Optical Properties of Crystals with Spatial Dispersion: Josephson Plasma Resonance in Layered Superconductors

Abstract

We derive the transmission coefficient, $T(ω)$, for grazing incidence of crystals with spatial dispersion accounting for the excitation of multiple modes with different wave vectors ${\bf k}$ for a given frequency $ω$. The generalization of the Fresnel formulas contains the refraction indices of these modes as determined by the dielectric function $ε(ω,{\bf k})$. Near frequencies $ω_e$, where the group velocity vanishes, $T(ω)$ depends also on an additional parameter determined by the crystal microstructure. The transmission $T$ is significantly suppressed, if one of the excited modes is decaying into the crystal. We derive these features microscopically for the Josephson plasma resonance in layered superconductors.

4 pages, 2 figures, epl.cls style file, minor changes