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Chinese Physics Letters

Mean First-Passage Time in Optical Bistable Systems

Ning Li-Juan, Xu Wei

Published Nov 29, 2006• 6 citations
Publisher

Abstract

The transient properties of an optical bistable system driven by multiplicative and additive noises are investigated. The effects of multiplicative and additive noises intensities on the mean first-passage times (MFPTs) in two opposite directions are discussed. The results show that the intensities of multiplicative and additive noises affect the MFPTs on two directions in the same way.

DOI
10.1088/0256-307x/23/12/016

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The transient properties of an optical bistable system driven by multiplicative and additive noises are investigated. The effects of multiplicative and additive noises intensities on the mean first-passage times (MFPTs) in two opposite directions are discussed. The results show that the intensities of multiplicative and additive noises affect the MFPTs on two directions in the same way.
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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.
Investigated are the effects of the cross-correlation time τ or the self-correlation times τ1 and τ2 on the relaxation time T of an optical bistable system using the Mei's method(Mei D C, Xie C W, Zhang L 2003 Phys. Rev. E 68 051102). It is found that the relaxation time T increases with the increase of the cross-correlation time τ between the two noises or the self-correlation time τ1 of the multiplicative noise, and that a one-peak structure appears on the T－τ2 plot. T increases with the increase of correlation intensity λ but decreases with the increase of multiplicative noise intensity Q.
The stochastic resonance (SR) in an optical bistable system under the simultaneous action of multiplicative and additive noises and periodic signal is studied using the adiabatic approximation theory. The signal-to-noise ratio(SNR)is a non-monotonic function of intensity of additive noise, in which the SR phenomenon appears. The SNR decreased with the intensity of multiplicative noise, and SR phenomenon does not appear. So the effects of additive and multiplicative noise on the output SNR are different.