Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

Physical Review A

Transient bimodality in optically bistable systems

G. Broggi, L. A. Lugiato, A. Colombo

Published Nov 1, 1985• 39 citations
Publisher

Abstract

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.

DOI
10.1103/physreva.32.2803

Related papers

Study of fluctuations in transient optical bistability

Wulfhard K. Lange, Fedor M. Mitschke, R. Deserno +1 more

The effect of external noise on the dynamic behavior of an intrinsic optical-bistable system is studied experimentally. Under conditions of critical slowing down we observe a transient bimodality in the intensity distribution as well as a reduction of the switching delay due to fluctuations. Our experimental results are in good qualitative agreement with theoretical predictions.

Physical Review A•Aug 1, 1985•35 citations

Transients in optical bistability: Experiments with external noise

Fedor M. Mitschke, R. Deserno, J. Mlynek +1 more

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.

IEEE Journal of Quantum Electronics•Sep 1, 1985•30 citations

Theory of Transient Optical Bimodality

G. Broggi, Luigi A. Lugiato, A. Colombo

From a statistical viewpoint, the signature of optical bistability is the two-peaked character of its stationary probability distribution. However, the exceedingly long lifetime of the two metastable states makes the experimental observation very difficult. We recently showed (1) that the critical slowing down can produce the emergence of a double-peaked distribution during the transient, with a scenario that is accessible to experimental observation, a goal that has been brilliantly achieved by the Hannover group (2) using optically pumped sodium vapour. This phenomenon, called transient bimodality, is universal in the sense that it arises in all systems that, at a deterministic level, exhibit a long induction stage followed by a fast switching to the steady state (3). And, in fact, the Hannover team observed this phenomenon also in an electronic system (4).

Topical Meeting on Optical Bistability (OB)•Jan 1, 1985•0 citations

Transient noise-induced optical bistability

G. Broggi, L. A. Lugiato

Abstract We show that, as a consequence of critical slowing-down and noise, the intensity probability distribution becomes double-peaked during its approach to the single-peak steady-state distribution. Even for very low noise levels, the switching time undergoes remarkable fluctuations. On average it is shorter than predicted by the deterministic theory, hence noise counteracts, in part, critical slowing-down.

Philosophical Transactions of the Royal Society of London Series A Mathematical and Physical Sciences•Dec 18, 1984•11 citations

Noisy dynamics in optically bistable systems

E. Arimondo, Daniel Hennequin, P. Glorieux

Introduction Lasers are part of a large class of non-linear systems which covers a great deal of scientific domains, including physics, chemistry, biology, sociology, etc. All these non-linear systems have common properties and present universal features which become more and more extensive as new studies are performed. In recent years, the interest in these non-linear systems has considerably increased. In particular, it is now well established that the role of fluctuations in non-equilibrium systems is far more relevant than in systems at thermodynamical equilibrium, and the study of their influence on stationary and transient states has become very important. Among the different aspects presented by the non-linearity in lasers, two of them will be particularly studied here: (i) The first one is the optical bistability (OB). An optical system is bistable if it has two output states I for the same value of the excitation A over some range of excitation values (see Gibbs, 1985, for a recent review). A typical response curve of such a system is given in Figure 5.1. Here, the system is defined as bistable between A ↓ and A ↑ , where the effectively occupied state depends on the history of the input parameter (see the caption to Figure 5.1). If OB is a common phenomenon in different fields, the OB transient phenomena have far more general features.

Cambridge University Press eBooks•Apr 6, 1989•4 citations

Experimental studies of transient noise-induced bistability

Wulfhard K. Lange, Fedor M. Mitschke, R. Deserno +1 more

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.

International Meeting on Instabilities and Dynamics of Lasers and Nonlinear Optical Systems•Jan 1, 1985•0 citations
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.
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.
From a statistical viewpoint, the signature of optical bistability is the two-peaked character of its stationary probability distribution. However, the exceedingly long lifetime of the two metastable states makes the experimental observation very difficult. We recently showed (1) that the critical slowing down can produce the emergence of a double-peaked distribution during the transient, with a scenario that is accessible to experimental observation, a goal that has been brilliantly achieved by the Hannover group (2) using optically pumped sodium vapour. This phenomenon, called transient bimodality, is universal in the sense that it arises in all systems that, at a deterministic level, exhibit a long induction stage followed by a fast switching to the steady state (3). And, in fact, the Hannover team observed this phenomenon also in an electronic system (4).
Introduction Lasers are part of a large class of non-linear systems which covers a great deal of scientific domains, including physics, chemistry, biology, sociology, etc. All these non-linear systems have common properties and present universal features which become more and more extensive as new studies are performed. In recent years, the interest in these non-linear systems has considerably increased. In particular, it is now well established that the role of fluctuations in non-equilibrium systems is far more relevant than in systems at thermodynamical equilibrium, and the study of their influence on stationary and transient states has become very important. Among the different aspects presented by the non-linearity in lasers, two of them will be particularly studied here: (i) The first one is the optical bistability (OB). An optical system is bistable if it has two output states I for the same value of the excitation A over some range of excitation values (see Gibbs, 1985, for a recent review). A typical response curve of such a system is given in Figure 5.1. Here, the system is defined as bistable between A ↓ and A ↑ , where the effectively occupied state depends on the history of the input parameter (see the caption to Figure 5.1). If OB is a common phenomenon in different fields, the OB transient phenomena have far more general features.
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.