Solitary vortices in two-dimensional waveguide matrix

Abstract

We consider the nonlinear propagation of an optical beam in a two-dimensional waveguide matrix, which is described by the discrete nonlinear Schrödinger equation with a self-focusing nonlinearity. Our study focuses on the stability domain of the discrete vortex solitons with its topological invariant S equal to 1. Such domain is identified with the propagation constant k and the coupling constant C. Our simulations show that there is a critical value C cr for any fixed value of k. At C ≤ C cr , the stable domain is continuous. However, at C > C cr , the stable domain becomes discontinuous and fuzzy. The distribution of the continuous stable regions is identified and plotted. Moreover, we give the relation of the total power P to C and k, which enable us to figure out the continuous stability area through the (P, C) plane.