Effects of multiplicative colored noise in the growth of dye-laser radiation: The projection operator method

It has been well established by Roy, Fox, Yu and Zhu that in the growth of dye-laser radiation the multiplicative colored noise leads to an increase of the variance and skewness of first-passage time distribution (FPTD) as the laser intensity approaches steady state. In this paper, we develop an analytic method for the approximate treatment of the colored noise effects in the FPTD problem based on the Hanggi ansatz. The mean, variance, and skewness of the FPTD with multiplicative colored noise are obtained by means of the projection operator technique used by the authors to develop a theory of nonlinear external noises. The theoretical results are compared with those obtained from numerical simulations.     

染料激光瞬态过程中的噪声

本文用首次通过时间的方法来分析染料激光瞬态的统计性质.提出了单模染料激光的理论模型,用白噪声简化泵浦涨落,通过福克-曾朗克方程求出首次通过时间分布的平均值、方差和偏斜度的解析解.与实验数据和用蒙特卡罗模拟获得的曲线相比较,解析解的结果与实验测量和数值计算符合得很好.     

Intensity Correlation,Relaxat ion Time,Intensity Fluctuation and First-Order-Like Transition of Dye Laser

Statistical properties of dye laser are studied by using the colored gain-noise model which has been presented recently. We calculate the intensity correlation function and relaxation time driven by colored pump noise and white spon taneous-emission noise simultaneously. Intensity fluctuation and first-order-like transition are analyzed too in this paper. It is found that the colored gain-noise model can describe well the anomalous statistical properties of dye laser.     

Colored noise in a two-dimensional nonlinear system

A two-dimensional decoupling theory is developed when colored noise is included in a nonlinear dynamical system. By a functional analysis, the colored noise is transformed to an effective noise that includes the noise correlation time, the mean dynamical variable, and the original noise strength. When the two-dimensional decoupling theory is applied to single-mode and two-mode dye laser systems, the mean, variance, and effective eigenvalue of laser intensity are calculated. Excellent agreement between theoretical analysis, numerical simulations, and experimental measurements are obtained. It is seen that the increase of noise correlation time can reduce the fluctuations in the laser system. It is also shown that there is relatively large fluctuation in the phase when the laser undergoes from thermal light to coherent light when the theory is applied to a single mode dye laser. Received 20 August 2001 and Received in final form 4 December 2001     

染料激光色立方模型定态性质的描述

应用一般形式的统一色噪声近似得到了洒料激光色立方模型光强分布的福克－普朗克方程。导出了光强分布函数，描述了光强涨落的实验和数值模拟结果以及色噪声对光强涨落的影响。     

The Time-Dependent Moments and Correlation Functions of the Intensity of a Single-Mode Dye Lase

By combining linear approximation with Novikov theorem we derive first the time-dependen tmoments of laser intensity for colored saturation loss-noise, colored gain-noise and coloredloss-noise models of a singlemode dye laser. We analyze and compare the time-evolutioncharacter of timedependent moments of laser intensity for three models. The intensitycorrelation functions and correlation time for the colored saturation loss-noise model arederived and compared to the corresponding quantities for colored gain-noise and coloredloss-noise models. We show that, due to saturation effects in the considered laser model, theeffect of which the correlation time of the noise hides the differences between the in tensitycorrelation functions of the models is weakened. It can be seen from the evolution curves ofthe intensity correlation time versus the pump parameter that the dye laser exists criticalslowing-down.     

Fluctuations of Single-Mode Laser Driven by Two Different Kinds of Colored Noise

A single-mode laser with coupling between additive and multiplicative noise terms is investigated when the multiplicative noise and the coupling between two noise terms are colored fluctuations with finite correlation times T1 and τ2. Combining the unified colored noise approximation (UCNA) and the functional analysis, the stationary probability distribution (SPD) and the variance of the laser intensity is derived. It is found that the colored nature of multiplicative noise and the coupling strength between two noise terms can affect both the structure and the height of the SPD, while the colored nature of the coupling between two noise terms can only affect the height of the SPD. The multiplicative noise can enhance the intensity fluctuations while the additive noise can reduce the fluctuations in a laser system. Numerical simulations are presented and consistent to the analytical results.     

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

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.     

Steady-State Analysis of a Single-Mode Laser Driven by Colored Pump Noise with Cross-Correlation Between Real and Imaginary Parts of Quantum Noise

Applying the method of the unified colored noise approximation and phase lock, we study in this paper the stationary intensity distribution of the single-mode laser driven by colored pump noise with cross-correlation between the real and imaginary parts of the quantum noise. We present a thorough discussion of how the cross-correlation λq between the real and imaginary parts of the quantum noise and the self-correlation time τ of the pump noise determine the behaviors of the stationary distribution Qst(I), the mean (I）, and the variance λ2(0) of the laser intensity. It is shown that cross-correlation intensity λq of the complex quantum noise can induce a first-order-like transition. When the pump noise is colored noise (τ≠0), improving the pump parameters monotonously will make the curves of Qst(I) exhibit reentrant phase transition. The fluctuations of laser intensity are strongly influenced by λq and τ when the laser is operated near or below threshold. Especially when τ≠0, the heights of the peaks of the curves of λ2(0)-α0 and α3(0)-α0, (here a0 is the net gain coefficient) go up as λq increases. However the entire curves λ2(0)-α0 and λ3(0)-α0 are abruptly suppressed when λq = 1, in similarity to phase transition of stationary intensity distribution.     

色关联的色噪声驱动的分段非线性模型的平均首次穿越时间

研究了色关联的乘性高斯色噪声和加性高斯色噪声驱动的分段非线性系统中, 噪声强度和相关时间对平均首次穿越时间的影响. 利用一致有色噪声近似方法和最速下降方法, 推导出系统平均首次穿越时间的表达式. 研究结果表明: 系统的平均首次穿越时间随着乘性噪声的增加会出现单峰结构, 即“共振”现象, 峰值会随着加性噪声强度和噪声之间关联强度的增加而减小. 而平均首次穿越时间作为加性噪声的函数呈单调曲线, 说明乘性噪声和加性噪声对平均首次穿越时间的影响不同. 此外, 乘性和加性噪声关联时间以及互关联时间在正关联时和负关联时 对系统平均首次穿越时间的影响是不同的. 关键词： 色噪声 分段非线性系统 平均首次穿越时间     

偏置信号调制下色关联噪声驱动的单模激光的光强相对涨落

采用线性化近似，计算了由具有色关联的受偏置信号调制的色泵噪声和色量子噪声驱动 的单模激光增益模型的光强相对涨落，发现相对涨落随噪声强度的变化曲线中存在极小值，分析了偏置信号的强度、周期信号频率、噪声间的互关联强度和互关联时间对曲线的影响； 对单模激光增益模型在偏置信号调制和直接信号调制两种方式下的输出光强相对涨落进行了比较，发现光强涨落与偏置信号的强度密切相关. 关键词： 偏置信号调制 光强相对涨落 线性化近似     

负关联噪声驱动下单模激光的定态分析

研究了负关联的加法和乘法高斯白噪声驱动下单模激光损失模型的定态情况。文中推导了负关联情况下，定态时的激光场幅的几率分布，光强的平均值，光强的协方差以及光强的偏斜率。并和文献〔１，２〕中正关联时的定态分析作了比较，发现了有意义的新现象。     

非线性激光场中量子噪声之间的耦合效应

用二维气体激光模型对量子噪声的实部和虚部存在耦合的激光场进行了理论分析，通过福克－普朗克方程导出了定态激光光场强度和位相的分布函数，算出了定态激光强度和位相的平均值，方差和偏斜度，与量子噪声的两个分量为独立随机变量的激光场相比，噪声间的耦合极大地改变了激光场强度和位相的涨落，并引起了激光场强度与位相之间的耦合。     

First-Order-Like Transition of Dye Laser Colored Gain Model

A unified colored-noise approximation, a novel approximative theory, is applied to solve the colored gain model for dye laser. The stationary probability of the colored gain model is derived. The first-order-like transition is discussed. The effect of the noise correlation time τ on the first-order-like transition is analysed. It's found that the size of the regions in the parameter plane is related with r and three different regions are turned into two different regions in the parameter plane as r >> 1/2a₁. By comparison, we find that the res.ults of the unified colored-noise approximation are more close to simulation's results than those of the best Fokker-Planck equation.     

Enhancement of density divergence in an insect outbreak model driven by colored noise

The steady states and the transient properties of an insect outbreak model driven by Gaussian colored noise are studied in this paper.According to the Fokker-Planck equation in the unified colored-noise approximation,we analyse the stationary probability distribution and the mean first-passage time of this model.By numerical analysis,the effects of the self-correlation time of insect birth rate and predation rate respectively reveal a manifest population divergence on the insect density.The decrease of the mean first-passage time indicates an enhancement dynamic on the density divergency with colored noise of a large self-correlation time based on the insect outbreak model.     

单模激光系统线性化近似适用范围的分析

采用线性化近似方法计算了具有实虚部关联的量子噪声和泵噪声驱动的单模激光损失模型的光强相对涨落,为了对线性化近似的适用范围进行详细的分析,分别讨论了量子噪声强度、泵噪声强度、量子噪声实虚部间关联系数对光强相对涨落的影响,得出在小噪声、远离阈值时,线性化近似适用范围扩大;小噪声、远离阈值且当量子噪声实虚部无关联时,线性化近似适用范围极大的结论.     

Time-Delayed Feedback Control in a Single-Mode Laser System

The effects of time-delayed feedback control in a single-mode laser system is investigated. Using the small time delay approximation, the analytic expression of the stationary probability distribution function of the laser field is obtained. The mean, normalized variance and skewness of the steady-state laser intensity are calculated. It is found that the time-delayed feedback control can suppress the intensity fluctuation of the laser system. The numerical simulations are in good agreement with the approximate analytic results.     

非高斯噪声激励下FHN神经元系统的定态概率密度与平均首次穿越时间

研究了非高斯噪声激励下的FHN神经元系统,应用路径积分法和统一色噪声近似得到系统的定态概率密度函数和平均首次穿越时间表达式.发现了加性噪声强度Q能够诱导非平衡相变的产生,乘性噪声强度D、偏离参数p及关联时间τ₀均不能诱导非平衡相变发生;非高斯噪声的存在缩短了细胞神经元系统静息态和激发态之间的转化时间,有利于神经元信息的传递. 关键词： FHN神经元系统 非高斯噪声 定态概率密度 平均首次穿越时间     

Dynamical Properties of a Single-Mode Laser with Both Colored Noise and Injected Signal

The colored noise in a single-mode laser with injected signal is investigated by the method of two-dimensional unified colored noise approximation. The normalized correlation function λ₂(0), the intensity correlation time T_c and effective eigenvalue λ_eff are calculated. The effects of the injected signal I₀, colored noise strength P^ˊ and the noise correlation time τ on the dynamical properties of the single-mode laser are discussed.     

实虚部关联的量子噪声和泵噪声对单模激光动力学性质的影响

采用具有实虚部关联的量子噪声和泵噪声驱动的单模激光损失模型，用线性化近似方法研究了反映激光动力学性质的光强关联函数，讨论了光强关联函数随时间的演化；并对线性化近似方法的适用范围进行了详细分析，分别讨论了量子噪声强度、泵噪声强度、量子噪声实虚部关联系数对光强相对涨落的影响，得出在小噪声、远离阈值时，线性化近似方法适用范围扩大；小噪声、远离阈值且当量子噪声实虚部无关联时，线性化近似方法适用范围最大的结论. 关键词： 单模激光 光强关联函数 光强相对涨落