Chaos in Nonlinear Optics

Abstract

There has recently been great interest in the field of deterministic chaos. By deterministic chaos, one refers to the situation in which the output of a physical system fluctuates erratically in time, even though the system is governed by deterministic equations. It is known theoretically that chaotic behavior can occur only in nonlinear systems. We have been particularly interested in studying chaos in nonlinear optical systems.1 Our motivation for studying chaos in nonlinear optical systems has been two-fold: One is that studies of deterministic chaos can provide some insights into the origin of uncertainty in physics, and optical systems provide good systems in which to perform exacting studies of such effects. The other reason is that chaos can lead to limitations in the performance of practical optical devices. To illustrate this latter point, we consider some hypothetical optical device which was intended to provide a steady output but which instead produces the highly erratic output illustrated in Fig. 1. In order to stabilize the output of such a device, it is necessary to know whether the fluctuations which appear in the output are the result of random noise or of deterministic chaos, because the proper procedure for stabilizing the output would be different in the two cases. If the fluctuations are due to random noise, one might stabilize the output by shielding the system from its environment, whereas if these fluctuations are due to deterministic chaos one would need to decrease the magnitude of the nonlinearity in order to reduce the fluctuations.