Theory of the propagation of high-power laser radiation in a nonlinear medium

The propagation of high-power laser beams in media with the Kerr nonlinearity is discussed allowing for various types of nonlinear absorption. A parabolic equation for the complex amplitude of the electric field is derived from the Maxwell equations under conditions of greatest practical interest. This equation is analyzed under steady-state conditions and for laser pulses of 10$^{-8}$ sec or shorter duration. A numerical solution of the steady-state problem shows that a multifocus structure appears in a beam of supercritical power. It is shown that this multifocus structure is universal, i.e., it appears irrespective of the nature of the nonlinear absorption in the medium and of other factors allowed for in the theory. The structure of the foci is studied in detail. Within light beams such foci usually move at velocities close to that of light. A theory of moving foci is presented. The trajectories of the motion of the foci and their parameters are calculated and the broadening of the laser pulse spectra due to the motion of the foci is evaluated. Explanations are given of various experimental data on the stimulated scattering, optical breakdown, and broadening of the laser radiation spectra.