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 $ω_p$ below the superconducting gap. Propagation is assumed to be parallel to the surfaces in the dielectric medium, where amplitudes decay exponentially.Below $ω_p$, the amplitude also evanesces inside the film, and we retrieve the experimentally measured lower dispersion relation branch, $ω\propto \sqrtβ$, and the recently proposed higher frequency branch, $ω\propto 1/\sqrtβ$.Above $ω_p$, 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 $ω\approx ω_p \sqrt{ 1+ (β/β_0)^2}$, where $β_0$ is discussed here.