Lecture 10 Light-Matter Interaction Part 4 Surface Polaritons 2. EECS Winter 2006 Nanophotonics and Nano-scale Fabrication P.C.

Transcription

1 Lecture 10 Light-Matter Interaction Part 4 Surface Polaritons 2 EECS Winter 2006 Nanophotonics and Nano-scale Fabrication P.C.Ku

2 Schedule for the rest of the semester Introduction to light-matter interaction (1/26): How to determine ε(r)? The relationship to basic excitations. Basic excitations and measurement of ε(r). (1/31) Structure dependence of ε(r) overview (2/2) Surface effects (2/7 & 2/9): Surface EM wave Surface polaritons Size dependence Case studies (2/14 2/21): Quantum wells, wires, and dots Nanophotonics in microscopy Nanophotonics in plasmonics Dispersion engineering (2/23 3/9): Material dispersion Waveguide dispersion (photonic crystals) 2

3 Optical excitation of surface plasmons ω Photon in air Surface plasmon k glass metal air 3

4 Excitation of surface plasmons via gratings The TM solution in a 1-D periodic structure (grating) is: 2π m x Hk ( z) = H ( ) x m kx e Λ m= i( k 2 π m/ Λ) z The grating couples different kx components together. air metal ω c 2π m ε1 sinθ+ = k Λ x 4

5 Excitation of surface plasmons via rough surface The surface profile can be decomposed into a set of gratings with different periods. ε( x) = ε( G) e igx dg G 5

6 Localization of surface plasmons When the surface becomes rather rough, the scattering of the surface plasmons is strong enough that the propagation of surface plasmons along the interface approaches a diffusion process surface plasmons become localized. Closer to a sinusoidal grating Random; non-statistical 6

7 Surface plasmons on the sphere surface Scattered wave The scattering cross section from a small particle is proportional to ε s ε ε + 2ε s When ε s = 2ε, the scattering cross section infinity surface EM wave can be supported. 7

8 Modulation of the plasmon resonance If we put another object very close to the metal sphere, the effective dielectric constant of the metal is modified. The plasmon resonance position is shifted. d 8

9 Field enhancement Because of the incredibly large scattering cross section, the electric field on the surface is greatly enhanced. ikx E = zee ˆ ze ˆ as kx 1 i i i 3 ( ) ˆ2cos ˆ a Es r = r θ + θsinθ E r At the surface along the z direction: εs ε 3εs E ( a) = 2 E + E = E ε + 2ε ε + 2ε total i i i s s The enhancement is: E 2 2 ( a) 3ε s E ε '' total i s s 9

10 Enhanced Raman scattering ω ω ω ph Au 10

11 Surface plasmon induced Raman enhancement Ref: S. Kawata, Near-Field Optics and Surface Plasmon Polaritons, Springer (2001) ch.1. 11

12 Plasmons in reduced dimensional structures 1. Plasmons 2. Surface plasmons 3. Plasmons in 2D structures 4. Plasmons in 1D structures Ref: H. Raether, Surface Plasmons, Springer-Verlag (1986). 12

13 ε(r) at small size The absorption spectrum for metal nanoparticles is different from that of a bulk metal piece. Ref: S. Link and M. A. El-Sayed, J. Phys. Chem. B 103 (1999)

14 Surface-plasmons near surface Plasmon dispersion relation: Near surface: ( ) ε ω AvF γ γ() r = γ0 + r v F ω 2 p = 1 2 ε0 ω + iγω where is the velocity of electrons at the Fermi s energy. For surface-plasmons near the surface: The resonance is at ε s' + iεs'' = 2ε The spectral width of the resonance absorption ~ ε s '' Both depend on r. 14

15 Au particles resonance shift Ref: S. Link and M. A. El-Sayed, J. Phys. Chem. B 103 (1999)

16 Size-dependent emission wavelength Ref: M. Bruchez Jr. et al, Science 281 (1998)

17 Reading Kawata, chapter 1 by P. W. Pohl. 17