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 P-st(I) 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 P-st(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 (tau(1) = tau(2) = tau(3) = tau). For this case, the effect of noise cross-correlation is investigated emphatically, and we detect that only when lambda not equal 0 can the noise-induced transition occur in the P-st(I) curve, and only when tau not equal 0 and lambda not equal 0, can the "reentrant noise-induced transition" occur. The other case is that the three correlation times are not the same value, tau(1not equal) tau2 not equal tau3. For this case, we find that the noise-induced transition occurring in the P-st(I) curve is entirely different when the values of tau(1), tau(2), and tau(3) are changed respectively. In particular, when tau(2) (self-correlation time of additive noise) is changing, the ratio of the two maximums of the P-st(I) curve R exhibits an interesting phenomenon, "reentrant noise-induced transition", which demonstrates the effect of noise "color" (non-Markovian effect).