The analysis of Bespalov and Talanov concerning small scale self-focusing or filamentation effects for plane waves is generalized to a tapered beam case in this paper. A model of nonlinear phase and amplitude perturbations different from Siegman’s is suggested. The previous conclusion that self-focusing is very ineffectual for strongly tapered, both divergent and convergent, beams in optical Kerr media as compared to small-scale self-focusing in plane waves is found to be inappropriate. Moreover, the different conditions of phase matching in cases of cylindrical and spherical waves are explicated, which could throw some light on the issue.
© 2012 Optical Society of America
Original Manuscript: July 11, 2012
Manuscript Accepted: August 2, 2012
Published: August 27, 2012
Huaiting Jia, Bing Xu, Fang Wang, and Lidan Zhou, "Small-scale self-focusing in a tapered optical beam," Appl. Opt. 51, 6089-6094 (2012)