Many-parameter routes to optical turbulence

The output of an externally pumped passive nonlinear-optical ring resonator is known to exhibit chaotic dynamics under variation of one or more external control parameters. The dynamics of the internal transverse laser beam profile is described, in the good-cavity limit, by an infinite-dimensional discrete-time map in function space. We find that the asymptotic dynamical behavior of the internal resonator field is in marked contrast to earlier plane-wave predictions. Instead, self-focusing, self-defocusing nonlinearities, and linear diffraction, combined with the pump and feedback of the ring resonator, give rise to strong spatial modulation of the transverse profile. For a self-focusing nonlinearity, spatially coherent robust transverse solitonlike structures persist even though the beam is undergoing temporally chaotic motion. Using attractor embedding techniques on our numerical solutions, we isolate distinct routes to optical turbulence under variation of a number of different control parameters. In particular, we provide examples of Ruelle-Takens-Newhouse sequences, intermittency, and a nongeneric bifurcation involving period doubling of invariant circles. A main result of the paper is that many few-dimensional attractors can coexist in different regions of the infinite-dimensional phase space at fixed values of the external control parameters. These attractors are accessed by varying the systems initial conditions and can, under variation of an appropriate control parameter, independently undergo transition to chaos. Interaction between neighboring attractors appears to be responsible for numerically observed departures from generic behavior. We note striking similarities between some of our numerically generated instability sequences and recent experimental observations in low-aspect-ratio fluid systems. © 1986 The American Physical Society.