Surface Plasmon Resonance

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

2. Sensing Layer Cladding Diode Laser Core Detector Cladding Metal Layer 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 . Detector Prism Metal Medium 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. -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: D is displacement field H is magnetic field Transverse Wave equation

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

6. 1- Oscillator ModelThis 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. (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. IF Low-Frequency In This Regime Material Highly Absorptive Absorption coefficient is:

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

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

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

17. Dispersion Relation for surface plasmons

18. air Cladding Glass Metal medium Diode Laser Core Detector Cladding Metal Layer 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 Signal n0 a n1 b 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

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: 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 Base line : a Change in light intensity with proportionality factor New base line: