Effects of Nonlinearly Induced Inhomogeneity on Solitary Wave Formation

Abstract

The chapter presents a new scalar model of optical beam propagation in nonlinear media, as it is developed in [1, 2, 3, 4]. The model addresses narrow beams and stresses on nonlinearly induced diffraction, an effect of medium inhomogeneity introduced by the spatial variation of the nonlinear polarization. Strarting from the vector nonparaxial model of beam propagation in nonlinear media, it is shown that not the vectorial nature of the carrier wave field, but a scalar effect which comes out from the (div/E)-term in the wave equation and has the meaning of nonlinear diffraction, controls predominating over the nonparaxiality, the balance between diffraction and nonlinearity in the formation of the spatial solitons. The conclusion is based on analytical and numerical solutiuons of the nonlinear equations for the beam envelopes and on analysis of the wave power conservation laws derived. Both third (Kerr-type)- and second- order nonlinearities are treated as well as both planar waveguides and bulk media are covered. Single beam propagation and beam interaction and coupling are described. New solitary-wave solutions are presented.