title: Self-similar parabolic beam generation and propagation.
abstract: The (1+1) -dimensional and (2+1) -dimensional amplified nonlinear Schrödinger equations incorporating diffraction, Kerr nonlinearity, and gain are solved analytically and numerically. An asymptotic solution is found corresponding to self-similar propagation of a beam with parabolic amplitude and phase profiles. While the (1+1) -dimensional solution is directly analogous to parabolic pulse propagation in nonlinear dispersive media, the existence of self-similar propagation in (2+1) dimensions is a nontrivial question, given that spatial solitons are unstable in bulk media with nonsaturating nonlinearities. We show that self-similar parabolic beams are possible in such media with gain and a negative nonlinear index.
authors.affiliation: FOCUS Center and Center for Ultrafast Optical Science, University of Michigan, 2200 Bonisteel Boulevard, Ann Arbor, Michigan 48109-2099, USA.
authors.forename: Guoqing
authors.initials: G
authors.lastname: Chang
authors.forename: Herbert G
authors.initials: HG
authors.lastname: Winful
authors.forename: Almantas
authors.initials: A
authors.lastname: Galvanauskas
authors.forename: Theodore B
authors.initials: TB
authors.lastname: Norris