NORMAL AND ANOMALOUS DISPERSION OF WEAKLY NONLINEAR LOCALIZED MODES IN PLATE OF LAYERED SUPERCONDUCTOR

Abstract

Weakly nonlinear localized electromagnetic modes in a plate of layered superconductor are theoretically studied. It is assumed that the plate is embedded in the uniform dielectric environment, the superconducting layers are perpendicular to the surface of the plate, and the modes propagate across the layers. Due to the strong anisotropy of the Josephson plasma in layered superconductors, localized modes can possess 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, which satisfies the system of coupled sin-Gordon equations. Based on the solution of these equations, as well as the Maxwell equations in the dielectric environment, dispersion relations can be obtained for localized electromagnetic modes. It is established that the dispersion of such localized modes turns out to be anomalous in a certain range of parameters. In addition, the points on the dispersion curves are found, at which the group velocity of the modes can vanish. In addition, the nonlinearity leads to the fact that the dispersion relations contain the amplitude of the localized mode. Due to the fact that in the nonlinear case the dispersion relations contain the amplitude of the localized mode, it is possible to observe the stop-light phenomenon for the localized modes in the layered superconductor plate.

Keywords

• anomalous dispersion
• layered superconductor
• localized modes