中国物理B ›› 2003, Vol. 12 ›› Issue (10): 1109-1119.doi: 10.1088/1009-1963/12/10/311

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Statistical properties of a single-mode laser driven by additive and multiplicative coloured noises with a coloured cross-correlation for different correlation times

梁贵云1, 张莉1, 曹力2, 吴大进2   

  1. (1)State Key Laboratory of Laser Technology, Huazhong University of Science and Technology, Wuhan 430074, China; (2)State Key Laboratory of Laser Technology, Huazhong University of Science and Technology, Wuhan 430074, China; China Centre of Advanced Science and Technology (World Laboratory), Beijing 100080, China
  • 收稿日期:2003-02-10 修回日期:2003-05-18 出版日期:2003-10-16 发布日期:2005-03-16
  • 基金资助:
    Project supported by the National Natural Science Foundation of China (Grant No 10275025).

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   

  1. 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
  • Received:2003-02-10 Revised:2003-05-18 Online:2003-10-16 Published:2005-03-16
  • Supported by:
    Project supported by the National Natural Science Foundation of China (Grant No 10275025).

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摘要： 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 , the variance, λ_2(0), and the skewness,λ_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 -τ_i, λ_2(0)-τ_i, and λ_3(0)-τ_i (i=1,2,3) (where τ_i is the correlation time) shows that the output intensity not only increases with the additive noise correlation time τ_2 and the cross-correlation time τ_3, but also the quality of the output of laser beams is optimized.

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.

Key words: single-mode laser, coloured cross-correlation, statistical properties

中图分类号:  (Modulation, tuning, and mode locking)

  • 42.60.Fc
42.60.Mi (Dynamical laser instabilities; noisy laser behavior) 02.50.Ey (Stochastic processes)