Nonlinear localized modes in a plate of a layered superconductor

Abstract

We present a theoretical study of nonlinear localized electromagnetic modes in a plate of a layered superconductor. Despite the symmetry of the system, the plate is assumed to be in a homogenous dielectric environment, with superconducting layers lying perpendicular to the plate surface and the modes propagating across the layers. Due to the nonlinearity of the Josephson plasma, the plate can contain localized modes that are symmetric, antisymmetric and nonsymmetric with respect to the magnetic field. It is shown that under certain conditions the dispersion of the localized modes can be anomalous whereas the group velocity vanishes. By virtue of the nonlinearity, the dispersion relations contain the amplitude of the localized mode. This opens the possibility of observing the stopping of mode light in a plate of a layered superconductor.