Stationary Intensity Distribution of Single－Mode Laser Driven by Additive and Multiplicative Colored Noises with Colored Cross－Correlation

Applying the approximate Fokker-Planck equation we derived, we obtain the analytic expression of the stationary laser intensity distribution Pst(l) by studying the single-mode laser cubic model subject to colored cross-correlation additive and multiplicative noise, each of which is colored. Based on it, we discuss the effects on the stationary laser intensity distribution Pot(I) by cross-correlation between noises and “color“ of noises (non-Markovian effect) when the laser system is above the threshold. In detail, we analyze two cases: One is that the three correlation-times (i.e.the self-correlation and cross-correlation times of the additive and multiplicative noise) are chosen to be the same value(Tl=T2=T3=T). For this case, the effect of noise cross-correlation is investigated emphatically, and we detect that only when λ≠ 0 can the noise-induced transition occur in the Pst (I) curve, and only when T≠ 0 and λ≠0, can the “reentrant noise-induced transition“ occur. The other case is that the three correlation times are not the same value,T1≠T2≠T3. For this case, we find that the noise-induced transition occurring in the Pst(I) curve is entirely different when the values of T1,T2, and T3 are changed respectively. In particular, when T2 (serf-correlation time of additive noise) is cha~g~g, the ratio of the two maximums of the Pst( I) curve R exhibits an interesting phenomenon,“reentrant noise-induced transition“, which demonstrates the effect of noise “color“ (non-Markovian effect).