We present a new, to the best of our knowledge, formalism based on the propagation of variances in an ABCD optical system to study nonlinear effect in a Kerr medium. This theory, developed for the first order in the beam power, is applied to modal laser fields (Gaussian, Hermite–Gaussian, and Laguerre–Gaussian beams) and permits one to obtain a simple analytical formulation for self-focusing and Z-scan experiments, whatever the thickness of the nonlinear medium.
© 2007 Optical Society of America
Original Manuscript: September 27, 2006
Revised Manuscript: February 21, 2007
Manuscript Accepted: March 30, 2007
Published: July 19, 2007
Sylvain Rivet and Lionel Canioni, "Aberrationless theory of self-focusing via spatial and angular variances for modal laser fields," J. Opt. Soc. Am. B 24, 1901-1908 (2007)