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Advances in intelligent systems and computing

Associated Relaxation Time for an Optical Bistable System with Coupling Between Non-Gaussian and Gaussian Noise Terms

Bing Wang, Wu Xiu-Qing

Published Jan 1, 2013• 0 citations
Publisher
DOI
10.1007/978-3-642-37502-6_68

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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.
The stochastic nature of initial stimulated Brillouin scattering (SBS) can lead to a deep modulation of Stokes intensity in fibers, even under conditions of strong pump depletion. It is known that at a moderate pump depletion, when parameter T1/T2 ≫ 1 (T1 is the light propagation time through the effective amplification length and T2 is the hypersound relaxation time), fluctuations correspond to the Gaussian statistics of temporal field distribution. As T1/T2 → 1 the statistics of fluctuations can change. Gaeta and Boyd1 were the first to show that at a sufficient pump depletion (by our estimate, parameter T1/T2 in Ref. 1 was ~4) the correlation function of the Stokes intensity c(τ) = (〈I(t)I(t + τ)〉 - 〈I(t))2)/(/(t)〉2 differs from the Gaussian by a more rapid initial fall and the presence of the region in which it is negative.