Abstract

In an earlier numerical study¹ it was shown that, under self-focusing conditions, transverse spatial rings slowly evolved across the on spot of a switched-on beam in a bistable ring resonator. Subsequently, it was established that these structures were solitary waves of the nonlinear propagation equation.² These studies assumed a single transverse spatial dimension, and with this restriction it was also found that the solitary wave’s period doubled while maintaining spatial coherence. Solitary waves evolve across the beam for saturable media, whereas solitons are expected for Kerr media. In the latter case the nonlinear wave equation describing propagation through a Kerr medium is identical to the nonlinear Schrödinger equation, an integrable system with soliton solutions.² In this present work we extend our numerical study to the full three-dimensional problem (two transverse dimensions) and study the time evolution of an incident Gaussian beam as it switches to the high transmission state. Both saturable and Kerr media are studied, and both the dynamical evolution and asymptotic state of the system are significantly different for each case. We emphasize that these structures appear within the nonlinear medium and that they are not far-field patterns!

© 1984 Optical Society of America