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IEEE Journal of Quantum Electronics

Transients in optical bistability: Experiments with external noise

Fedor M. Mitschke, R. Deserno, J. Mlynek, Wulfhard K. Lange

Published Sep 1, 1985• 30 citations
Publisher

Abstract

The influence of noise on an optical bistable system in the vicinity of one of the bifurcation points is investigated by studying the transient response to a step input of light. The experiment is performed under absorptive conditions in a sodium-filled nonlinear Fabry-Perot in the bad cavity limit. Alternatively, a bistable electronic circuit (Schmitt trigger) is shown to exhibit the same type of behavior while admitting more detailed studies. On the monostable side of the bifurcation point, we observe a transient bimodality as well as a shift of the average switching delay to shorter times with increasing noise. Both results are in accord with a recent prediction by Broggi and Lugiato. We also present indications that the average switching time is smoothly connected with the lifetime of the metastable state on the bistable side of the bifurcation point.

DOI
10.1109/jqe.1985.1072841

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The influence of noise on an optical bistable system in the vicinity of one of the bifurcation points is investigated by studying the transient response to a step input of light. The experiment is performed under absorptive conditions in a sodium-filled nonlinear Fabry-Perot in the bad cavity limit. Alternatively, a bistable electronic circuit (Schmitt trigger) is shown to exhibit the same type of behavior while admitting more detailed studies. On the monostable side of the bifurcation point, we observe a transient bimodality as well as a shift of the average switching delay to shorter times with increasing noise. Both results are in accord with a recent prediction by Broggi and Lugiato. We also present indications that the average switching time is smoothly connected with the lifetime of the metastable state on the bistable side of the bifurcation point.
The role of external noise in the process of critical slowing down (CSD) has been analysed theoretically by Broggi and Lugiato/1/; these authors recently predicted a transient noise-induced optical bistability due to amplitude fluctuations in the light input. They found that under conditions of CSD the probability distribution of light field amplitudes becomes double-peaked in a sizeable time interval during the approach to the single-peaked steady state distribution. Moreover they found that in the presence of fluctuations the delay times τD observed in an experiment on CSD should have a broad distribution, which can be very asymmetric. With increasing noise levels the mean value of the delay time should be considerably shorter than in the deterministic case.
We analyze the main features of transient bimodality in optically bistable systems. This phenomenon is proved to exhibit a nonmonotonic behavior in its dependence on the noise level, because a decrease of noise first enhances and subsequently damps the transient bimodality. Hence we identify a range of noise levels which characterizes the phenomenon. In this range the most probable switching time exhibits a remarkably linear dependence on the logarithm of the noise parameter. We discuss the dependence of the phenomenon on the distance from the critical point, especially in connection with the experiments on critical slowing down. Our results show a very satisfactory qualitative agreement with the recent experiments on transient bimodality performed by Lange and collaborators. We argue that our picture holds in general for a large class of systems which exhibit the phenomenon of transient bimodality.
Introduction The transient behavior of nonlinear optical resonators which display bistability and its reaction to fluctuations of system parameters are of extreme importance in all possible applications of these devices. Moreover, however, studies on these processes may give insight into some more general aspects of the behavior of nonlinear dynamical systems. In fact it has been emphasized in the early stages of the development of the field that optically bistable systems, in a suitable model, may exhibit a first-order phase transition (Bonifacio and Lugiato, 1978). Since the threshold behavior of a laser can be described as an example of a second-order phase transition (Haken, 1964,1975; see also Haken, 1977), optical bistability in (passive) nonlinear resonators complements nicely lasers as nonlinear dissipative systems in optics. Both types of optical systems are easily accessible to measurements, and the time scales coming into play are convenient for detailed experimental studies of the dynamics. It is worth mentioning that there is a close connection between laser operation and optical bistability in nonlinear (passive) resonators (see Lugiato, 1984). The standard single-mode laser model with distributed losses (Haken, 1970; Sargent, Scully and Lamb, 1974) can be generalized to include the effect of an external field that continuously drives the atoms within the optical resonator. The standard model of absorptive bistability, the Bonifacio–Lugiato model, is a special case of this generalized model. It represents the situation of a pumping mechanism being absent.