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Modern Physics Letters B

CRITICAL EXPONENTS AND CRITICAL SLOWING DOWN IN OPTICAL BISTABILITY — A PHENOMENOLOGICAL APPROACH

Pei-Hsi Tsao, Wei-Chih Liu

Published Mar 20, 1992• 1 citation
Publisher

Abstract

A phenomenological approach is adopted for investigating the critical behavior related to optical bistability (OB). This method is similar to Landau theory of critical phenomena and is applied to find the critical exponents and to analyze critical slowing down. It is shown in general that critical exponents for OB are classical ones and the relaxation time of critical slowing down varies with the external parameter p as (p − pc)−1/2 around the transition point p = pc.

DOI
10.1142/s0217984992000442

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A phenomenological approach is adopted for investigating the critical behavior related to optical bistability (OB). This method is similar to Landau theory of critical phenomena and is applied to find the critical exponents and to analyze critical slowing down. It is shown in general that critical exponents for OB are classical ones and the relaxation time of critical slowing down varies with the external parameter p as (p − pc)−1/2 around the transition point p = pc.
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.
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..