Nonlinear diffraction in inhomogeneous superlattice

We considered the propagation of laser monochromatic radiation in a superlattice that contains regions with an elevated concentration of carriers. The model of the energy spectrum of electrons is chosen in the strong coupling approximation. The electromagnetic field is described quasiclassically with Maxwell equations, which, as applied to the problem under study, are reduced to a non-one-dimensional sine-Gordon wave equation for the vector-potential. We analyzed the wave equation in the approximation of slowly varying amplitudes and phases and obtained and numerically solved an effective equation that describes the electromagnetic field in the superlattice. We studied different regimes of propagation of laser radiation, analyzed diffraction by regions with an elevated electron concentration.