Plasma waves in anisotropic superconducting films below and above the plasma frequency

We consider wave propagation inside an anisotropic superconducting film sandwiched between two semi-infinite nonconducting bounding dieletric media such that along the c axis, perpendicular to the surfaces, there is a plasma frequency omega(p) below the superconducting gap. Propagation is assumed to be parallel to the surfaces in the dielectric media, where amplitudes decay exponentially, Below omega(p), the amplitude also evanesces inside the film. and we retrieve the experimentally measured lower dispersion relation branch, omega(proportional to)root beta, and the recently proposed higher frequency branch, omega(proportional to)1/root beta. Above omega(p), propagation is of the guided a wave type, i.e.: a dispersive plane wave confined inside the film that reflects into the dielectric interfaces, and the modes are approximately described by omega approximate to omega(p) root 1 + (beta/beta(0))(2), where beta(0) is discussed hen.