Chap 23 Optical properties of metals and inelastic scattering Propagation of EM wave Plasma wave Optical properties Angle resolved photo-emission M.C. Chang Dept of Phys

Attenuation of EM wave (I) Attenuation of plane wave due to nI Reflectivity (or reflectance, normal direction)

Attenuation of EM wave (II) Decay of intensity (energy density) Penetration depth Power loss (per unit volume) dielectric function for metal

(A) Low frequency (Hagen-Ruben’s) regime ωτ<<1 τ ～10-13~10-14 ∴ω can be as large as 100 GHz (H.W.) Plasma edge transparent Dressel and Gruener, p.99, 308

Longitudinal EM wave (plasma) ωτ >>1 EM wave is damped Signal blocked Longitudinal EM wave (plasma) Plasma edge EM wave propagates with phase velocity

Plasma wave Al For copper, n=81022 /cm3 ωp=1.6×1016/s, λp=1200A (ultraviolet) A simple picture of plasma oscillation: εcore correction 10.3 eV surface plasmon 15.3 eV bulk plasmon Al

Dynamic susceptibility (long wavelength limit) (chap 20) For longitudinal EM wave → Energy dispersion for the plasma wave 2D: for long wavelength There is NO plasma gap Collective excitation vs quasiparticle (e-h pair) excitation in metal plasma excitation decays into pair excitations e-h continuum

Optical properties of alkali metals Reσ for Na, K, and Rb 0.64 εF Drude peak Fermi energy Na: 3.24 eV K: 2.12 eV Rb:1.85 eV T. Inagaki et al , Phys. Rev. B 13, 5610 (1976). N.V. Smith PRB2 2840 1970 n=(ε0+4πiσ/ω)1/2 Absorption ～ Im(n) ～ Re(σ)

Tremblay A.M.- N-corps, p.114

Optical properties of noble metals Cu: low threshold (2 eV, orange) d →s copper s →s Ag: high threshold (4 eV, ultraviolet) s →s d →s d→s d →s Empty lattice http://www.webexhibits.org/causesofcolor/9.html