Quantization of electromagnetic modes in a hyperbolic negative-index layered superconductor slab

We theoretically study the infrared reflectivity and transmissivity of a high-temperature layered superconductor slab. Both infrared spectra exhibit very narrow Fabry-Perot resonances associated with the quantization of the wave vector of the TM electromagnetic modes. The resonances are observed in a pass band where the refractive index of the layered superconductor is negative. The pass band of negative dispersion is above the Josephson plasma frequency which appears in the expression for the effective permittivity component, corresponding to the direction perpendicular to the layers. It was found that the Fabry-Perot resonances undergo a blue shift as the slab thickness or the angle of incidence are increased. Moreover, the quantized electromagnetic modes turn out to be quasi-longitudinal because of the strong anisotropy of the infrared dielectric response of the layered superconductor.