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

摘要

Conducting media with the spatial dispersion may be described formally by a single 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 the permittivity operator, similar to the problem of the wave propagation in hollow waveguides and resonators, but non-self conjugated. Dispersion relations 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 surface impedances for the anomalous skin effect, for superconductors, as well as four novel solutions, obviously related to a polarization, two of which correspond to waves with an amplitude increasing into the depth of a conductor, and two else describe solutions with unusual properties.