Dielectric response functions in the problem of longitudinal collective mode excitation in superconductors

General methods of the electrodynamics of media with spatial and frequency dispersion are used to develop a formalism for the dielectric functions of the response of a superconducting metal to electromagnetic perturbations. The transformation of electromagnetic waves into long-wave oscillations of the longitudinal field in a superconductor is investigated. The temperature and frequency dependences of the collective mode contribution to the superconductor surface impedance are found. Resonant excitation of a collective mode in superconducting samples of finite size is predicted, which may result in selective transparency of superconducting films.