Small-scale self-focusing in a tapered optical beam.
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.