Average radius of a beam in the case of resonant steady-state self-focusing and weak nonlinearity saturation

An analysis is made of resonant self-focusing of high-intensity laser radiation in a medium consisting of two-level atoms and exhibiting a homogeneously broadened transition. An ordinary nonlinear differential equation with exponential factors is used to describe the change in the average radius of the beam. It is shown that in the absence of absorption this average radius oscillates periodically. The spatial period of the oscillations is determined. Calculations are made of the transverse and longitudinal dimensions of a caustic of nonlinear foci. It is shown that the dependence of these dimensions on the detuning from a resonance is V-shaped, whereas the dependences on the density of the medium, on the radius of curvature of the beam, and on the average radius of the beam at the entry to the medium are monotonic.