Past exam of the quantum condensed matter course of the University of Cambridge / 2022 / Section B / 4 / f / Solution

At normal incidence from vacuum, the Fresnel equations give the reflectanceA good metal has $R$ close to one below its plasma frequency. At very low frequency the electromagnetic field penetrates only a skin depth; the local Drude limit gives $1-R\simeq \sqrt{8{ϵ}_0\omega /{\sigma }_0}$. In the collisionless negative-permittivity range the transmitted field is evanescent and reflection remains strong. Near the plasma edge the reflectance drops sharply; above it ${ϵ}_r^{\prime }>0$ and propagating waves become possible. In the ideal free-electron high-frequency limit,Finite damping rounds the plasma edge, and interband absorption changes the detailed response of actual metals.