surface plasmon resonance ppt

1. Surface Plasmon Resonance
Dr. Amir Reza Sadrolhosseini Dr. A.S.M Noor

2. 1- Refractive index of prism
2-Refractive index and thickness of gold layer
3- Refractive index or thickness of medium
Main question:
What is the relationship between Reflectivity and angle of
incident at the interface?
What is condition of resonance?
How can we determine the thickness and refractive index
of layers?
How can we determine the resonance angle shift?
The SPR is an optical- electrical phenomenon that due to a charge density oscillation at the interface between a dielectric media
and a metal layer .
Medium
Detector
Cladding
Cladding
Core
Metal Layer
Sensing Layer
Detector
Diode
Laser

3. -Reminder
-Theory
1-Oscillator Model
2-Plasma Osillation and Plasmons
3-Surface Plasmons condition
4- Matrix metodes
-Surface plasmon sensor
-Data Analysis and simulation with matlab
-Condition of sensing layer

4. Reminder
1
0
1
0
H
E
c
D
H
c
D
t
t
H

  




 




D is displacement field
H is magnetic field
D E


( . )
0
i q r t
E E e 


2
2
2 2
E E
c t
 
 

Transverse Wave equation
Maxwell equation:

5. Reminder
( ) ( )
2 ( )
cn

   



( ) 2 ( )
   

i
  
 
 
2 2
1
( ) ( ) ( )
2
n    
 
  
  
 
Dielectric Function
Absorption coefficient=2×Extinction coefficient
Refractive index
( ) ( )
n n ik
 
 
2 2
n k
   2nk
 
2 2
1
( ) ( ) ( )
2
k    
 
  
   
 

6. 1- Oscillator Model
This model describe the medium and we can obtain absorption
coefficient and refractive index.
We assume that the Crystal consists of charges which can be set in motion an
oscillating electric field of light .
From Newton´s second law ,we can write equation of motion :
(1)
For monochromatic field
(2)
)
(
)
(
2
2
t
eE
dt
t
dx
m
t
d
x
d
m e
e 



t
i
e
E
E 

 0
t
i
e
x
x 

 0

7. (3)
polarization density of the conduction electron
(4)
Induce polarization (background polarization )
This background polarization is due to the displacement of bound particles.
TOTAL Polarization is
Susceptibility :
Displacement field:
Relation between susceptibility and dielectric function
(5)
1
2
2
0
0







 i
E
m
e
x
e
c
b P
P
P 

1
)
( 2
2
2
0










 i
E
m
ne
t
nex
P
e
c
c
P
b
P
E
P


E
D
P
E
D




 4
E
P
P c
b 




 


 4
1
4
1

8. substituting in Eq(5) :
If then
1
4
4
1 2
2
2














i
m
ne
E
P
e
b
E
Pb


4
1


c
P



2 2 2
2 2 2 2
4 4
( 1) ( 1)
e e
ne ne
i
m m
   
 
    

  
 


 



 i

9. • IF Low-Frequency
In This Regime Material Highly Absorptive
Absorption coefficient is:
1


2
2
2
2
4
( 1)
4
e
e
n
i
e
m
ne
i
m
i

 


 







 
2
c

 

2
8
e
ne
c m
  



2 2 2
2 2 2 2
4 1 4 1
1 1
e e
ne ne
m m
   
    
   
 
2
4
e
ne
m
 


 

10. • IF High-Frequency
Highly Transparent
Highly Reflecting
1


2
2
4




e
m
n
e

 
2
2 4
p
e
e n
m




)
1
( 2
2




p

 
1
2
2







p
p 0


1
2
2







p
p 0


2 2 2
2 2 2 2
4 4
( 1) ( 1)
e e
ne ne
i
m m
   
 
    

  
 
Plasma frequency
Plasma Frequency is the frequency of collective oscillation of the electron .
2 2 2
2 2 2 2
4 1 4 1
1 1
e e
ne ne
m m
   
    
   
 
2 2
2 2
4 1
( )
1
e
ne
m
 
  
 

   


11. 2.183×1015 Hz
2.18×1015 Hz
Gold
Silver
300 nm 9.993×1014Hz
700 nm 4.282×1014Hz
1
2
2







p
p

12. What is the Plasmon?
Physically, plasma frequency is the frequency of collective
oscillation of electron gas( plasma)
If the electron density oscillates at plasma frequency,
collective excitations will be occurred.
This oscillation is plasma oscillation and is longitudinal.
The quantum of plasma oscillation is plasmon
or
Quantum of collective electron density oscillation
plasmon p
E 

Plasmons may be exited
for example by inelastic electron scattering
Prism coupling
Grating coupling
Waveguide coupling
0
1
2
2
1
2

 n
dt
n
d
p

1
0 n
n
n 

n
1
n Density at time t

13. 2-Plasma Osillations and Plasmons
Mean density of free electron plasma is
At time t the electron number density changes slightly from the mean value
is small
Continuity equation:
Velocity at t time:
Charge Density:
Current Density:
differentiating
1
n
0
n
1
0 n
n
n 

1
1
0 v
v
v
v 


0






t
J

en



env
J 


4


 E
0
1
1
0 



dt
dn
v
n 0
1
0
2
1
2








t
v
n
t
n
eE
t
v
me 


 1
0
1
2
2
1
2

 n
dt
n
d
p


14. The electron density oscillates at the plasma frequency.
The quantum of the plasma oscillation is plasmon.
Plasmons may be exited
for example by inelastic electron scattering
Prism coupling
Grating coupling
Waveguide coupling
0
1
2
2
1
2

 n
dt
n
d
p


15. 3-Surface Plasmons Theory
Surface Plasma waves:
The interface between a medium with a positive dielectric constant
and a medium with negative dielectric constant such as metals, can
give rise to special propagation electromagnetic waves called surface
plasma waves.
0


0


Glass
Metal
medium
In this case the Energy and
momentum conservation is
satisfied and the wave vector of
light is increased
30 35 40 45 50 55 60 65 70
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
SPR (%90M %10P)
Angle
%R
0
METAL
 
0
PRISM
 
Surface Plasmon Wave

16. Electric Field:
Magnetic Field:
Boundary condition :
0

ε
x
z
0


0

z z
t
kx
i
e
e
E
E 1
)
(
1

 




)
,
0
,
(
1
1 B
A
E
E



0

z z
t
kx
i
e
e
E
E 2
)
(
2





 )
,
0
,
(
2
2 D
C
E
E



0

z z
t
kx
i
e
e
H
H 1
)
(
1

 




)
0
,
,
0
(
1
1 y
H
H
H



0
z  z
t
kx
i
e
e
H
H 1
)
(
2

 




)
0
,
,
0
(
2
2 y
H
H
H



0
2
2
1
1
2
1



n
n
t
t
E
E
E
E


y

17. Dispersion Relation for surface plasmons
  )
,
,
(
)
,
,
( 2
2
2
2
z
y
x
z
y
x E
E
E
dt
d
c
E
E
E
dt
E
d
c
E









2
2
1
2
2
1 


c
k 

2
2
2
2
2
2 


c
k 

)
,
0
,
(
)
,
0
,
( z
x
y
y
E
E
t
c
x
H
z
H
t
E
c
H

















t
E
c
z
H x
y







2
1
2
1






1
2
1
2
2
2
2
2
1
2
1
2
)
(
)
( 





c
k
c
k 











2
1
2
1
2
2
2





c
kplasmon
res
nSin
k 


2




18. The surface plasmon and
the photon dispersion curves
do not cross each other
anywhere
Glass
Metal
medium
In this case the Energy and
momentum conservation is
satisfied and the wave
vector of light is increased
plasmon
i
glass
i
glass k
n
c
k 
 

 sin
sin
2 2
1 2
2 2
1 2
p R
n n
n Sin
n n




c
k



2 2
1
2 2 2
1
sin
sin
p p
p p
n n
n
n n




Cladding
Cladding
Core
Metal Layer
air
Detector
Diode
Laser

19. 0 0 0 0 1 1 0 0 1 1
1 0 0 2 2 2 0 0 1
0 1 0 1 1 1
2 2 1 2 2
( ) ( )
( )
( )cos ( )cos
( )cos
a r t i
b i r t
a r t i t
b i r t t t
B n E E n E E
B n E E n E
E E E E E
E E E E cos
   
   
 
 
   
  
   
  

i
r
i e
E
E 
 2
1

i
t
i e
E
E 
 1
2

i
r
i e
B
B 
 2
1

i
t
i e
B
B 
 1
2
E
c
n
B 
0
0
1



c
1
( cos ) ( sin )
i
i
a b b
e
E e E i B


 



 
1
( sin ) ( cos )
i i
a b b
B ie E e B
 
  
 
  
0
0
cos




N
t
N
N
n

1
1
sin
cos
sin cos
i
M
i



  
 

 

 

 
 
1
cos
2
1 t
tn 


 
Matrix Methods For Simulation and analysis the SPR Signal
11 12
21 22
a b
a b
E E
m m
B B
m m
   
 

   
 
 
   
Matrix of layer
a
b
n1
n0 0

2
t

n2
1
t


20. 21 22 2 11 0 12 2 0
21 22 2 11 0 12 2 0
m m m m
r
m m m m
   
   
  

  
1 2 3............. N
M M M M M

11 12
21 22
m m
M
m m
 
  
 
*
R rr

1
0
r
E
r
E

   
   
2 2 1
2 2 1
2 2
0 2 0 0 1 0 0 0
2 2
0 2 0 0 1 0 0 0
cos cos cos
cos cos cos
A B
t t t
t t t
C D
n i n
r
n i n
         
         
  

  
1 2 1
1 2
0 0 11 12
21 22
0 0 0 0 2 0 0
( )cos cos
( )
r t t
r t
E E E
m m
m m
n E E n E
 
   

   
 

   
 

   
 
   
1 2 3.....
a b
N
a b
E E
M M M M
B B
   

   
   
1
2
3
4
N

21. 30 40 50 60 70
0
0.2
0.4
0.6
0.8
1
Angle
R%
SPR
30 40 50 60 70
0
0.2
0.4
0.6
0.8
1
Angle
R%
ethanol
Methanol
n=.25+3.21i
er =-10.24
ei=1.605
Thickness=52.5 nm
Refractive index Resonance angle Reflectance
1.331+0.001i 52.34 0.0252
1.331+0.005i 52.364 0.0663
1.331+0.01i 52.405 0.1221
1.331+0.05i 52.864 0.4140
1.331+0.1i 53.523 0.5546
1.331+0.2i 54.628 0.6587

22. The effect of refractive index

23. Data Processing
• 1-Centroid Method
this method uses a simple algorithm which
finds the geometric center of the portion of the
SPR dip under a certain threshold. Although
the geometric center does not necessarily
coincide with the minimum of the spectrum, as
SPR sensing usually relies on relative
measurements, the offset of the geometric
center does not affect the final measurements.
The centroid is calculated as follows:






j
j
thresh
j
j
thresh
j
C
I
I
I
I
x
Y
)
(
)
(
j
x represent the spectral positions of the contributing intensities j
I
thresh
I denotes the threshold value.




 2
1
2
1
))
(
(
))
(
(










d
P
P
d
P
P
B
B
res
B
P is the baseline,
)
(
P the response from a detector array at the angle of incidence onto the metal film θ

24.   




2
1
2
1
))
(
(
))
(
( 1
0









 d
P
P
A
d
P
P
A B
B
),
(
)
( 2
1 
 P
P
PB 



 

 1
0
b
aP
P 

 )
(
)
( 














2
1
2
1
))
(
(
))
(
(








 d
P
P
d
P
P B
B
),
(
)
( 2
1 
 





 P
P
PB


 



 1
0
b
aP
P B
B 





 





2
1
2
1
))
(
(
))
(
(








 d
P
P
d
P
P B
B
1
1 
 

2
2 
 

0
1
A
A

 are the area above and
under the base line
0
1, A
A
a
Base line :
a Change in light intensity with proportionality factor
New base line:
)
(
)
( 2
2 
 P
P 

)
(
)
( 1
1 
 P
P 


25. res
B
B
B
B
res
d
P
P
d
P
P
d
P
P
d
P
P











 


























2
1
2
1
2
1
2
1
))
(
(
))
(
(
))
(
(
))
(
(
30 35 40 45 50 55 60 65 70
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
SPR (%90M %10P)
Angle
%R
40 42 44 46 48 50 52 54 56 58 60
0
0.002
0.004
0.006
0.008
0.01
0.012

26. 30 35 40 45 50 55 60 65 70
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
SPR FOR BIODIESEL BASE PALM OIL AND METHANOL
Angle
R%
%90M %10P
%80M %20P
%70M %30P
%60M %40P
%50M %50P
%40M %60P
%30M %70P
%10M %90P
%20M %80P
PERCENTAGE OF PALM
OIL
%10 %20 %30 %40 %50 %60 %70 %80 %90
Percentage of methanol %90 %80 %70 %60 %50 %40 %30 %20 %10
Resonance Angle 54.3235 55.0416 55.8516 56.6699 57.4381 59.2083 59.3586 60.3439 61.4043
Refractive Index 1.349 1.359 1.370 1.381 1.391 1.413 1.415 1.427 1.439