Effect on Intensity Correlation Time by Input Signal in a Single-Mode Laser with Bias Signal Modulation

The effect on intensity correlation time T by input signal is studied for gain-noise model of a single-mode laser driven by colored pump noise and colored quantum noise with colored cross-correlation with a bias signal modulation in this paper. By using the linear approximation method, we detect that there exists maximum (i.e., resonance) in the curve of the intensity correlation time T upon bias-current i0 when the noise correlation coefficient λ is positive; and there exists minimum (i.e., suppression) in the T-i0 curve when λ is negative. And when λ is zero, T increases monotonously with increasing i0. Furthermore, the curve of T upon the signal frequency Ω is also studied. Our study shows that no matter what the value ofλ is, there exists minimum (i.e., suppression) in the T-Ω curve.     

Effecfs of Cross-Correlation Between Real Noise in Transient Process of Single-Mode and Imaginary Parts of Colored Pump Laser

A two-dimensional single-mode laser model with cross-correlation between the real and imaginary parts of the colored quadric pump noise is investigated. A novel laser amplitude Langevin equation is obtained, in which the cross-correlation λp between the real and imaginary parts of the pump noise appears. The mean, variance, and skewness of first-passage-time are calculated. It is shown that the mean, variance, and skewness of first-passage-time are strongly affected by λp.     

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 thestationary 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 stationarylaser intensity distribution Pst(Ⅰ) by cross-correlation between noises and “color“ of noises (non-Markovian effect) whenthe 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 thatonly 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 differentwhen the values of τ1, τ2, and τ3 are changed respectively. In particular, when τ2 (self-correlation time of additivenoise) is changing, the ratio of the two maximums of the Pst(Ⅰ) curve R exhibits an interesting phenomenon, “reentrantnoise-induced transition“, which demonstrates the effect of noise “color“ (non-Markovian effect).