Download Lecture 8: Light-Matter Interaction in Nanophotonics and Nanoscale Fabrication - Prof. Pc and more Study notes Electrical and Electronics Engineering in PDF only on Docsity! Lecture 8 – Light-Matter Interaction Part 2 Basic excitation and coupling EECS 598-002 Winter 2006 Nanophotonics and Nano-scale Fabrication P.C.Ku 2EECS 598-002 Nanophotonics and Nanoscale Fabrication by P.C.Ku 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) 5EECS 598-002 Nanophotonics and Nanoscale Fabrication by P.C.Ku Review of the concept of polaritons In a dielectric medium: where the index denotes the n-th kind of basic excitation or SHO. QM analogue: 2 2 2 0 2 2 basic 0 n 0 excitations or oscillators 2 0 2 2 0 ( ) 1 where ( ) = ( ) pn n n pn n n n p N q i m i ω ε ω ε ω ω ω γ ω ε ω ε ε ω ω γω∞ ⎡ ⎤ ⎢ ⎥ = − ≡⎢ ⎥ − +⎢ ⎥ ⎢ ⎥⎣ ⎦ − − + ∑ 22 2 0 0 ˆ p exnq m ω ε ε = → 6EECS 598-002 Nanophotonics and Nanoscale Fabrication by P.C.Ku Transverse and longitudinal vibrations Longitudinally vibrated SHO’s Vertically vibrated SHO’s 7EECS 598-002 Nanophotonics and Nanoscale Fabrication by P.C.Ku Transverse and longitudinal polaritons ( ) 0 0 0 0 or 0 D E k E k E ε ε ε ∇⋅ = ⇒∇⋅ = ⇒ ⋅ = ⇒ ⋅ = = For homogeneous media: Normally EM wave couples only to transverse SHO’s unless the dielectric constant vanishes. 10EECS 598-002 Nanophotonics and Nanoscale Fabrication by P.C.Ku Orders of magnitude At optical frequencies, k=ω/c~107. For typical crystal lattice, π/a~1010. Only optical phonons couple to the light. 0 For optical branch: u v For acoustic branch: u 1 v k M m ≈ ≈ − ≈ Can generate the dipole moment 11EECS 598-002 Nanophotonics and Nanoscale Fabrication by P.C.Ku Examples of phonon dispersion curves silicon GaAs Taken from P. Yu and M. Cardona. 12EECS 598-002 Nanophotonics and Nanoscale Fabrication by P.C.Ku Dispersion curve for phonon polaritons ω k Photons In free space 2 2 0 p LOω ω ω+ = 0 TOω ω= Photon-like but with strong phonon influence Free-space-photon-like 15EECS 598-002 Nanophotonics and Nanoscale Fabrication by P.C.Ku Hot carriers relaxation processes k Carrier capture Phase relaxation Thermalization Recombination (T1~ns) T2~100fs - ps 16EECS 598-002 Nanophotonics and Nanoscale Fabrication by P.C.Ku Size dependence (quantum confinement) g(E) = Density of states Eg E g(E) Eg E g(E) Eg E g(E) Eg E g(E) bulk sheet wire dot 3D 2D 1D 0D 17EECS 598-002 Nanophotonics and Nanoscale Fabrication by P.C.Ku Exciton absorption in low-dim structures 2 3 , 1 , 14 d d B n B nE E= == Exciton binding energy: 2D: 1D: a0=exciton Bohr radius~100A Exciton absorption: 2D: 1D:
