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Stationary Intensity Distribution of Single-Mode Laser Driven byAdditive and Multiplicative Colored Noises with ColoredCross-Correlation
LIANG Gui-Yun,, CAO Li,, WANG Jun,, and WuDa-Jin,
Communications in Theoretical Physics
Applying the approximate Fokker-Planck equation we derived, we obtain the
analytic expression of the stationary laser intensity distribution
Pst(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 Pst(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 (τ1=τ2=τ3=τ). 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 τ≠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, τ1≠τ2≠τ3. For this case, we find that the noise-induced transition occurring in the Pst(I) curve is entirely different when the values of τ1, τ2, and τ3 are changed respectively. In particular, when τ2 (self-correlation time of additive noise) is changing, 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).
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