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

Acta Optica Sinica

Forced oscillation model of optical bistability

Fa Ou

Published Jan 1, 1988• 1 citation
OpenAlex

Abstract

This paper presents a new model of optical bistability (OB). In view of the ideas of the mean field approximation, the slow envelope approximation and the adiabatic approximation, the OB system can be regarded as a box. Comparing with the theory of nonlinear oscillation, we find that the courses in different OBS's-includingdifferent substances and different cavities (E-P. C. or E. C. )-can be describedconsistently, in both steady state and temporal respect, with an appropriate nonlinear forced oscillation equation, in which the coefficients are measurable macroscopical parameters. Using the method of slowly changing phase and amplitude in oscillation theory, we develop the equation into a coupling and autonomous dynamic equation set of phase and amplitude. The general solutions of the equation set for OB steady state and transient behavior are obtained conveniently from this form. Several concrete results in literature are compared as the examples for the verification of the widely applicability o del.

Related papers

Long-time behavior of optical bistability

Yoshio Nishiyama

Long-time behavior of transmitted and reflected field amplitude of optical bistability by a cavity including an absorptive resonant medium from an initial to a final steady state on switching the incident field is investigated by solving numerically the semiclassical dynamical equations without the mean-field approximation. The transmitted field amplitude as a function of time is monotonic as a whole, and an oscillatory character is seen on it in a shorter period. The dynamical character such as the oscillation amplitude and the duration of a whole process depend strongly on two parameters included in the equations.

Physical Review A•May 1, 1980•8 citations

Pit Bistable optical devices: physical processes and practical applications

David A. B. Miller

Optical bistability (OB) can be defined as the existence of two stable states for one set of optical input conditions. It can be seen in many different systems which generally combine some microscopic nonlinearity (e.g., intensity-dependent refractive index) with some macroscopic feedback (e.g., a Fabry-Perot cavity). OB shows not only hysteresis but also switching transitions. By adjusting the degree of feedback various related effects are also possible (e.g., optical limiters, optical transistors, and several kinds of oscillation phenomena).

Conference on Lasers and Electro-Optics•Jan 1, 1982•0 citations

Instabilities in dispersive OB on the low transmission branch

Thomas Erneux, Paul Mandel

We study the mean field limit equations for optical bistability using two-level atoms as a model for the nonlinear medium. The resulting standard equations are /1/: The steady state equation is.

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

Use of an electronic model as a guideline in experiments on transient optical bistability

Wulfhard K. Lange

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.

Cambridge University Press eBooks•Apr 6, 1989•0 citations

Single- and two-mode models

Luigi A. Lugiato, Franco Prati, Massimo Brambilla

In the first section we discuss the stationary solutions for a laser with an injected signal, the active counterpart of the optical bistability analyzed in Chapter 11. Next, in Section 13.2 we consider another very interesting system, namely a laser with a saturable absorber, a free-running laser in which the optical cavity contains a passive medium in addition to the active medium. The single-mode model for this system can be constructed by combining the single-mode models for the free-running laser and for optical bistability. The discussion is then focussed on its stationary states. In Section 13.3 we return to the single-mode model for optical bistability and, by introducing an appropriate “cubic limit” on the parameters in play, we derive a cubic model for dispersive optical bistability with two-level atoms. The stationary equation for such a model formally coincides with that derived and discussed for a Kerr medium in Section 11.2. In the last section we start from the equations for a quadratic nonlinear medium in the degenerate configuration derived in Chapter 6 and combine them with the appropriate boundary conditions for the two field envelopes in play, assuming that the quadratic medium is contained in a ring cavity as happens in an optical parametric oscillator or in second-harmonic generation in a cavity. Next, by introducing the low-transmission limit and the single-mode limit we derive a two-mode model that describes the dynamics of a degenerate optical parametric oscillator or of second-harmonic generation in a cavity. Finally, for the case of a parametric oscillator we illustrate extensively the stationary solutions of the equations. A laser with an injected signal From a technical point of view, this system is interesting because of the possibility of stabilizing the frequency and the phase of separate lasers by taking advantage of the known affinity of nonlinear oscillators to lock onto a periodic forcing element. In 1972 Spencer and Lamb [125] predicted the possibility of bistable behavior in a laser with an injected signal before the surge of interest in optical bistability in the passive configuration.

Cambridge University Press eBooks•Feb 28, 2015•0 citations

PHASE TRANSITIONS AT CRITICAL POINTS IN OPTICAL BISTAB1LITY

Fa Ou, Wenji Deng, 华南理工大学,广州,510641

Critical phenomena in optical bistability (OB) are studied in some detail. Theoretical an-alyeses, mainly based on the steady solution of the "thermodynamic" Fokker-Plank equation for absorptive OB, show that the critical phenomena in OB also can be brought into the framework of Landau's theory of scond-order phase transitions, and the relations between different kinds of critical index numbers obey the scaling laws.

Acta Physica Sinica•Jan 1, 1990•0 citations
This paper presents a new model of optical bistability (OB). In view of the ideas of the mean field approximation, the slow envelope approximation and the adiabatic approximation, the OB system can be regarded as a box. Comparing with the theory of nonlinear oscillation, we find that the courses in different OBS's-includingdifferent substances and different cavities (E-P. C. or E. C. )-can be describedconsistently, in both steady state and temporal respect, with an appropriate nonlinear forced oscillation equation, in which the coefficients are measurable macroscopical parameters. Using the method of slowly changing phase and amplitude in oscillation theory, we develop the equation into a coupling and autonomous dynamic equation set of phase and amplitude. The general solutions of the equation set for OB steady state and transient behavior are obtained conveniently from this form. Several concrete results in literature are compared as the examples for the verification of the widely applicability o del.
Long-time behavior of transmitted and reflected field amplitude of optical bistability by a cavity including an absorptive resonant medium from an initial to a final steady state on switching the incident field is investigated by solving numerically the semiclassical dynamical equations without the mean-field approximation. The transmitted field amplitude as a function of time is monotonic as a whole, and an oscillatory character is seen on it in a shorter period. The dynamical character such as the oscillation amplitude and the duration of a whole process depend strongly on two parameters included in the equations.
Optical bistability (OB) can be defined as the existence of two stable states for one set of optical input conditions. It can be seen in many different systems which generally combine some microscopic nonlinearity (e.g., intensity-dependent refractive index) with some macroscopic feedback (e.g., a Fabry-Perot cavity). OB shows not only hysteresis but also switching transitions. By adjusting the degree of feedback various related effects are also possible (e.g., optical limiters, optical transistors, and several kinds of oscillation phenomena).
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.
In the first section we discuss the stationary solutions for a laser with an injected signal, the active counterpart of the optical bistability analyzed in Chapter 11. Next, in Section 13.2 we consider another very interesting system, namely a laser with a saturable absorber, a free-running laser in which the optical cavity contains a passive medium in addition to the active medium. The single-mode model for this system can be constructed by combining the single-mode models for the free-running laser and for optical bistability. The discussion is then focussed on its stationary states. In Section 13.3 we return to the single-mode model for optical bistability and, by introducing an appropriate “cubic limit” on the parameters in play, we derive a cubic model for dispersive optical bistability with two-level atoms. The stationary equation for such a model formally coincides with that derived and discussed for a Kerr medium in Section 11.2. In the last section we start from the equations for a quadratic nonlinear medium in the degenerate configuration derived in Chapter 6 and combine them with the appropriate boundary conditions for the two field envelopes in play, assuming that the quadratic medium is contained in a ring cavity as happens in an optical parametric oscillator or in second-harmonic generation in a cavity. Next, by introducing the low-transmission limit and the single-mode limit we derive a two-mode model that describes the dynamics of a degenerate optical parametric oscillator or of second-harmonic generation in a cavity. Finally, for the case of a parametric oscillator we illustrate extensively the stationary solutions of the equations. A laser with an injected signal From a technical point of view, this system is interesting because of the possibility of stabilizing the frequency and the phase of separate lasers by taking advantage of the known affinity of nonlinear oscillators to lock onto a periodic forcing element. In 1972 Spencer and Lamb [125] predicted the possibility of bistable behavior in a laser with an injected signal before the surge of interest in optical bistability in the passive configuration.