Optical Properties of Free-Electron-Like Foils

Abstract

The dielectric response of a noninteracting electron gas contained within a thin foil of thickness $D$ has been calculated in the long-wavelength limit for long-mean-free-path electrons undergoing specular reflection at the boundaries. Sinusoidal wave functions are employed to account properly for the boundary conditions. The longitudinal response to $p$- polarized light leads to an absorbing power which is an approximate superposition of the ordinary Drude contribution, proportional to ${\tau }^{-1\mathrm{}}$, and a collisionless contribution, proportional to $D^{-1\mathrm{}}$. The thickness-dependent conductivity is predicted to be of the same order of magnitude as the bulk experimental conductivity of the alkali metals at low temperature in the near infrared spectral region for foils with $D\simeq 300$ Å. This contribution should also be detectable from optical polarization studies on $n$-doped semiconductor foils, but appears to be masked by the Drude background for other free-electron-like films.