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.
© 1993 Optical Society of America
Original Manuscript: July 16, 1992
Published: October 20, 1993
Miguel A. Porras, Javier Alda, and Eusebio Bernabeu, "Nonlinear propagation and transformation of arbitrary laser beams by means of the generalized ABCD formalism," Appl. Opt. 32, 5885-5892 (1993)