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Communications in Theoretical Physics

First-Order-Like Phase Transition Induced by Two Different Kinds of Noise in Dispersive Optical Bistability

He Ying, Zhu Shi-Qun

Published Oct 15, 2003• 1 citation
Publisher

Abstract

With unified colored noise approximation, the steady state distribution function in dispersive optical bistability including both intensity and phase fluctuations is obtained. The parameter plane of the first-order-like phase transition is also derived with numerical method. It is found that the number of extremes at non-zero values of the output field in the steady state distribution function is changed from zero, two to four. It is shown that the strengths of the intensity fluctuation and the phase fluctuation have great effect on the first-order-like phase transition.

DOI
10.1088/0253-6102/40/4/435

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With unified colored noise approximation, the steady state distribution function in dispersive optical bistability including both intensity and phase fluctuations is obtained. The parameter plane of the first-order-like phase transition is also derived with numerical method. It is found that the number of extremes at non-zero values of the output field in the steady state distribution function is changed from zero, two to four. It is shown that the strengths of the intensity fluctuation and the phase fluctuation have great effect on the first-order-like phase transition.
With unified colored noise approximation, the steady state distribution function in dispersive opticalbistability including both intensity and phase fluctuations is obtained. The parameter plane of the first-order-like phasetransition is also derived with numerical method. It is found that the number of extremes at non-zero values of theoutput field in the steady state distribution function is changed from zero, two to four. It is shown that the strengths of the intensity fluctuation and the phase fluctuation have great effect on the first-order-like phase transition.
The first-order-like phase transition (FOLT) in the dispersive optical bistability is investigated when the fluctuation in the incident light field is considered as colored noise. A unified colored-noise approximation is applied to obtain the steady state distribution (SSD) when either the intensity or phase fluctuations of the incident field are included in the system. For intensity fluctuations only, the curve of SSD is changed from single extreme to two extremes, and then to three extremes. The colored nature of the noise can reduce the fluctuation in the system. However, for phase fluctuations only, the FOLT is mainly induced by the colored nature of the noise. The curve of SSD is changed from single extreme to three extremes directly. There is no FOLT existing for white noise.
Systems exhibiting dispersive optical bistability are considered as examples of nonequilibrium steady states lacking detailed balance. Methods for describing such states are developed. The Fokker-Planck equation for the steady-state distribution function of the transmitted electromagnetic field is derived. In the limit of small fluctuations the Fokker-Planck equation is reduced to the form of a Hamilton-Jacobi equation for a "nonequilibrium thermodynamic potential." This equation is solved in various approximations. The nonequilibrium thermodynamic potential acts like a free-energy for the first-order-type transition far from thermodynamic equilibrium lacking detailed balance. The potential entirely determines the steady-state distribution, the coexistence curve in the bistable domain, a Lyapunoff function of the deterministic equations of motion, and allows us to cast the deterministic equations of motion into the standard form of nonequilibrium thermodynamics.
Fluctuational transitions between stable states of an all-optical lumped-parameter bistable system have been observed. The dependences of the transition probabilities, and of the statistical distribution of the transmitted-light intensity, on the intensities of incident light and noise have been investigated. Two types of stochastic modulation, that of the incident-light intensity and that of the device itself, have been used. They correspond to multiplicative and additive noise for the intracavity-phase gain and give rise to qualitatively different pictures of the fluctuations. In particular, for the latter type of noise the logarithm of the statistical distribution of the transmitted-light intensity is described by a multibranch function, and the peaks of the distribution are strongly asymmetric. The onset of a zero-frequency peak in the power spectrum of the transmitted light in the range of the kinetic phase transition has been observed. The experimental data are in good qualitative and quantitative agreement with the theory.
With the unified colored noise approximation theory,the steepest descent method and the two-state approach theory,the effects of noise on the stochastic resonance and the mean first passage time of the dispersive optical bistability system are investigated.It is found that when there is a weak periodic signal included in the system,with both multiplicative colored noise and multiplicative white noise,the signal-to-noise ratio and the mean first passage time of the system are affected not only by the noise correlation time,but also by the intensity of both multiplicative colored noise and multiplicative white noise.It is shown that the stochastic resonance phenomenon depends on the initial conditions of the system.
Fluctuational transitions between the stable states of a passive optically bistable device have been observed and investigated theoretically and experimentally in the absence of spatial effects (for a lumped-parameter system). The problem of calculation of transition probabilities in dynamical systems driven by weak Gaussian noise has been reduced to logarithmic accuracy to a variational problem which is solved for some types of colored noise. The procedure of the experimental determination of the transition probabilities from the data on transmitted intensity is proposed for the case of a broad-band noise in the intensity of incident radiation. The onset of an extremely narrow peak in the power spectrum of the system in the range of the kinetic phase transition is revealed.