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Acta Optica Sinica

Coupled dynamical equations of the increasing absorption optical bistability and it' s dynamical state situation

Zhou Yu-chang, Fa Ou

Published Jan 1, 1993• 0 citations
OpenAlex

Abstract

In this paper a set of coupled dynamical equations for describing or stimulating common features of the increasing absorption optical bistability (IAOB) is put forward in a phenomenological way. By computers analyzing, IAOB' s dynamical characteristics have been studied.

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It is demonstrated that the mean field (Landau) theory of critical phenomena (including the two kinds of critical point) and transitions can also be applied to the increasing absorption optical bistubility (IAOB), far from equilibrium. On the basis of analysing the dynamical fea Lures of the IAOB model proposed recently[９］, the socalled quasi-thermodynamic potential is introduced. This potential, near the critical point (of the second kind), reflects not only the general properties of phase transitions in bistable systems, but also the specific characteristics of the IAOB.
Some results of probing to the common properties, including bistability, transient behavior, and instability of the excitonic optical nonlinear dynamic systems, such as interaction of light field with carrier in semiconductor, or anharmonic vibration of lattice in ionic crystal, are presented. Since the excitonic optical bistability (EOB) was found, it has garnered much attention for its advantage in properties and application prospects. Some models have been proposed for different kinds of OB. However, so far as we know, there has been relatively less concern given to the common dynamic characteristics of these systems, which are significant for applications. On the other hand, the instability of the EOB device certainly has the same importance, the study for which is not ample yet. In this paper we study the increasing absorptive OB, the behaviors of responding to inject signal, also the self-pulsing and chaotic phenomena in the excitonic OB systems.
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.
A recently developed nonlinear complex eikonal approximation which was previously employed to the study of dispersively nonlinear resonators is applied to absorptively nonlinear resonator configurations. The nonlinear absorption is introduced phenomenologically, encompassing a large variety of intensity-dependent absorption mechanisms. Conditions for obtaining optical bistability are derived. Dynamically increasing absorption was not considered, and optical bistability in free propagation was not obtained.
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..
An extended theoretical discussion of a novel general method of obtaining optical bistability is given. The method uses absorption that increases as the material becomes more excited and requires no mirrors or other external feedback. Criteria for bistability and differential gain are derived for a simple case, and specific illustrative analytic results are given. Limiting relations are derived for the switching powers and the width of the bistable region. It is shown that this general class of bistability encompasses at least six previous independent and unrelated investigations of mirrorless bistability in specific physical systems. The common general requirements for this bistability are discussed together with its attributes.