Chang Guoqing, Winful Herbert G, Galvanauskas Almantas, Norris Theodore B
FOCUS Center and Center for Ultrafast Optical Science, University of Michigan, 2200 Bonisteel Boulevard, Ann Arbor, Michigan 48109-2099, USA.
Phys Rev E Stat Nonlin Soft Matter Phys. 2005 Jul;72(1 Pt 2):016609. doi: 10.1103/PhysRevE.72.016609. Epub 2005 Jul 12.
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.
