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

Switching from a stable state to a periodic attractor in optical bistability

B. Macke, E. M. Pessina, Bernard Ségard, J. Zemmouri

Published Nov 1, 1991• 2 citations
Publisher

Abstract

The dynamics of a bistable optical system suddenly brought in a domain of multimode instability is studied both experimentally and numerically. The sine-wave self-pulsing is shown to start with an initial amplitude dramatically depending on the switching conditions.
DOI
10.1103/physreva.44.r5350

Related papers

Dynamical aspects in optical bistability

Luigi A. Lugiato, Franco Prati, Massimo Brambilla

Although the discovery of oscillatory instabilities (both single-mode and multimode) in free-running lasers was achieved in the 1960s, investigations on oscillatory instabilities in optical bistability did not take place until the 1970s and 1980s. The first section of this chapter does not deal with oscillatory instabilities, but instead concerns an interesting dynamical phenomenon in optical bistability that arises when the input field approaches a boundary of the bistable domain, and is called critical slowing down . This has been investigated both theoretically and experimentally. The remainder of this chapter is entirely devoted to oscillatory instabilities, following a historical order. With an inverse approach with respect to the laser case, we discuss multimode instabilities first. In Section 24.2.1 we start with the description of the instability which arises under exactly resonant conditions. While this is the counterpart in optical bistability of the resonant multimode laser instability discussed in Section 22.5, a striking difference from the laser case is that in the passive configuration there is no corresponding single-mode instability. This difference disappears, however, when we consider the generalization of the multimode instability of optical bistability to the detuned configuration. Finally we show that in the detuned case it has been possible to achieve a convincing experimental observation of the multimode instability in a long microwave cavity. After some relevant miscellaneous considerations in Section 24.2.2, in Section 24.2.3 we address the subject of the multimode Ikeda instability which leads to period doubling and chaos and aroused a lot of interest in optical chaos. We emphasize also the intrinsic connections with the standard multimode instability discussed in Section 24.2.1, showing, in particular, that the Ikeda instability requires conditions far from the low-transmission limit, i.e. that ∝L is not small. In Section 24.3 we discuss single-mode instabilities in optical bistability. In Section 24.3.1 we illustrate a configuration for the single-mode instability that includes also the Gaussian shape of the electric field in the beam section, and leads to periodic, close-to-sinusoidal self-pulsations.

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

Multimode instability in optical bistability

Bernard Ségard, B. Macke, L. A. Lugiato +2 more

We compare theoretical predictions and experimental data for the multimode instability of optical bistability, which arises from the coherent dynamics of a system of two-level molecules contained in an optical cavity and driven by an external stationary laser field. Considerable insight into this phenomenon is provided by two ``rules of thumb'' that govern the behavior of the self-pulsing frequency, and establish its relation with the Rabi frequency of the intracavity field. We describe in detail the experimental apparatus and the main features of the experimental findings. The theoretical results are based on the Maxwell-Bloch equations for a ring cavity in the plane-wave approximation. Despite the crudeness of this model, the numerical data display a satisfactory qualitative agreement with the experimental results. Additional period-doubling and chaotic phenomena, predicted by the theory and not observed in the experiment, are presumably washed out by the longitudinal and radial variation of the electric field in the cavity.

Physical Review A•Jan 1, 1989•49 citations

Dynamic Optical Bistability, Switching and Control of Self-Pulsations of Excitons and Biexcitons

Vasile Tronciu, Anatol Rotaru

The theory of dynamic optical bistability and self-pulsations in condensed media is elaborated. The nonlinearity is due to a process in which two excitons are bound into a biexciton by virtue of their Coulomb interaction. A computer experiment is used to study the switching times between the optical bistability branches. The scenario for the transition to the dynamical chaos mode is found. The action of external periodical force upon the system is investigated and the range of amplitude values and frequencies of external harmonic pump were found at which the chaotic regime becomes nonlinear periodic by transformation of strange attractor into a limit cycle. Finally, we discuss the possibility of detecting these phenomena in experiments.

physica status solidi (b)•Apr 1, 1999•0 citations

Dynamic Optical Bistability, Switching and Control of Self-Pulsations of Excitons and Biexcitons

Vasile Tronciu, Anatol Rotaru

The theory of dynamic optical bistability and self-pulsations in condensed media is elaborated. The nonlinearity is due to a process in which two excitons are bound into a biexciton by virtue of their Coulomb interaction. A computer experiment is used to study the switching times between the optical bistability branches. The scenario for the transition to the dynamical chaos mode is found. The action of external periodical force upon the system is investigated and the range of amplitude values and frequencies of external harmonic pump were found at which the chaotic regime becomes nonlinear periodic by transformation of strange attractor into a limit cycle. Finally, we discuss the possibility of detecting these phenomena in experiments.

physica status solidi (b)•Apr 1, 1999•4 citations

Multimode Instability in Intrinsic Optical Bistability: A Quantitative Experimental Investigation

Bernard Ségard, B. Macke

We have recently observed a sinewave self-pulsing in the beam transmitted by a passive cavity containing 2-level molecules, driven by a continuous wave. In this experiment made at a wavelength λ ≅ 3.5 mm, the intracavity Rabi frequency is comparable to the free spectral range ( 830 kHz ) of the very long cavity used (l =182 m) {1} and much larger than the collisional linewidth (≅ 25 kHz) .The medium is then strongly saturated by the driving field ( saturation parameter > 1000) so that its absorption , heavy in the linear regime (αl > 100), is in fact quite moderate. We claim that the self-pulsing observed in these conditions is the first experimental evidence of the multimode instability, predicted a long time ago by Bonifacio and Lugiato {2} but not yet observed. This instability is the multimode counterpart of the single mode instability, recently observed by Orozco et al {3}.

Topical Meeting on Optical Bistability (OB)•Jan 1, 1988•0 citations

Self-pulsing in other optical systems

Luigi A. Lugiato, Franco Prati, Massimo Brambilla

This chapter concludes the discussion about temporal instabilities and self-oscillations, considering the instabilities that arise in the systems analyzed in Chapter 13, with the exception of optical bistability, which has been discussed separately in Chapter 11. Section 25.1 focuses on the laser with an injected signal. As already mentioned in Section 13.1, in this system self-pulsing instabilities are rather ubiquitous, and on exploring the parameter space one meets an extremely rich variety of oscillatory behaviors. For example, under extremely high-gain conditions, breathing, spiking and chaos have been identified over various ranges of the driving field strength [294]. In this section we show some results that arise under parametric conditions that are more accessible experimentally. We illustrate especially the coexistence, for the same parametric values, of different oscillatory behaviors that are reached by starting from different initial conditions. On the other hand, Section 25.2 deals with a laser with a saturable absorber. In this system even the full scenario of stationary intensity solutions in the single-mode model is very complex. For the sake of simplicity, in this section we focus on a simpler rate-equation model that is obtained from the single-mode model of Eqs. (13.13)–(13.17) by adiabatically eliminating the atomic polarization of both active and passive medium. As in Chapter 13, we assume that the atomic transition frequencies are equal and also coincide with a cavity frequency. In this way all the variables in the model can be assumed real, and the linearization around the stationary solution described in Section 13.2 leads to a cubic eigenvalue equation. The spontaneous oscillations which arise from this instability are called repetitive passive Q-switching in the literature. Section 25.3 considers the stability of the stationary solutions of the degenerate optical parametric oscillator described in Section 13.4 and outlines the scenario of period doubling and chaos that arises under appropriate parametric conditions.

Cambridge University Press eBooks•Feb 28, 2015•0 citations
Although the discovery of oscillatory instabilities (both single-mode and multimode) in free-running lasers was achieved in the 1960s, investigations on oscillatory instabilities in optical bistability did not take place until the 1970s and 1980s. The first section of this chapter does not deal with oscillatory instabilities, but instead concerns an interesting dynamical phenomenon in optical bistability that arises when the input field approaches a boundary of the bistable domain, and is called critical slowing down . This has been investigated both theoretically and experimentally. The remainder of this chapter is entirely devoted to oscillatory instabilities, following a historical order. With an inverse approach with respect to the laser case, we discuss multimode instabilities first. In Section 24.2.1 we start with the description of the instability which arises under exactly resonant conditions. While this is the counterpart in optical bistability of the resonant multimode laser instability discussed in Section 22.5, a striking difference from the laser case is that in the passive configuration there is no corresponding single-mode instability. This difference disappears, however, when we consider the generalization of the multimode instability of optical bistability to the detuned configuration. Finally we show that in the detuned case it has been possible to achieve a convincing experimental observation of the multimode instability in a long microwave cavity. After some relevant miscellaneous considerations in Section 24.2.2, in Section 24.2.3 we address the subject of the multimode Ikeda instability which leads to period doubling and chaos and aroused a lot of interest in optical chaos. We emphasize also the intrinsic connections with the standard multimode instability discussed in Section 24.2.1, showing, in particular, that the Ikeda instability requires conditions far from the low-transmission limit, i.e. that ∝L is not small. In Section 24.3 we discuss single-mode instabilities in optical bistability. In Section 24.3.1 we illustrate a configuration for the single-mode instability that includes also the Gaussian shape of the electric field in the beam section, and leads to periodic, close-to-sinusoidal self-pulsations.
We compare theoretical predictions and experimental data for the multimode instability of optical bistability, which arises from the coherent dynamics of a system of two-level molecules contained in an optical cavity and driven by an external stationary laser field. Considerable insight into this phenomenon is provided by two ``rules of thumb'' that govern the behavior of the self-pulsing frequency, and establish its relation with the Rabi frequency of the intracavity field. We describe in detail the experimental apparatus and the main features of the experimental findings. The theoretical results are based on the Maxwell-Bloch equations for a ring cavity in the plane-wave approximation. Despite the crudeness of this model, the numerical data display a satisfactory qualitative agreement with the experimental results. Additional period-doubling and chaotic phenomena, predicted by the theory and not observed in the experiment, are presumably washed out by the longitudinal and radial variation of the electric field in the cavity.
The theory of dynamic optical bistability and self-pulsations in condensed media is elaborated. The nonlinearity is due to a process in which two excitons are bound into a biexciton by virtue of their Coulomb interaction. A computer experiment is used to study the switching times between the optical bistability branches. The scenario for the transition to the dynamical chaos mode is found. The action of external periodical force upon the system is investigated and the range of amplitude values and frequencies of external harmonic pump were found at which the chaotic regime becomes nonlinear periodic by transformation of strange attractor into a limit cycle. Finally, we discuss the possibility of detecting these phenomena in experiments.
The theory of dynamic optical bistability and self-pulsations in condensed media is elaborated. The nonlinearity is due to a process in which two excitons are bound into a biexciton by virtue of their Coulomb interaction. A computer experiment is used to study the switching times between the optical bistability branches. The scenario for the transition to the dynamical chaos mode is found. The action of external periodical force upon the system is investigated and the range of amplitude values and frequencies of external harmonic pump were found at which the chaotic regime becomes nonlinear periodic by transformation of strange attractor into a limit cycle. Finally, we discuss the possibility of detecting these phenomena in experiments.
We have recently observed a sinewave self-pulsing in the beam transmitted by a passive cavity containing 2-level molecules, driven by a continuous wave. In this experiment made at a wavelength λ ≅ 3.5 mm, the intracavity Rabi frequency is comparable to the free spectral range ( 830 kHz ) of the very long cavity used (l =182 m) {1} and much larger than the collisional linewidth (≅ 25 kHz) .The medium is then strongly saturated by the driving field ( saturation parameter > 1000) so that its absorption , heavy in the linear regime (αl > 100), is in fact quite moderate. We claim that the self-pulsing observed in these conditions is the first experimental evidence of the multimode instability, predicted a long time ago by Bonifacio and Lugiato {2} but not yet observed. This instability is the multimode counterpart of the single mode instability, recently observed by Orozco et al {3}.
This chapter concludes the discussion about temporal instabilities and self-oscillations, considering the instabilities that arise in the systems analyzed in Chapter 13, with the exception of optical bistability, which has been discussed separately in Chapter 11. Section 25.1 focuses on the laser with an injected signal. As already mentioned in Section 13.1, in this system self-pulsing instabilities are rather ubiquitous, and on exploring the parameter space one meets an extremely rich variety of oscillatory behaviors. For example, under extremely high-gain conditions, breathing, spiking and chaos have been identified over various ranges of the driving field strength [294]. In this section we show some results that arise under parametric conditions that are more accessible experimentally. We illustrate especially the coexistence, for the same parametric values, of different oscillatory behaviors that are reached by starting from different initial conditions. On the other hand, Section 25.2 deals with a laser with a saturable absorber. In this system even the full scenario of stationary intensity solutions in the single-mode model is very complex. For the sake of simplicity, in this section we focus on a simpler rate-equation model that is obtained from the single-mode model of Eqs. (13.13)–(13.17) by adiabatically eliminating the atomic polarization of both active and passive medium. As in Chapter 13, we assume that the atomic transition frequencies are equal and also coincide with a cavity frequency. In this way all the variables in the model can be assumed real, and the linearization around the stationary solution described in Section 13.2 leads to a cubic eigenvalue equation. The spontaneous oscillations which arise from this instability are called repetitive passive Q-switching in the literature. Section 25.3 considers the stability of the stationary solutions of the degenerate optical parametric oscillator described in Section 13.4 and outlines the scenario of period doubling and chaos that arises under appropriate parametric conditions.