In this paper we deduce a vectorial non-paraxial equation describing the se
lf-focusing of light in a homogeneous isotropic Kerr medium. The equation i
s derived via transformation to the spatial frequency domain, which clarifi
es the physical nature of the approximations made. We also present numerica
l solutions for a linearly polarized Gaussian input beam and discuss the de
pendence of the self-focusing length on beam width and input power. (C) 200
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