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IEEE Journal of Quantum Electronics

Saturable interferometer theory of optical bistability

N. M. Lawandy, R. Willner

Published Oct 1, 1983• 3 citations
Publisher

Abstract

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.

DOI
10.1109/jqe.1983.1071762

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Time\|dependent bifurcation and dynamical behaviors of the absorptive optical bistability equation are investigated systematically from the point of view of vector field.Internal relations for delayed bifurcation transitions are discussed.When the input optic field is constant,the existence of optical bistability and the phenomenon of critical slowing down are analyzed through a new way.When the input optic field is varied slowly with time linearly or periodically,different scaling relations are given by scaling balances.When the amplitude or frequency of the input optic field is varied slowly and linearly with time,the bifurcation and dynamical behaviors for the time\|dependent system of bistability are also studied .A new strange atractor is revealed..

Acta Physica Sinica•Jan 1, 2000•3 citations
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.
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.
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.
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.
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.
We present a novel approach to achieving intrinsic optical bistability and multistability through the interplay between saturable and reverse saturable absorption. Our findings reveal that the stable points on the optical bistability curve align with the switching points of intensity-dependent nonlinear absorption. By analyzing the optical properties of a four-level cascade quantum system, we demonstrate that these switching behaviors can be triggered by applying laser fields to induce nonlinear absorption. Furthermore, we propose a comprehensive model to describe the intensity-dependent nonlinear absorption within this quantum system. Finally, it is shown that the optical bistability switches to the multistability when the detuning of applied fields exceeds the multi-photon resonance condition.
Time\|dependent bifurcation and dynamical behaviors of the absorptive optical bistability equation are investigated systematically from the point of view of vector field.Internal relations for delayed bifurcation transitions are discussed.When the input optic field is constant,the existence of optical bistability and the phenomenon of critical slowing down are analyzed through a new way.When the input optic field is varied slowly with time linearly or periodically,different scaling relations are given by scaling balances.When the amplitude or frequency of the input optic field is varied slowly and linearly with time,the bifurcation and dynamical behaviors for the time\|dependent system of bistability are also studied .A new strange atractor is revealed..