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Physics Letters A

Intensity correlation function of an optical bistable system subjected to cross-correlated noises

Luchun Du, Dong-Cheng Mei

Published Jun 28, 2008• 6 citations
Publisher
DOI
10.1016/j.physleta.2008.06.056

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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 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.
In this paper we focus on the state equation of absorptive optical bistable system with cross-correlated multiplicative noise $\ensuremath{\xi}(t)$ and additive noise $\ensuremath{\eta}(t)$. We find that the area of optical bistability with positive cross-correlation expands in comparison with the deterministic case. Furthermore, a very peculiar phenomenon is shown, namely when the cooperativity parameter C<4C<4C<4, noise still can induce optical bistability. The phenomenon of noise-induced optical bistability in this paper is just the example of noise-induced phase transition.