Solitons and chaos in a ring optical cavity by numerical simulation

Abstract

It is well known that the nonlinear Schrodinger equation (GNLSE) has bistable soliton -- like solutions for a nonlinear form of the functions f(E 2 ). Such kind of solitary bistable waves doesn't appear in the case of the Kerr -- like nonlinearities of the medium. The stability of these solitary bistable waves was later on studied by Enns et al., who have established, by numerical simulations, the soliton- like nature of these solutions for a certain category of functions f(E 2 ). Our numerical simulations, based on similar mathematical models are presented in this work. By comparing our results to those obtained by Enns, Rangnekar and Avity, as well as to Ikeda's results, who have used a similar model, we have obtained results which are in good agreement with theirs, for small values of A. For larger values of A, the system doesn't return to period 1, but continues to have a chaotic behavior. Such kind of bistable soliton solutions for the GNLSE equation is very important for several applications, such as: optical fiber communications, optical switching, bistable optical devices, etc.