NONLINEAR PROPAGATION AND TRANSFORMATION OF ARBITRARY LASER-BEAMS BY MEANS OF THE GENERALIZED ABCD FORMALISM

The evolution of non-Gaussian and nonspherical high-power laser beams in cubic nonlinear media is described by means of their mean or gross parameters: width, mean curvature radius, and quality factor. The infl uence of the beam over its own propagation is contained in a new mean parameter that measures the ability of a beam to build its own wavegui de. Beam quality and threshold power for self-focusing are connected. The ABCD and invariance laws for modified complex beam parameter and q uality factor allow one to transform in one step the mean beam paramet ers through a sequence of nonlinear propagations, lenses, mirrors, and nonlinear quadratic graded index.