Eigenvalue problem for permittivity operator of conductors with the spatial dispersion in a microwave field

Abstract

Conducting media with spatial dispersion may be described formally by the single operator – operator of dielectric permittivity, which, as it is well known, completely defines the microwave response of conductors with spatial dispersion. So the eigenvalue problem for permittivity operator of conductors and superconductors possessing strong spatial dispersion at low temperatures is of a great importance since the corresponding solutions are the stable waves for constitutive equation in a self-consistent microwave field. Here a wave problem is formulated to search the solutions, which correspond to the eigenvalues of permittivity operator, similar to the problem of wave propagation in hollow waveguides and resonators, but non-self conjugated. Dispersion relations and general solutions are obtained. Significant role of the spatial-type force resonances is considered. Conditions for the spatial resonances are derived. The obtained resonances includes particular solutions corresponding to traditional surface impedance for anomalous skin effect, surface impedance of superconductor, as well as four novel solutions, obviously related to polarization, two of which correspond to the waves with amplitude increasing into the depth of conductor, and two else describe solutions with unusual properties.