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

Topical Meeting on Optical Bistability (OB)

A Saturable Interferometer Theory of Absorptive Optical Bistability

N. M. Lawandy, R. P. Willner

Published Jan 1, 1983• 0 citations
Publisher

Abstract

In this paper we will utilize the method of summing transmitted waves routinely used to analyze interferometer structures to develop an OB equation. The method yields a different state equation than the usual mean-field model. However, for small C values and or large input intensities a Taylor expansion of our state equation yields the mean field pure absorptive OB equation. Our equation also gives a different condition for hysteresis. Due to the simplicity of this approach which utilizes the sum of a geometric series, we are able to interrogate the system after any given number of round trips via the analytic expression for the sum at that point. This allows us to obtain an inverted function of time and to determine the time evolution of the system. Using these expressions, we are able to give switching times for both the up and down processes.

DOI
10.1364/obi.1983.thb36

Related papers

Saturable interferometer theory of optical bistability

N. M. Lawandy, R. Willner

The phenomenon of purely absorptive bistability is examined using a self-consistent multibeam interference method. A state equation is derived and shown to be identical to that derived from mean-field theory (MFT) in the limit of small absorption length products and high saturation. Using the theory given, we are able to examine the time evolution of the system analytically. The results show a critical slowing behavior near the bistable points of the system and are used to examine switching times. In addition, we give a different condition for bistability which results in a larger range of admissibleCvalues.

IEEE Journal of Quantum Electronics•Oct 1, 1983•3 citations

Temporal aspects of absorptive optical bistability

Thomas Erneux, Paul Mandel

We study the semiclassical mean-field theory of absorptive optical bistability in the limit of a fully developed hysteresis cycle, i.e., in the limit of large values of the bistability parameter $C$. We show by multiple time-scale perturbation analysis that it is possible to describe the transition between the two stable branches by simple equations. Near the low-transmission branch, the behavior of the system is governed by an equation for the atomic population, whereas, near the high-transmission branch, it is an equation for the field amplitude which determines the long-time evolution of the system. We then present an analytic study, completed by numerical results whenever necessary, of the time-dependent response of the system when the input field is swept across the bistable region. We study the influence of the initial conditions, the sweeping velocity, and the ratio of the atomic relaxation times on the dynamical hysteresis as well as its relation with the stationary hysteresis.

Physical Review A•Aug 1, 1983•44 citations

Transient behavior in absorptive optical bistability by the Hamilton-Jacobi method

Sarben Sarkar, J.S. Satchell

One-, two-, and five-dimensional Fokker-Planck equations for absorptive bistability are solved with use of small-noise asymptotic expansions, which are different from Gaussian linearized analysis. The cases studied are the bifurcation point for the start of hysteresis, where there is critical slowing down and the fluctuations are large, and the evolution of a steady-state distribution when the input field has a step change. The time evolution of the probability distribution is calculated.

Physical Review A•Apr 1, 1986•3 citations

Dispersive optical bistability: Stability of the steady states

Thomas Erneux, Paul Mandel

We study the semiclassical mean-field theory of single-mode dispersive optical bistability in the limit of a fully developed hysteresis cycle (i.e., in the limit of large values of the bistability parameter C) and when all decay rates have comparable magnitude. We locate (i) on the upper branch instabilities leading to time periodic regimes, (ii) on the lower branch instabilities leading to a switching before the limit point is reached. None of these instabilities are observed in the case of purely absorptive optical bistability.

Physical Review A•Mar 1, 1986•8 citations

Micom program in optical bistability

Charles M. Bowden, D. W. Howgate

Some years ago, a number of people independently suggested the use of the saturable absorber to induce optical bistability (hereafter referred to as OB). The phenomenon was demonstrated and studied recently by Gibbs, McCall and Venkatesan who used a cw dye laser to excite atoms of sodium vapor in a cell between the plates of a Fabry Perot interferometer. Under certain experimental and material conditions, they observed a nonlinear dependency of the transmitted field as a function of the dye-laser input which exhibited hysteresis, differential gain, and bistable behavior. Interest in OB from the practical applications standpoint stems from obvious device applications as the optical analog of the transistor, optical clipper or limiter and digital optical memory element. The recent demonstration of the phenomenon has generated considerable interest from the fundamental point of view as a clear example of spontaneous ordering in an open, stationary system of matter interacting with light. This has led to a surge of recent theoretical activity. (Author)

•Jun 1, 1980•0 citations

Spatial Effects in Optical Bistability

J.A. Hermann

Within the framework of the theories of absorptive bistability recently proposed by various authors, the different sets of coupled differential equations describing the steady-state fields inside the Fabry-Perot cavity are solved analytically. Expressions are obtained for the bistability equation, which links the incident and transmitted fields, for different ranges of the mirror transmission coefficient. Comparison is made with the mean-field theory of Bonifacio and Lugiato. Conditions for stationary points in the bistability curve are derived.

Optica Acta International Journal of Optics•Feb 1, 1980•34 citations
In this paper we will utilize the method of summing transmitted waves routinely used to analyze interferometer structures to develop an OB equation. The method yields a different state equation than the usual mean-field model. However, for small C values and or large input intensities a Taylor expansion of our state equation yields the mean field pure absorptive OB equation. Our equation also gives a different condition for hysteresis. Due to the simplicity of this approach which utilizes the sum of a geometric series, we are able to interrogate the system after any given number of round trips via the analytic expression for the sum at that point. This allows us to obtain an inverted function of time and to determine the time evolution of the system. Using these expressions, we are able to give switching times for both the up and down processes.
The phenomenon of purely absorptive bistability is examined using a self-consistent multibeam interference method. A state equation is derived and shown to be identical to that derived from mean-field theory (MFT) in the limit of small absorption length products and high saturation. Using the theory given, we are able to examine the time evolution of the system analytically. The results show a critical slowing behavior near the bistable points of the system and are used to examine switching times. In addition, we give a different condition for bistability which results in a larger range of admissibleCvalues.
We study the semiclassical mean-field theory of absorptive optical bistability in the limit of a fully developed hysteresis cycle, i.e., in the limit of large values of the bistability parameter CCC. We show by multiple time-scale perturbation analysis that it is possible to describe the transition between the two stable branches by simple equations. Near the low-transmission branch, the behavior of the system is governed by an equation for the atomic population, whereas, near the high-transmission branch, it is an equation for the field amplitude which determines the long-time evolution of the system. We then present an analytic study, completed by numerical results whenever necessary, of the time-dependent response of the system when the input field is swept across the bistable region. We study the influence of the initial conditions, the sweeping velocity, and the ratio of the atomic relaxation times on the dynamical hysteresis as well as its relation with the stationary hysteresis.
We study the semiclassical mean-field theory of single-mode dispersive optical bistability in the limit of a fully developed hysteresis cycle (i.e., in the limit of large values of the bistability parameter C) and when all decay rates have comparable magnitude. We locate (i) on the upper branch instabilities leading to time periodic regimes, (ii) on the lower branch instabilities leading to a switching before the limit point is reached. None of these instabilities are observed in the case of purely absorptive optical bistability.
Some years ago, a number of people independently suggested the use of the saturable absorber to induce optical bistability (hereafter referred to as OB). The phenomenon was demonstrated and studied recently by Gibbs, McCall and Venkatesan who used a cw dye laser to excite atoms of sodium vapor in a cell between the plates of a Fabry Perot interferometer. Under certain experimental and material conditions, they observed a nonlinear dependency of the transmitted field as a function of the dye-laser input which exhibited hysteresis, differential gain, and bistable behavior. Interest in OB from the practical applications standpoint stems from obvious device applications as the optical analog of the transistor, optical clipper or limiter and digital optical memory element. The recent demonstration of the phenomenon has generated considerable interest from the fundamental point of view as a clear example of spontaneous ordering in an open, stationary system of matter interacting with light. This has led to a surge of recent theoretical activity. (Author)
Within the framework of the theories of absorptive bistability recently proposed by various authors, the different sets of coupled differential equations describing the steady-state fields inside the Fabry-Perot cavity are solved analytically. Expressions are obtained for the bistability equation, which links the incident and transmitted fields, for different ranges of the mirror transmission coefficient. Comparison is made with the mean-field theory of Bonifacio and Lugiato. Conditions for stationary points in the bistability curve are derived.