Stationary Intensity Distribution of Single-Mode Laser Driven byAdditive and Multiplicative Colored Noises with ColoredCross-Correlation**The project supported by National Natural Science Foundation of China under Grant No. 10275025

Abstract

Applying the approximate Fokker-Planck equation we derived, we obtain the analytic expression of the stationary laser intensity distribution 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 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 . For this case, the effect of noise cross-correlation is investigated emphatically, and we detect that only when can the noise-induced transition occur in the curve, and only when and , can the “reentrant noise-induced transition” occur. The other case is that the three correlation times are not the same value, . For this case, we find that the noise-induced transition occurring in the curve is entirely different when the values of and are changed respectively. In particular, when (self-correlation time of additive noise) is changing, the ratio of the two maximums of the curve R exhibits an interesting phenomenon, “reentrant noise-induced transition”, which demonstrates the effect of noise “color” (non-Markovian effect).