Gaussian light beam in a lens-like medium with a nonlinear complex susceptibility

An analytic solution is obtained of the equation for a Gaussian light beam propagating in an inhomogeneous medium with a nonlinear complex susceptibility. It is shown that an allowance for nonlinear absorption alters greatly the condition for the waveguide propagation regime. The limits of validity of the parabolic approximation for the wave equation are identified. It is shown that self-focusing is possible even in the case when the real part of the nonlinear susceptibility is negative.