Conducting media with spatial dispersion in a microwave field: eigenvalue problem for permittivity operator

Abstract

Conducting media with the spatial dispersion may be described formally by a singly operator – an operator of a dielectric permittivity, which completely defines a microwave response of conductors with the spatial dispersion. So the eigenvalue problem for the permittivity operator of conductors and superconductors possessing a strong spatial dispersion at low temperatures is of a great importance since the corresponding solutions are the stable waves for the constitutive equation in a self-consistent microwave field. Here a wave problem is formulated to search the solutions, which correspond to the eigenvalues of a permittivity operator, similar to the relationship and the general solutions are obtained. A significant role of the spatial-type conjugated. Dispersion relationship and general solutions are obtained. A significant role of the spatial-type force resonances is considered. Conditions for the spatial resonances are derived. The obtained resonances include particular solutions corresponding to the related to a polarization, two of which correspond to waves with an amplitude increasing into the depth of a conductor, and two else describes solutions with unusual properties.