Optical properties of layered superconductors near the Josephson plasma resonance

We study the optical properties of strongly anisotropic crystals with spatial dispersion and show that the usual Fresnel approach becomes invalid near frequencies where the group velocity of the wave packets inside the crystal vanishes. Near these special frequencies the reflectivity depends on the atomic structure of the crystal provided that disorder and dissipation are very low. This is demonstrated explicitly by a detailed study of layered superconductors with identical or two different alternating junctions in the frequency range near the Josephson plasma resonance. Accounting for both inductive and charge coupling of the intrinsic junctions, we show that multiple modes are excited inside the crystal by the incident light, we determine their relative amplitude by the microscopic calculation of the additional boundary conditions, and finally obtain the reflectivity. Spatial dispersion also provides a method to stop light pulses, which has possible applications for quantum information processing and the artificial creation of event horizons in a solid.