Abstract

Since Ikeda’s earlier prediction,¹ numerous models have been suggested that predict chaotic dynamics in a nonlinear optical scenario. Most models assume a plane-wave approximation and rely on local linear stability analysis plus numerical solutions at interesting parameter values. In the present work we adopt a more general and more powerful approach of global-phase-space analysis. Returning to the plane-wave model of a bistable ring cavity studied by Ikeda we show that a whole series of new dynamical phenomena can be predicted for this system. Most notable of these phenomena are (1) the preimage of the chaotic attractor is present in the complex E plane (phase plane) long before one reaches the accumulation point of a period-doubling cascade, (2) multiple attracting periodic cycles with their own basins of attraction can coexist in the phase plane at certain parameter values. These additional cycles are created via saddle-node bifurcations in the vicinity of homoclinic tangencies, and (3) explosion (interior crisis) and destruction (boundary crisis) of strange attractors occur as a result of heteroclinic orbits’ being formed linking the basins of coexisting attractors.

© 1984 Optical Society of America