Fourier analysis of non-paraxial self-focusing

In this paper we deduce a vectorial non-paraxial equation describing the self-focusing of light in a homogeneous isotropic Kerr medium. The equation is derived via transformation to the spatial frequency domain, which clarifies the physical nature of the approximations made. We also present numerical solutions for a linearly polarized Gaussian input beam and discuss the dependence of the self-focusing length on beam width and input power. (C) 2000 Elsevier Science B.V. All rights reserved.