Normal and anomalous dispersion of weakly non-linear localized modes in a slab of a layered superconductive material

Weakly nonlinear localized electromagnetic modes in a slab of a layered superconductor are investigated theoretically. It is assumed that the slab is located in a homogeneous dielectric environment, the superconducting layers are oriented perpendicular to the slab surface and the modes propagate across the layers. Owing to the strong anisotropy of the Josephson plasma in layered superconductors, the localized modes can show unusual dispersion properties. The electromagnetic field in a layered superconductor is determined by the distribution of the gauge-invariant phase difference of the order parameter that satisfies the set of coupled sine- Gordon equations. Based on the solutions of these equations and also on the Maxwell equations for the dielectric environment, it is possible to obtain dispersion relations for the localized electromagnetic modes. It is shown that the dispersion properties of the localized modes prove to be anomalous within a certain range of the parameters. Specifically, there have been found points on the dispersion curves at which the group velocity of the modes turns to zero. In addition, the nonlinearity results in that the dispersion relations contain the localized mode amplitude. Owing to the fact that the dispersion relations in the nonlinear case contain the localized mode amplitude, it makes possible to observe the stop-light effect for the localized modes in a slab of a layered superconductor. © 2018 by Begell House, Inc.