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 non-conducting 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 medium, where amplitudes decay exponentially.Below \(\omega_p\), the amplitude also evanesces inside the film, and we retrieve the experimentally measured lower dispersion relation branch, \(\omega \propto \sqrt{\beta}\), and the recently proposed higher frequency branch, \(\omega \propto 1/\sqrt{\beta}\).Above \(\omega_p\), propagation is of the guided 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 \(\omega \approx \omega_p \sqrt{ 1+ (\beta/\beta_0)^2}\), where \(\beta_0\) is discussed here.