title: Nonlinear propagation and transformation of arbitrary laser beams by means of the generalized ABCD formalism.
abstract: 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 influence 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 waveguide. Beam quality and threshold power for self-focusing are connected. The ABCD and invariance laws for modified complex beam parameter and quality factor allow one to transform in one step the mean beam parameters through a sequence of nonlinear propagations, lenses, mirrors, and nonlinear quadratic graded index.
authors.forename: M A
authors.initials: MA
authors.lastname: Porras
authors.forename: J
authors.initials: J
authors.lastname: Alda
authors.forename: E
authors.initials: E
authors.lastname: Bernabeu