Gaussian beam evolution in logarithmically saturable nonlinear media

The method of paraxial complex geometrical optics (PCGO) is presented, which describes Gaussian beam (GB) diffraction and self-focusing in smoothly inhomogeneous and nonlinear media of cylindrical symmetry. PCGO reduces the problem of Gaussian beam diffraction in nonlinear and inhomogeneous media to the system of the first order ordinary differential equations for the complex curvature of the wave front and for GB amplitude, which can be readily solved both analytically and numerically. The power of the PCGO method is exemplified by GB evolution in a logarithmically saturable medium with a defocusing refractive profile. The solutions obtained by the PCGO method are compared with numerical results of a Nonlinear Schrodinger Equation by the beam propagation method (BPM).