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Journal of Henan Normal University

The Steady Bifurcation and Phenomenon of Critical Slowing Down of the Absorptive Optical Bistability Equation

Hua Cun

Published Jan 1, 2000• 0 citations
OpenAlex

Abstract

The steady bifurcation and phenomenon of critical slowing down of the absorptive optical bistability equation are investigated by using new methods.The existence of optical bistability is proved.It is shown that steady bifurection diagram is the known S shape curve of bistability.The phenomenon of critical slowing down is analyzed.The time of crtical slowing down is estimated.

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The steady bifurcation and phenomenon of critical slowing down of the absorptive optical bistability equation are investigated by using new methods.The existence of optical bistability is proved.It is shown that steady bifurection diagram is the known S shape curve of bistability.The phenomenon of critical slowing down is analyzed.The time of crtical slowing down is estimated.
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..
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.
The critical phenomenon analogy in an absorptive optical bistability system is studied. The asymptotic form of the family of potential functions for the system near threshold is obtained by using catastrophe theory. The well-known scaling hypothesis in the general homogeneous function form in critical phenomena is shown to be a characteristic of the asymptotic family. Four threshold exponents beta , delta , gamma , alpha and their four accompanied threshold amplitudes B, D, Gamma , A on both bistability and monotonic regions are estimated. The threshold exponents obey the same scaling laws as those in critical phenomena, while the threshold amplitudes obey the definite relations between exponents and amplitudes.
In this paper, some new results of the study on the bistability and the instability of semiconductor optical amplifier are presented, which may be expected to be available to a class of excitonic optical bistable and amplifying systems. For these systems, both saturation and increasing absorptive bistability will product, depending on the competition among the interactions in the medium, especially the nonlinear couplings, and the lasing conditions. Particularly, the output curve appears a novel feature of optical hysteresis, with amplifying effect as well. On the other hand, the instability of the stationary states is investigated by linear stability analyzing. Some new phenomena of 'critical slowing down' are discovered near the relevant critical points, in the dynamic responding course.