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.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 AAug 1, 198344 citations

Universal Scaling in the Dynamic Hysteresis, and Non-Markovian Dynamics, of a Tunable Optical Cavity

Z. Geng, K. J. H. Peters, Aurelien A. P. Trichet +4 more

We investigate, experimentally and theoretically, the dynamics of a laser-driven cavity with noninstantaneous effective photon-photon interactions. Scanning the laser-cavity frequency detuning at different speeds across an optical bistability, we find a hysteresis area that is a nonmonotonic function of the speed. In the limit of fast scans comparable to the memory time of the interactions, we demonstrate that the hysteresis area decays following a universal power law with scaling exponent -1. We further demonstrate a regime of non-Markovian dynamics emerging from white noise. This regime is evidenced by peaked distributions of residence times in the metastable states of our system. Our results offer new perspectives for exploring the physics of scaling, universality, and metastability, in non-Markovian regimes using arrays of bistable optical cavities with low quality factors, driven by low laser powers, and at room temperature.We investigate, experimentally and theoretically, the dynamics of a laser-driven cavity with noninstantaneous effective photon-photon interactions. Scanning the laser-cavity frequency detuning at different speeds across an optical bistability, we find a hysteresis area that is a nonmonotonic function of the speed. In the limit of fast scans comparable to the memory time of the interactions, we demonstrate that the hysteresis area decays following a universal power law with scaling exponent -1. We further demonstrate a regime of non-Markovian dynamics emerging from white noise. This regime is evidenced by peaked distributions of residence times in the metastable states of our system. Our results offer new perspectives for exploring the physics of scaling, universality, and metastability, in non-Markovian regimes using arrays of bistable optical cavities with low quality factors, driven by low laser powers, and at room temperature.

arXiv:1911.00463Physical Review LettersApr 15, 202039 citations

Dynamics of nascent hysteresis in optical bistability

Paul Mandel, Thomas Erneux

Optics CommunicationsDec 1, 198225 citations

Simultaneous nonlinear polarization rotation and dispersive optical bistability: theoretical and experimental analysis

Saif A. Al Graiti, Aiswarya Kannan, Claudio E. Ippolito +1 more

We study the simultaneous occurrence of dispersive optical bistability and nonlinear polarization rotation in a nonlinear photonic resonator. The demonstrated bistable hysteresis curves of the Stokes parameters broaden the notion of optical bistability in nonlinear resonators beyond that of the traditional optical-power hysteresis curve. We present a theoretical model to fully understand the polarization hysteresis curves observed in the laboratory and to establish the relevant scaling parameters for bistable action. By optimizing the optical-signal power injected into each polarization mode of the resonator and optimizing the small-signal birefringence of the resonator by selection of the signal wavelength, a polarization rotation of 30% orthogonality was achieved between stable polarization states in the lab. The theoretical and experimental methods reported here are carried out for the case of a Fabry–Perot semiconductor optical amplifier, and are extendable to the investigation of simultaneous occurrence of these phenomena in other nonlinear media (such as Kerr media) and other photonic resonators.We study the simultaneous occurrence of dispersive optical bistability and nonlinear polarization rotation in a nonlinear photonic resonator. The demonstrated bistable hysteresis curves of the Stokes parameters broaden the notion of optical bistability in nonlinear resonators beyond that of the traditional optical-power hysteresis curve. We present a theoretical model to fully understand the polarization hysteresis curves observed in the laboratory and to establish the relevant scaling parameters for bistable action. By optimizing the optical-signal power injected into each polarization mode of the resonator and optimizing the small-signal birefringence of the resonator by selection of the signal wavelength, a polarization rotation of 30% orthogonality was achieved between stable polarization states in the lab. The theoretical and experimental methods reported here are carried out for the case of a Fabry–Perot semiconductor optical amplifier, and are extendable to the investigation of simultaneous occurrence of these phenomena in other nonlinear media (such as Kerr media) and other photonic resonators.

Journal of the Optical Society of America BNov 25, 20193 citations

Dynamical hysteresis in optical bistability: from the deterministic to the fluctuation-dominated case

N. E. Fettouhi, J. Zemmouri, Bernard Ségard +1 more

European Quantum Electronics Conference (EQEC)Aug 24, 20050 citations

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.