Propagation of a Gaussian light beam in a nonlinear medium with a complex susceptibility

The problem of transformation of the parameters of a Gaussian light beam in a nonlinear medium with a complex susceptibility is solved. The parabolic approximation for the wave equation is employed. The results obtained can be used in the design of resonators and waveguides with nonlinear components. A study is made of the influence of the complex part of a nonlinear susceptibility of a substance on the threshold conditions for the self-focusing in the case of resonant absorption in a two-level system. It is shown that in this case it is possible to expect self-focusing of radiation on the low-frequency side of an absorption line.