1. 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

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

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

4. (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

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

6. 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

7. 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

8. 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 PRB
n=(ε0+4πiσ/ω)1/2
Absorption ～ Im(n) ～ Re(σ)

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

10. 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