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

2. 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 .
Prism
Metal
Medium
Detector
Cladding
Core
Metal Layer
Sensing Layer
Detector
Diode Laser
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?

3. -Surface plasmon sensor -Data Analysis and simulation with matlab
-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 Maxwell equation: Transverse Wave equation
D is displacement field
H is magnetic field
Transverse Wave equation

5. Reminder Refractive index Dielectric Function
Absorption coefficient=2×Extinction coefficient
Refractive index

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)

7. polarization density of the conduction electron
(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)

8. substituting in Eq(5) :
If then

9. In This Regime Material Highly Absorptive
IF Low-Frequency
In This Regime Material Highly Absorptive
Absorption coefficient is:

10. Highly Transparent Highly Reflecting IF High-Frequency
Plasma frequency
Plasma Frequency is the frequency of collective oscillation of the electron .

11. 300 nm 9.993×1014Hz 700 nm 4.282×1014Hz Gold Silver 2.183×1015 Hz

12. This oscillation is plasma oscillation and is longitudinal.
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
Density at time t
Plasmons may be exited
for example by inelastic electron scattering
Prism coupling
Grating coupling
Waveguide coupling

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

14. The quantum of the plasma oscillation is plasmon.
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

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.
Surface Plasmon Wave
Glass
Metal
medium
In this case the Energy and momentum conservation is satisfied and the wave vector of light is increased

16. z x y
Electric Field:
Magnetic Field:
Boundary condition :

17. Dispersion Relation for surface plasmons

18. Glass
Metal
medium
Cladding
Core
Metal Layer
air
Detector
Diode Laser
The surface plasmon and the photon dispersion curves do not cross each other anywhere
In this case the Energy and momentum conservation is satisfied and the wave vector of light is increased

19. Matrix Methods For Simulation and analysis the SPR Signalb n2
Matrix of layer

20. 1 2 3 4 N

21. n=.25+3.21i er =-10.24 ei=1.605 Thickness=52.5 nm Refractive index
Resonance angle
Reflectance i
52.34
0.0252 i
52.364
0.0663 i
52.405
0.1221 i
52.864
0.4140 i
53.523
0.5546 i
54.628
0.6587
n= i
er =-10.24
ei=1.605
Thickness=52.5 nm

22. The effect of refractive index

23. Data Processing 1-Centroid Method is the baseline,
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:
represent the spectral positions of the contributing intensities
is the baseline,
denotes the threshold value.
the response from a detector array at the angle of incidence onto the metal film θ

24. are the area above and under the base line
a Change in light intensity with proportionality factor
New base line:

26. PERCENTAGE OF PALM OIL
%10
%20
%30
%40
%50
%60
%70
%80
%90
Percentage of methanol
Resonance Angle
Refractive Index
1.349
1.359
1.370
1.381
1.391
1.413
1.415
1.427
1.439