Statistical properties of a single-mode laser driven by additive and multiplicative coloured noises with a coloured cross-correlation for different correlation times
Liang Gui-Yun (梁贵云)a, Cao Li (曹力)ab, Zhang Li (张莉)a, Wu Da-Jin (吴大进)ab
a State Key Laboratory of Laser Technology, Huazhong University of Science and Technology, Wuhan 430074, China; b China Centre of Advanced Science and Technology (World Laboratory), Beijing 100080, China
Abstract We study a system for a single-mode laser driven by additive and multiplicative coloured noises with a coloured cross-correlation. The analytical expression of the stationary intensity distribution (SID) for the laser is derived in the case of three different correlation times. The influences of each stochastic parameter on the SID are discussed, the effects of the noise "colour" and the cross-correlation of noises on the mean intensity $\langle I\rangle$, the variance, $\lambda_2(0)$, and the skewness, $\lambda_3(0)$ of the single-mode laser are investigated. We find that there are colourful phase transitions for the SID above a threshold, and re-entrant transitions induced by the "colour" of the additive noises. Further research of the curves of $\langle I\rangle -\tau_i$, $\lambda_2(0)-\tau_i$, and $\lambda_3(0)-\tau_i (i=1,2,3)$ (where $\tau_i$ is the correlation time) shows that the output intensity not only increases with the additive noise correlation time $\tau_2$ and the cross-correlation time $\tau_3$, but also the quality of the output of laser beams is optimized.
Received: 10 February 2003
Revised: 18 May 2003
Accepted manuscript online:
Fund: Project supported by the National Natural Science Foundation of China (Grant No 10275025).
Cite this article:
Liang Gui-Yun (梁贵云), Cao Li (曹力), Zhang Li (张莉), Wu Da-Jin (吴大进) Statistical properties of a single-mode laser driven by additive and multiplicative coloured noises with a coloured cross-correlation for different correlation times 2003 Chinese Physics 12 1109
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