Understanding Surface Plasmonics in detail.pptx

Explanation and derivations of dispertive properties of surface plasmons along with discusion on a peer reviewd research paper.

1. 1 Surface Plasmons Suyog Hawal Assistant Professor Department of Electronics and Computer Engineering, Sharad Institute of Technology College of Engineering , Yadav, Kolhapur, Maharashtra

2. Dispersive nature of metals Introduction to plasmons Dispersion Relations Bulk Plasmon Surface Plasmon Polaritons Paper Discussion 2 Content

3. At lower frequencies up to visible part of spectrum metals acts as highly reflective and do not allow EM wave to propagate through them. (Negligible field penetration) Whereas at NIR and Visible part of spectrum field penetration increases leading to increased dissipation. At UV metal acquires dielectric character and allows EM wave propagation with various degrees of attenuation depending upon details of band structure . This behaviors of metals of strong frequency dependence can be explained with complex dielectric function This strong frequency dependence induces due to change in the phase of the induced currents with respect to the driving field for frequencies approaching the reciprocal of the characteristic electron relaxation time τ 3 Dispersive Nature of Metals

4. At low frequencies preference is given to the conductivity σ Whereas at optical experiments observations are done with dielectric constant 4 Relation between ε and σ

5. Over wide frequency range optical properties of metals ar.e tailored by plasma model Gas of free electrons of number density ‘n’ moves against fixed background of positive ion cores For alkali metals, this range extends up to the ultraviolet, while for noble metals interband transitions occur at visible frequencies, limiting the validity of this approach Details of the lattice potential and electron-electron interactions are not taken into account. Instead, one simply assumes that some aspects of the band structure are incorporated into the effective optical mass m of each electron 5 Dielectric Function of free electron gas

6. 6 Dielectric Function of free electron volume plasmons A collective displacement of the electron cloud by a distance u leads to a surface charge density σ =± neu at the slab boundaries. This establishes a homogeneous electric field inside the slab

7. 7 Dispersive Nature of Metals

8. 8 Dispersive Nature of Metals

9. 9 Dispersive Nature of Metals

10. 10 Surface Plasmons

11. 11 Local Field Intensity Depends on Wavelength

12. 12 Surface Plasmons

13. 13 Dispersion Relation: Bulk Plasmons

14. 14 Dispersion Relation : Bulk Plasmons

15. 15 Dispersion Relation : Surface Plasmons Polaritons

16. 16 Dispersion Relation : Surface Plasmons Polaritons

17. 17 Dispersion Relation : Surface Plasmons Polaritons

18. 18 Dispersion Relation : Surface Plasmons Polaritons

19. 19 Plasma modes and SPP

20. 20 Why Plasmonics ?

21. 21 Fig : (a) Real-space (left) and k-space (right) depictions of the modes scattering from the exit of a slit in a metal film with different dielectric environment conditions Paper Discussion (Enhancing the efficiency of slit-coupling to surface-plasmon-polaritons via dispersion engineering , R. Mehfuz et all.) Dielectric layer thickness variation can tune“ K SPP mode on the metal surface to match the wavevector magnitude of the modes emanating from the slit exit K i which enablins high-efficiency radiation coupling into the SPP mode at the slit exit.” K 0 (free space) K i K radient K evanescent K evanescent Fig : Components of incident wave K SPP K SPP

22. 22 Light exiting the slit in the region z > 0 consists of radiating and evanescent modes with wavevector magnitude Wavevector of Surface Plasmon Polariton given by, Diffraction at the slit exit disperses the modes at the slit exit into a continuum of directions described by Assuming that the field at the exit of the slit in the plane z = 0 has the form The amplitude distribution of the diffraction spectrum is given by

23. 23 Diffracted modes that assume a real Wavevector x-component k x < k i possess a real Wavevector z-component corresponding to radiative modes that propagate away from the slit exit Diffracted modes that assume a real Wavevector x-component k x > k i possess an imaginary Wavevector z-component corresponding to evanescent modes confined to the slit region A fraction of the evanescent modes with values of k x , matching the Wavevector of the SPP mode on the air-silver interface couple from the slit exit to the positively and negatively directed SPP modes

24. 24 Intensity and Coupling Efficiency Calculation Radiation Intensity Total intensity confined to the slit-exit plane, I e A fraction of I e constitutes the SPP mode intensity I SPP and the remainder constitutes the intensity of decaying modes I d .

25. 25 The time-averaged intensities of the SPP mode and the radiated modes are quantified by In this work, the dependence of the SPP coupling efficiency studied to fully characterize this SPP coupling methodology on the following parameters.. The dielectric-layer thickness, Slit width The incident wavelength

26. 26 Fig : Simulation geometry used to study SPP coupling from an illuminated slit. Simulation Scheme

27. 27 Control Study

28. 28 Dielectric Thickness Dependence Fig : Intensity Vs Dielectric Thickness Fig : Coupling Efficiency Vs Dielectric Thickness Fig : FDTD results

29. 29 Fig : SPP wavelength measured from the FDTD simulations (blue squares) and predicted from the mode solver (red line) as a function of dielectric layer thickness d.

30. 30 Slit Width Dependence Fig : Intensity Vs Slit Width Fig : Coupling Efficiency Vs. Slit width Fig : FDTD results

31. 31 conclusion, Varying the thickness of the dielectric layer enables tuning of the SPP Wavevector. When the SPP wavevector is matched with the wavevector magnitude of the modes exiting the slit, coupling efficiencies 0.80 can be achieved, 4-times enhancement relative to the case without the dielectric layer. In addition to enhancing SPP coupling efficiency, the dielectric layer has the added benefit of passivation and protection of the SPP-sustaining metal surface.

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