Soliton Propagation in Inhomogeneous Media with Sharp Boundaries

Abstract

Wave beam propagation in the smoothly nonuniform medium can be described in the framework of geometrical optics when the wave length is small in comparison with characteristic scales of the problem, namely, size of the beam, size of inliomogeneities etc. The propagation trajectories of linear and nonlinear wave beams do not differ when the nonlinearity coefficient does not depend on coordinates. However, in a case of sharp variations of the medium properties, especially on the boundary of two media, when the dielectric permittivity of the medium is described by discontinuous function, the behavior of the nonlinear wave beam considerably differs from the linear description of wave fields [1–5]. In the linear case the field on the boundary is splited on the reflected field and the transmitted field. The nonlinear beam practically either completely reflects, or completely transits into other medium, since the nonlinear focusing tries to conserve the concentration of the wave field. This feature of nonlinear fields allows to use the geometrooptical approach for the description of the wave packet propagation in the strongly nonuniform medium with sharp gradients of the dielectric permittivity.