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

Philosophical Transactions of the Royal Society of London Series A Mathematical and Physical Sciences

Transient noise-induced optical bistability

G. Broggi, L. A. Lugiato

Published Dec 18, 1984• 11 citations
Publisher

Abstract

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.

DOI
10.1098/rsta.1984.0132

Related papers

Transient noise-induced optical bistability

G. Broggi, L. A. Lugiato

We solve numerically the simplest Fokker-Planck equation which describes the effects of amplitude noise in absorbitive optical bistability. When the semiclassical solution exhibits critical slowing down, the probability distribution becomes two-peaked in a sizable time interval during the approach to the one-peaked steady-state distribution. The switching time undergoes considerable fluctuations, and on the average it is shorter than predicted by semiclassical theory. These noise effects seem accessible to experimental observation.

Physical Review A•May 1, 1984•48 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

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

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 bimodality in optically bistable systems

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

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.

Physical Review A•Nov 1, 1985•39 citations

Optical bistability switching with external noise

E. Arimondo, Didier Dangoisse, Leone Fronzoni +2 more

In an optically bistable system the switching time, i.e., the time required to switch the system between the off and on states, is a sensitive measure of noise and fluctuations. For a control parameter close to the threshold of the bistable operation, the critical slowing down takes place and large fluctuations in the switching times are originated.

International Laser Science Conference•Jan 1, 1986•1 citation
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.
We solve numerically the simplest Fokker-Planck equation which describes the effects of amplitude noise in absorbitive optical bistability. When the semiclassical solution exhibits critical slowing down, the probability distribution becomes two-peaked in a sizable time interval during the approach to the one-peaked steady-state distribution. The switching time undergoes considerable fluctuations, and on the average it is shorter than predicted by semiclassical theory. These noise effects seem accessible to experimental observation.
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.
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).
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.