or abstract

Surface plasmons (or surface plasmon
polaritons), Part 2: outline
1. Why SP named so?
2. Excitation of SPs: with a prism or a
grating
3. Spectroscopy of SPs in nanostructures:
(a) Nanoparticles
(b) Gratings, nanostructures
4. Applications: sensors, nanophotonics,
surface enhanced Raman spectroscopy
(SERS)
Surface Plasmons, Part 2, A. Kolomenski, 9/26/2012

Dielectric constant of a metal, Drude model
2
0
2
0
0 0 2
0 0
2
0 0
0 2 2
1
, ~ ( )
~ ( )
e
e
r
N
i
i e e
d x
m eE E E exp i t
dt
eE
then x x exp i t x
m
D E P E
eE Ne E
P ex Nex
m m



  
 

 
 
  
     

Consequently,
2 2
2 2
0
0
1 1 ,where
p
r p
e
e
Ne Ne
m
m

 

  
    
plasmon frequency
For free electrons!

Remarks to Drude’s formula
2
2 *
0
,where
p
b p
e
Ne
m

  
 
  
Bound electrons should be taken into account, then 1-> ,
b

which takes into account the contribution of bound electrons.
Also the mass of electron should be replaced with
the effective mass of electron in the metal, .
*
e
m
For g << p:
Influence of attenuation
t
i
eE
dt
dx
m
dt
x
d
m 
g e
0
2
2


2 2
2 3
' 1 , "
p p
 
  g
 
  
Plasmons correspond to , these are eigen (free)
oscillations of the electronic plasma.
0
 
Surface Plasmons, Part 2,
A. Kolomenski, 9/26/2012

Electrons oscillating in the SP field
metal
dielectric
 
 
   
Interface
There is a longitudinal component in the electric field of SP, because E-M field is
coupled to oscillations of the electronic density (plasmonic oscillations).
This is why tp exite SPs one needs a p-polarization of the incident light.

Graphing dispersion equation of SPs
,k
,

2
1 2 *
0
,where
p
b p
e
Ne
m

  
 
  
1/2
1 2
1 2
ck
 

 
 

  
 
(
Light line: ck
 
For excitation of SPs we need
to slow down light!

Surface plasmon excitation:
Coupling of light to SPs with a prism
metal film (n1)
prism (n0)
sample (n2)
incident
laser
beam
reflected
beam
SPW
evanescent
wave
0: critical angle Optical arrangement used to
excite the surface-plasmon wave
based on the Kretschmann-
Raether configuration where a
thin metal film is sandwiched
between the prism and the
sample.
E. Kretschmann, Z. Phys. 241, 313-324 (1971).

SPR curves for different wavelengths
Gold film (d=47nm) contacting water
50 60 70 80 90
0.0
0.2
0.4
0.6
0.8
1.0 l=1230 nm
l=633 nm
l=490 nm
REFLECTION
COEFFICIENT
INCIDENCE ANGLE (deg)

Conditions for the resonance
excitation of SPs
Conditions for the resonance excitation of SPs:
a photon is converted into a surface plasmon.
General laws must be observed:
(1) Energy conservation,
(2) Momentum conservation,
( / 2 )(2 )
light light SP light SP
h h h h
      
    
, ,
x light SP x light SP
hk hk k k
  
x
k
z
k
z
k is changing x
k is not changing
SP x
k k


Momentum conservation
)
(
sin
2
l

l

sp
k
n

Energy conservation
SP
Light 
 
Conditions for the Surface Plasmon Resonance (SPR): phase matching!!!
k
ck

SP
)
sin
/( 2 

ck
ck / 2
0
ksp
p
Resonance excitation with a prism

Graphing dispersion equation of SPs
2
1 2
2
*
0
,
where
p
b
p
e
Ne
m

 



 

1/2 1/2
2
2
2
2
1/2 2
2
1 2
2 2
1 2
2 2
2 2
,
p
p b
b
p p
b b
ck ck k
c

  
  
  


   
   
 
   
 
   
 

   
   
 
  
   
  
 
   
   
 
   
  
   
   
   
   
   
,k
,

(
Light line: 2
/
ck
 

For excitation of SPs we need
to slow down light!
2
2 2
2 1/2
2
, 0; . 1
2
( )
p p p
b m b m
b
k when then For we have
  
     
  
 
 
          
  
 
m
 


The influence of the thickness of the gold film
on the properties of SPs
40 42 44 46 48 50
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0
Reflectivity
Incidence angle (deg)
10 nm
20 nm
50 nm
80 nm
120 nm
(a)
20 40 60 80 100 120 140
0
20
40
60
80
100
120
140
160
180 (b)
l=633 nm
l=805 nm
Attenuation
length
(

m)
Film thickness (nm)
(a) SP resonance curves at 633 nm for different film thicknesses.
(b) The dependence of the attenuation length on the film thickness for 633 nm and
805 nm. The dielectric constants published by Palik are used.
Gold
Glass
Air
-1
res
0
0 )
cos
( 

 D
 k
L sp

Approximation of small losses
R
k k k
i i rad
p p i i rad
 

    
1
4 1 2
2
1 2
2
( )
[ ( )] ( )
  
D   
k n
p p
 ( / )
2 0
 l the metal film is infinitely thick
np r r r r
 
[ / ( )] /
   
1 2 1 2
1 2
Dkp describes the correction due to finite thickness
i1 2
, internal losses in the film and in the medium
rad radiative loss
A. Kolomenski et al., Applied Optics, Vol. 48, 5683-5691 (2009)

Examples: changes in the flow cell, bio-
molecular binding reactions
B
0 10 20 30 40 50 60
250
300
350
400
450
500
550
B
A
HRP
B
B
NHS/EDC
SPR
angle
(pixels) Time (min)
Example: binding of monoclonal antibody to
horseradish peroxidase protein
0.30
0.35
0.40
0.45
0.50
70.50 70.75 71.00 71.25 71.50
INCIDENCE ANGLE (deg)
C=0.82%
C=0%
0.64 deg
Applied this sensing technique to myofibers and tubulin molecule.
A. A. Kolomenskii, P. D. Gershon, and H. A. Schuessler, Applied Optics 36, 6539-6547 (1997).

Sensitivity and detection limit
(relationships between different quantities)
angular resolution D-4deg=2 RU
changes of the refractive index Dn-6
average thickness of the protein layer Dd=0.03 Å
surface concentration Dd=3 pg/mm2
with mprotein=24 Da surface concentration of molecules ns=1010 cm-2
A. A. Kolomenskii, P. D. Gershon, and H. A. Schuessler, Applied Optics 36, 6539-6547 (1997).

600 800 1000 1200 1400 1600 1800 2000 2200 2400
1
10
100
1000
exact,  from [1]
approximate,  from [1]
Attenuation
length
(

m)
Wavelength (nm)
Au
600 800 1000 1200 1400 1600 1800 2000 2200 2400
1
10
100
1000
approximate,  from [1]
Attenuation
length
(

m)
Wavelength (nm)
Ag
1. American Institute of Physics Handbook, D. E. Gray, ed. (McGraw-Hill, 1972), p.
105.
2. U. Schröder, Surf. Sci. 102, 118-130 (1981).
3. Handbook of Optical Constants of Solids, E.D. Palik, ed. (Academic1985).
Attenuation lengths of SPs for gold and silver films in
contact with air, calculated for a broad spectral range

SPs:
dielectric
2 

Z
E
1  metal
)
|
k
exp(|
~ 1z z
~ exp( | | )
 k2z z
2
1
)
Re( 
 

0
1
frequency;
plasmon
,
2
2
1
:
electrons
free
of
ion
Approximat
2
1
2
1
2
2
2
with
wave
g
Propagatin
p
< 

















p
c
x
k
Condition of existence:
•Spatially localized to the surface E-M wave
•Oscillations of the electronic density.
•Have E -longitudinal component
•Are excited with p-polarized light and the local
field can significantly exceed the field in the
exciting beam.
e
p
m
ne
0
2

 
Summary of surface plasmons
b


42 43 44 45 46
0
10
20
30
40
50
60
70
80
90
100
110
633nm
633nm with1,eff.
805nm
805nm with1,eff.
|t
012
(

)|
2
Angle  (deg.)
Dependence of the near field intensity enhancement factor on the back side
of the gold film vs. the angle for two wavelengths 633 nm and 805 nm

SP resonance: coupling with a grating
(conservation of momentum)
ki
θ
ki sin(θ)
kg
kSP
kSP = ki sin(θ) - kg
ki θ
ki sin(θ) kg
kSP
kSP = ki sin(θ) + kg
+1 order coupling -1 order coupling
grating

Conditions for the resonance excitation of SPs
Light line
( / )
c n k
 
0 frequency of the source
 
required
additional
momentum
Light line, suited
for resonance excitation
,k
,

SPs are slower than light, and therefore for the same frequency their momentum is larger.
To enable the resonance excitation additional momentum must be provided.
SP dispersion
curve
The crossing of the SP curve and the light
line means resonance excitation for
desired frequency 0


λ
θ
Schematic of experiment on spectroscopy of SP
modes in nanostructures :transmission
measurements in the far field
Charge
Coupled
Device
(CCD)
Sample
(nanostructure)
Laser
beam
Grating
This setup maps intensity distribution
over angle and wavelength and thus reveals
SP modes that affect transmission.

Study of the Interaction of 7 fs Rainbow Laser Pulses with Gold
Nanostructure Grating: Coupling to Surface Plasmons
Wavelength (nm)
Intensity
Angle of
Incidence
650
800
-5°
0°
5°
Transmission dependence
The valley area (x-structure) the laser light is
efficiently converted into SPs, about 80% .
AFM image of the nanostructure:
A. Kolomenskii et al., Optics Express, 19, 6587-6598 (2011). Surface Plasmons, Part 2, A. Kolomenski, 9/26/2012

Avoided crossing
We consider two counter-propagating SP waves with complex
amplitudes a and b; the total fields can be presented as linear
combinations of these two individual waves.
The amplitudes a(z) and b(z) satisfy:
b
iK
a
i
a
dz
d
ab
a 
 
b
i
a
iK
b
dz
d
b
ba 


where and are the coupling coefficients.
ba
K
ab
K

Experimental and calculational results:
interaction of SP modes and spectral gap
SPs travels in two opposite directions. The intersection of the straight line with
the dispersion curve gives the point of excitation. Two counter propagating waves
interact with each other when they are scattered on 2Kg. K=wavenumber of
grating.k=projection of light on plane of propagation
Kg
-Kg
2 107 1 107 0 1 107 2 107
5.0 1014
1.0 1015
1.5 1015
2.0 1015
2.5 1015
3.0 1015
3.5 1015
k


sin
)
(
n
k
k
c g




sin
)
(
n
k
k
c g



k

sp

sp

-6 -4 -2 0 2 4 6
650
700
750
800
Theory
Experiment
Wavelength
(nm)
Angle (deg.)
-1 Order
1 Order
Kg

Avoided crossing
By substituting: z
i
e
B
A
z
b
z
a 













)
(
)
(
We obtain: , I – unit matrix,
0
)
( 







B
A
I
M  0













 
B
A
K
K b
ab
ba
a




0
)
)(
(
det 




 ba
ab
b
a K
K
I
M 

















b
a
iM
b
a
dz
d







b
ab
ba
a K
K
M


The coupled-mode equations can be expressed in matrix form:
The two eigenvalues for are:

q
b
a



2



Where:
ba
abK
K
q 
D
 2
2
2
ab
K
q 
D

ab
b
a
K


2


q can be purely imaginary if
Spectral gap!
2
b
a 
 

D
4 2 2 4
720
740
760

Optical detection of
acoustic waves with
surface plasmons

For fast and sensitive detection of acoustic waves the surface
plasmon resonance (SPR) can be used, which responds to
variations of dielectric properties in close proximity to a metal
film supporting surface plasmon waves. When an acoustic wave
is incident onto a receiving plate positioned within the
penetration depth of the surface plasmons, it creates
displacements of the surface of the plate and thus modulates
the dielectric properties, affecting SPR and the reflection of the
incident light. Here we study characteristics and determine the
optimal configuration of such an acousto-optical transducer with
surface plasmons for efficient conversion of an acoustic signal
into an optical one. We simulate the properties of the
transducer and present estimates showing that it can have a
large frequency bandwidth and good sensitivity.
Abstract

Fig. 1. Schematic of the acousto-optical sensor with surface plasmons. The
arrangement consists of a glass prism (PR), the adjacent gold film (GF), a spacer
(SPA) and a receiving plate (RP). The field of the excited surface plasmon (SP)
decays away from the gold film. The acoustic wave (AW) induces displacements of
the RP face close to the GF, which results in a quantifiable modification of the SPR
curve featuring the resonance by a dip in the dependence of the intensity on the
incidence angle . The inset on the right shows a schematic of layers with
notations for the dielectric constants and thicknesses of the layers.

Changes of the SPR curve due to
RP displacement

•
Detection limit for the RP
displacement
Detection of ΔRmin change
Detection of ΔR change at the steep slope

10 15 20 25 30 35 40 45 50
1.0
1.2
1.4
1.6
1.8
2.0
2.2
2.4
2.6
2.8
Merit
factor,
|S

|x10
3
nm
-1
Gold film thickness (nm)
(a)
1.2 1.3 1.4 1.5 1.6 1.7 1.8 1.9
2.45
2.50
2.55
2.60
2.65
2.70
Merit
factor,
|S
1
|x10
3
nm
-1
Refractive index
(c)
Fig. 3 The merit factor |S1| for λ=800nm: (a). The
dependence of the (n4,d3)- optimized merit factor |S1| on
the gold film thickness calculated for λ=800nm. (b).
Density plot in false colors showing the merit factor |S1|
for the optimal gold film thickness d2=16nm at different
values of the gap d3 and the refractive index n4; the
overall maximum of |S1|=2.64x10-3nm-1 is obtained at
n4=1.45 and the gap value of d3=0.48μm and is shown by
a large white dot. Note that the sign of S1 is negative (the
value of Rmin decreases for the positive displacement Δζ)
above d3=0.395μm, at which value S1 is close to zero. (c).
The dependence of the d3- optimized merit factor |S1| for
different values of the refractive index n4.
Merit factor S1 for 800nm

26 28 30 32 34 36 38
1.05
1.10
1.15
1.20
Merit
Factor,
|S
2
|x10
3
nm
-1
Gold film thickness (nm)
(a)
1.2 1.3 1.4 1.5 1.6 1.7 1.8
0.90
0.95
1.00
1.05
1.10
1.15
1.20
1.25
Merit
factor,
|S

|x10
3
nm
-1
Refractive index
(c)
Fig. 6. The merit factor |S2| for λ=633nm: (a). The
dependence of the (n4,d3)- optimized merit factor
|S2| on the gold film thickness. (b). Density plot in
false colors showing the merit factor |S2| for the
optimal gold film thickness d2=29nm at different
values of the gap d3 and the refractive index n4; the
overall maximum of |S2|=1.19x10-3nm-1 is obtained
at n4=1.41 and the gap value of d3=0.61μm and is
shown by a large white dot. (c). The dependence of
the d3-optimized merit factor |S2| for different
values of the refractive index n4.
Merit factor S2 for 633nm

λ(nm) ParametersforS1 response ParametersforS2 response
800
S1 = −2.64 × 10−3
𝑛𝑚−1
(Fig.3)
S2 = −1.02 × 10−3
𝑛𝑚−1
(Fig.5)
d2(nm) n4 d3(nm) d2(nm) n4 d3(nm)
16 1.45 0.48 25 1.38 0.87
633
S1 = 3.56 × 10−3
𝑛𝑚−1
(Fig.4)
S2 = −1.19 × 10−3
𝑛𝑚−1
(Fig.6)
d2(nm) n4 d3(nm) d2(nm) n4 d3(nm)
22 1.52 0.25 29 1.41 0.61
Table 1. Parameters for realization of the transducer at optical wavelength of
800nm and 633nm with maximum |S1| and |S2| values corresponding to plots
of Figs. 3-6.
Conclusion:
Merit factors of about 10-3nm-1 can be obtained

(a) (c)
(b) (d)
0.010 0.005 0.005 0.010 0.015 0.020
m
0.015
0.010
0.005
0.005
R
0.15 0.10 0.05 0.05 0.10 0.15 0.20
m
0.4
0.2
0.2
R2
0.03 0.02 0.01 0.01 0.02 0.03
m
0.05
0.05
R
0.2 0.1 0.1
m
0.4
0.2
0.2
0.4
0.6
R2
Fig. 7. Variation of the reflection coefficient ΔR in response to acoustic
wave with displacements Δζ of different magnitudes is presented for
optimal parameters of Figs. (3-6) shown in Table 1: (a) and (b) for ΔR
response and the wavelengths of 800nm (Fig. 3) and 633nm (Fig. 4)
respectively; (c) and (d) for ΔR2 response and the wavelengths of
800nm (Fig. 5) and 633nm (Fig. 6) respectively. The solid blue lines
show the responses ΔR, ΔR2 and the dotted red lines depict the linear
fits; the vertical dashed lines show the limits within which the
response deviates from the linear dependence by less than 10%.

(a) (c)
(b) (d)
0.2 0.1 0.1
m
0.4
0.3
0.2
0.1
0.1
0.2
0.3
R
0.2 0.1 0.1 0.2
m
0.3
0.2
0.1
0.1
0.2
0.3
0.4
R2
0.2 0.1 0.1 0.2
m
0.4
0.2
0.2
0.4
R
0.3 0.2 0.1 0.1 0.2 0.3
m
0.6
0.4
0.2
0.2
0.4
0.6
R2
Fig. 8. Realizations of the linearity ranges of the sensor response to the
displacement Δζ for parameters presented in Table 2: (a) and (b) for ΔR
and the optical wavelengths l=800nm, and l=633nm respectively; (c)
and (d) for ΔR2 and the optical wavelengths l=800nm, and l=633nm
respectively. The solid blue lines show the response ΔR for (a,b) and ΔR2
for (c,d), the dotted red lines depict the fitted linear dependences; the
vertical dashed lines show the limits within which the response
deviates from linear dependences by less than 10%.
Quasi-linear response dependences
ΔRmin
l=800nm
l=633nm
ΔR2

Surface Plasmons Part 5
• Surface plasmon effects on nano particles

Mie theory and dipole approximation
)
(
)]
2
)
(
[
)
(
9
)
(
2
2
2
/
3














i
d
r
i
m
ext V
c
For small nanoparticles (R<<wavelength, or roughly 2R< wavelenght/10):
dipole approximation
where V is the particle volume,  frequency light, εm and
are the dielectric functions of the surrounding medium and the particle
material.
When is small or varies slowly, the resonance takes place
at
)
(
2 

2
2
1
,
0
)
2
(
)
(






p
r
d
r 




d
p





2
1
max
0
)
(
)
(
)
( 

 




 i
i
r
t=0 t=T/2
Electronic cluster
Ionic cluster
Electric field
Light Electronic plasma
oscillations
=>

Extinction spectra of Ag n-particles
in solution
350 375 400 425 450 475
0.0
0.2
0.4
0.6
0.8
1.0
1.2
Ag 27 nm particles
Ag 48 nm particles
Extinction
(a.u.)
Wavelength, nm
The oscillations of a n-particle, induced by a pump pulse, modulate (displace) the plasmon
absorption band. For efficient detection the probe wavelength was selected at the steeper
portion of the slope of this band.
S. N. Jerebtsov et al. Phys. Rev. B Vol. 76, 184301 (2007).

Bowtie nano-antenna and measured
intensity enhancement
Intensity enhancement vs wavelength
3D finite difference time domain (FDTD)
simulations
Fabricated by Electron Beam Lithography
(EBL) bowtie antennas. Indium tin oxide
substrate. Gap was varied, thickness 20 nm.
Kino et al. In: Surface Plasmon nanophotonics, p.125 (2007).

Experimental setup for study of “hot spots” for SERS
Raman signals from individual Ag n-particles
Raman microscope with sensitive CCD cameras for imaging the sample in scattering
and using Raman signal. Notch filters were used to suppress the excitation light. Low
concentration of n-particles needed to separate individual particles.
Futamata et al. Vibrational Spectroscopy 35, 121-129 (2004).

Raman spectroscopy
Photon scattering on molecules
Elastic or
Rayleigh scattering
Inelastic or
Raman scattering
h
h h( - ) h( + )
Stocks Anti-Stocks
Raman scattering increases when h produces electronic transition

Surface Enhanced Raman Spectroscopy (SERS) of DNA bases
Spectra of
individual
n-particles
Stongest enhancement ~1010 from pairs
of particles with axis parallel to polarization
Characteristic stretching modes in heterocycles suited
for DNA sequencing :
adenine 718 and 893 cm-1;guanine 641cm-1;
cytosine 791 cm-1; thymine 616, 743 and 807 cm-1.
Time evolution (whole scale 1 s) demonstrates
Raman peaks and blinking effect, known
for single molecule detection.
Futamata et al. Vibrational Spectroscopy 35, 121-129 (2004).

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