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Acta Physica Sinica

TIME-DEPENDENT BIFURCATION AND DYNAMICAL BEHAVIORS OF THE ABSORPTIVE OPTICAL BISTABILITY EQUATION

Hua Chen

Published Jan 1, 2000• 3 citations
OpenAlex

Abstract

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..

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Acta Optica Sinica•Jan 1, 1988•1 citation
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..
We investigate the temporal aspects of absorptive two-photon optical bistability described by a semiclassical theory in the limit of a fully developed hysteresis cycle and when all decay rates have comparable magnitude. We show by multiple time-scale perturbation analysis that near the high-transmission branch the behavior of the system is governed by an equation for the field amplitude which determines the long-time evolution of the system, whereas, near the low-transmission branch all dynamical variables vary on the long time scale, and it is possible to describe the transition between the two stable branch by simple equations.
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.
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.
A single-mode dynamical equation is obtained from the Maxwell equation with the slowly varying amplitude approximation and the boundary conditions of the cavity, here the mean field limir and the good quality cavity case have been used. This equation is useful in describing the dynamical behavior of intrinsic optical bistable systems and/or lasers with injected sig-nals for any kinds of materials including two-level atoms. Furthermore, according to the li-near stability analysis, a generalized instability criterion is derived.
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.