Abstract

The phenomenon of self-trapping has been extensively studied in the past for both cubic and saturable nonlinearity.¹ In this paper, by using a modified nonlinear Schrodinger equation, we analyze the possibility of a self-trapped beam propagating in a weakly saturated amplifying/absorb- ing medium. We consider the case of only one transverse dimension (for example, a semiconductor laser medium or a nonlinear planar waveguide structure such as the one used by Maneuf and Reynaud² for their recent observation of spatial solitary waves). A simple exact analytical solution is obtained with a sechlike amplitude profile and a nonuniform phase front. Near this axis, this wavefront is parabolic but becomes progressively linear off-axis. Selftrapping is also predicted for a defocusing nonlinearity. The stability of the solution is investigated by using the adiabatic approximation as well as by solving the equation of propagation numerically.

© 1989 Optical Society of America