Large-amplitude electromagnetic waves in conductors with a nonparabolic charge carrier dispersion law

Abstract

The propagation of large-amplitude electromagnetic waves is studied theoretically for conductors with a peculiar relation between the carrier energy and quasi-momentum. An exact general solution for longitudinal waves has been obtained. Steady-state, monochromatic and some types of time-dependent solutions for transverse waves specified apart from integration constants have been constructed and analysed in great detail. It is shown that for certain amplitude values of transverse electromagnetic waves individual harmonic components can propagate in the same way as in a linear medium. A peculiar nonlinear resonance has been investigated, which brings about a discontinuity of the dielectric permeability at some point. It occurs in the propagation of transverse monochromatic waves in a conductor placed in a d.c. magnetic field. On the basis of exact particular solutions for the transverse waves, their envelope is studied. Expressions for simple waves of the envelope have been obtained. Conditions for their stability and for the formation of shock waves are formulated. The chaotic behavior of an electron plasma in a one-dimensional superlattice and in a semiconductor with a non-parabolic dispersion law, located in an external magnetic field and excited by an electromagnetic wave, is considered. The nonparabolicity. The interaction between nonlinear electromagnetic waves in an electron plasma with a charged particle dynamically stochasticized by these waves is studied.