Bifurcations to chaos in optical bistability

Abstract

The details of the time-dependent output from a hybrid optical bistable device are investigated in the regime where the delay time of the feedback signal is much larger than the response time of the device (determined by electrical bandwidth of the feedback loop). The delayed feedback is produced by placing a computer equipped with fast $A-D$ and $D-A$ converters in the feedback loop. This bistable system exhibits periodic and chaotic instabilities as predicted by Ikeda. In particular, as the input intensity is increased, the device output goes through a series of bifurcations (second-order nonequilibrium phase transitions). First, the initially stable output changes to a periodic output (a square wave) followed by a second periodic region whose period is twice that of the previous region. Up to this point, the system behavior is in agreement with the period-doubling scheme of Feigenbaum. However, the period doubling which is predicted next is only rarely observed. Instead the system usually goes over into chaotic behavior. Within the chaotic region, the device largely follows the reverse bifurcation scheme of Lorenz. In addition, there is a small domain of frequency-locked behavior that exists within the chaotic domain. These bifurcations are not only of fundamental interest but may find applications in practical optical devices.