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Chinese Optics Letters

交叉关联的加性白噪声和乘性色噪声驱动的光学双稳系统的关联函数研究

Bing Wang, Shaoping Yan

Published Jan 1, 2009• 4 citations
Publisher

Abstract

Considering an optical bistable system with cross-correlated additive white noise and multiplicative colored noise, we study the effects of correlation between the noises on the correlation function C(s) using the unified colored noise approximation and the Stratonovich decoupling ansatz formalism.The effects of the self-correlation time τ of the multiplicative colored noise and the correlation intensity λ between the two noises are studied with numerical calculation.It is found that C(s) increases with the increase of the self-correlation time τ, but decreases with the increase of the correlation intensity λ.At large value of τ, there is almost no change for C(s) when τ changes.

DOI
10.3788/col20090709.0838

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Considering an optical bistable system with cross-correlated additive white noise and multiplicative colored noise, we study the effects of correlation between the noises on the correlation function C(s) using the unified colored noise approximation and the Stratonovich decoupling ansatz formalism.The effects of the self-correlation time τ of the multiplicative colored noise and the correlation intensity λ between the two noises are studied with numerical calculation.It is found that C(s) increases with the increase of the self-correlation time τ, but decreases with the increase of the correlation intensity λ.At large value of τ, there is almost no change for C(s) when τ changes.
The stochastic resonance (SR) of an optical bistable system with cross-correlated additive white and multiplicative colored noises and periodic signal is studied using the unified colored noise approximation and the theory of signal-to-noise ratio (SNR).Results show that cross-correlation intensity λ enforces the SR of the system.The position of the peak on the SNR-τ curves moves to the right direction along with the increase of λ (τ is the self-correlation time of the multiplicative colored noise).We find the SR phenomenon in the SNR-D and SNR-Q curves (D and Q are the intensities of the additive and multiplicative noises, respectively), but not in the SNR-λ curves.
The relaxation time T of an optical bistable system with cross-correlated color noises and small time delay is investigated. Using the Novikov theorem and Fox approach, the steady probability distribution is obtained. The expression of T is derived using the Stratonovich decoupling ansatz formalism. It is found that the relaxation time T increases with the increasing cross-correlation time τ 0 between the two noises or the self-correlation time τ 1 of the multiplicative noise, but decreases with the increasing self-correlation time τ 2 of the additive noise. T decreases with the increasing correlation intensity λ or the multiplicative noise intensity Q , but increases with the increasing additive noise intensity D . There exists a peak in the curve of T versus delay time τ.
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.
A single-mode laser system with colored cross-correlated additive and multiplicative noise terms is considered. By the means of projection operator method, we study the effects of the cross-correlation time 'tau' and the cross-correlation intensity 'lambda' between noises on the normalized intensity correlation function C(s). It is found that if 'lambda'g0 ('lambda'l0), the normalized intensity correlation function C(s) increases (decreases) with increasing the cross-correlation time 'tau', and at large value of 'tau', the variation of the normalized intensity correlation function C(s) becomes small. With the increase of the net gain a0, C(s) exhibits a maximum when 'lambda' is larger. However, a minimum and a maximum appear on C(s) curves with the increase of a0 when 'lambda' becomes smaller and smaller.
By adopting the linear approximation method,the signal-to-noise ratio of optical bistability system driven by colored pump noise and colored quantum noise was calculated. The influence on the signal-to-noise ratio of the pump noise intensity(P),quantum noise intensity(Q),pump noise self-correlation time (τ1) and quantum noise self-correlation time (τ2) was studied. The stochastic resonance was found in the curve of signal-to-noise ratio R versus the pump noise self-correlation time (τ1) was discussed,while the great influence on the stochastic resonance is posed by quantum noise self-correlation time,when (τ2) increases,the curve of signal-to-noise ratio R versus the pump noise self-correlation time (τ1) upgrates integratedly,and resonance-peak increases.It could prolong the quantum noise self-correlation time (τ2) to increase the signal-to-noise ratio R.There is a maximum in the curve of signal-to-noise ratio R versus the parameter of the optical bistability system c,while pump noise self-correlation time (τ1) greatly influences the curve of signal-to-noise ratio R versus the parameter of the optical bistability system c. With the increase of pump noise self-correlation time (τ1),the maximum declines and the curve becomes flat.It is indicated that the signal-to-noise ratio increases through reducing the pump noise self-correlation time (τ1).Besides,signal-to-noise ratio R monotonously increases with the increase of pump noise intensity P,and motonously decreases with the increase of quantum noise intensity Q.
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.