Propagation of (2 + 1)-dimensional solitary waves in dissipative/active saturable nonlinear media

Abstract

We investigate the propagation of (2 + 1)D bright solitary waves in a saturable nonlinear medium perturbed with gain or loss. We find that in the presence of loss (gain) the amplitude and width of the (2 + 1)D bright solitary waves may both increase (decrease) with their product varying adiabatically during evolution. This is in contrast to the (1 + 1)D Kerr bright (dark) solitons or (2 + 1)D vortex solitons whose amplitude decreases (increases) at the same rate as the width increases (decreases), keeping their product unchanged with the propagation distance. For a very weak nonlinear saturation approaching Kerr nonlinearity, it is found that the amplitude and the width change at a rate faster than the (1 + 1)D Kerr bright and dark solitons, whereas their variation in highly saturable media is slower than the (1 + 1) or (2 + 1)D Kerr dark solitons. In a medium of moderate nonlinear saturation, the beam width and amplitude may vary in the way following that of high nonlinear saturation or weak nonlinear saturation or a combination of the two, depending on loss or gain and propagation distance.