Propagating photonic modes below the gap in a superconducting composite

We show that there are propagating modes for electromagnetic waves in a periodic array of superconductor and insulator with two-dimensional symmetry. For waves polarized perpendicular to the array, the vector Maxwell equations reduce to a scalar wave equation for the nonvanishing component of electric field. This reduction is still valid if the superconducting component has an anisotropic dielectric tensor, as in the high-Tc CuO-based materials. Using the Mattis-Bardeen form for the finite-frequency conductivity of a superconductor below its gap, the wave equation becomes formally identical to a Schr\"odinger equation. We give numerical examples for the case of a two-dimensional array of air cylinders embedded in a superconducting host. The results suggest that these modes may be observable in a highly anisotropic high-Tc superconductor with c axis parallel to the direction of wave polarization.