ITERATIVE MODEL FOR WAVE PROPAGATION IN KERR MEDIA

An iterative method is developed to find exact solutions of wave propagation problems in Kerr media, taking into account backscattering effects. The method is based on the TE-mode Fourier-expansion eigenmode technique in the rigorous diffraction theory of gratings, but it permits an accurate treatment of non-periodic geometries as well. Self-focusing by a slab of Kerr medium is used to demonstrate the method and to compare it with the propagating-beam solution of the nonlinear Helmholtz equation, which ignores backscattering. The latter is shown to fail completely in many geometries, in particular, if the index modulation is high.