信号调制色泵噪声和实虚部间关联量子噪声驱动下单模激光的随机共振现象

计算了受信号调制的色泵噪声和实虚部间关联的量子噪声驱动的单模激光损失模型的输出光强信噪比.发现信噪比R随泵噪声自关联时间τ、调制信号频率Ω和量子噪声实虚部间关联系数λq的变化均存在随机共振,这种现象扩展了“信噪比R对噪声强度的变化曲线具有极大值”的典型随机共振. 若以Ω为参数,当Ω增加时,Ｒ随τ的关系曲线经历了从同时出现共振和抑制到单峰共振,最后到单调上升的变化,呈现多种形式的随机共振．若以τ为参数,当τ增加时,Ｒ随Ω的关系曲线经历了从单调上升到同时出现共振和抑制,最后又到单调下降的变化过程．Ｒ随λq的关 关键词： 噪声 信噪比 随机共振     

一级近似下的单模激光增益模型随机共振

把周期信号输入单模激光,对激光增益模型中的乘法噪声项取一级近似通过计算相关函数得到功率谱,发现输出信号是洛伦兹型的.信噪比随抽运噪声强度和量子噪声强度的变化均出现随机共振,但共振峰对应的噪声强度比零级近似下的小.     

STATIONARY PROBABILITY DISTRIBUTION FOR COLORED-LOSS-NOISE MODEL OF A SINGLE-MODE DYE LASER

We apply the interpolation procedure to calculate the stationary probability distribution of the colored-loss-noise model of a single-mode dye laser operating above the threshold with correlation time τ covering a very wide range. By stochastic Runge-Kutta algorithm, we also carry out numerical simulations of steady-state properties. Comparing the results of the interpolation procedure and the unified colored-noise approximation with simulation results, we find that the agreement between the results of the interpolation procedure and the simulation results is much better than that of the unified colored-noise approximation when correlation time τ covers a range from moderate to large. We conclude that the interpolation procedure really improve the accuracy of predictions for this system.     

Phenomenon of Repeated Current Reversals in the Brownian Ratchet

We study the probability current of the Brownian Particles in a tilted periodic piecewise linear “saw-tooth” Potential.It is found that the stationary probability current takes on a maximum value at a given additive noise if the intensity of the multiplicative noise is appropriate and at the same time both noises are correlated;and the direction of the stationary probability current is reversed more than once upon some certain corelation intensities between both noises.It is proven that the occurrence of current reversal is only dependent on the relative intensity of the multiplicative and additive noises,but has nothing to do with the absolute intensities of the two noises.     

Stochastic Resonance in a Bistable Sawtooth Potential Driven by COrrelated Multiplicative and Additive Noise

We Present and analytical investigation of the signal-to-noise ratio(SNR)by studying the bistable sawtooth system driven by correalted Gaussian white noise.The analytic expression of the SNR is obtained.We detect some novel results,as follows.(1) Stochastic resonance(SR) always occurs in the SNR-Q (the multiplicative noise intensity)curve for the whole range of correlation coefficients.(2)There is not only resonance but also suppression and monotony in the dependence of SNR upon the additive noise intensity.(3) There are two extrema(one is minimum,the other meximum)in the SNR-b(the barrier height)curve for different multiplicative noise intensities.     

Influence of the net gain on characteristic of stochastic resonance in a single-mode laser system

The phenomenon of stochastic resonance (SR) is found in a single-mode laser system driven by the colored pump noise with signal modulation and the quantum noise with cross-correlation between the real and imaginary parts. When the net gain a0 changes, it is found that, 1) the shape of the curve of the signal-to-noise ratio (SNR) versus the pump noise self-correlation time τ exhibits a changing process of multiform SR, from single-peak SR, to simultaneous existence of resonances and suppressions; 2) the curve of SNR. versus signal frequency Ω experiences a complicated changing process from the monotonous descending to the simultaneous appearances of a maximum and a minimum, and finally to monotonous descending; 3) the curve of SNR versus cross-correlation coefficient between the real and imaginary parts of the quantum noise λq appears an acute single-peak SR. Therefore, the net gain ao greatly influences the characteristic of SR of laser system.     

Intensity Correlation Time of a Single-Mode Laser Driven by Two Coloured Noises with Coloured Cross-Correlation with Bias Signal Modulation

The intensity correlation time T is studied by employing a gain-noise model of a single-mode laser driven by coloured pump noise τ1 and coloured quantum noise τ2 with coloured cross-correlation τ3 with a bias signal modulation. By using the linear approximation method, we detect that a maximum （i.e. resonance） exists in the curves of the intensity correlation time T versus the noise intensities D and Q when the noise correlation coefficient A is positive; and a minimum （i.e. suppression） exists in the T - D and T - Q curves when A is negative. When A is zero, T increases monotonously with increase of D and decreases monotonically with increase of Q. Furthermore, the curve of T versus the pump noise self-correlation time τ1 is also studied. Our study shows that, no matter what the value of A is, there exist one maximum and one minimum in the T - τ1 curve.     

Stochastic resonance of bias signal-modulated noise in a single-mode laser＊

Stochastic resonance (SR) for bias signal modulation is studied in a single-mode laser system. By investigating a gain-noise model driven by correlated pump noise and quantum noise, we find that, whether the correlation coefficient between both the noises is positive or negative, SR always appears in the dependence of signal-to-noise ratio (SNR) upon the noise correlation time and the frequency of the modulation signal. However, only when the correlation coefficient between both noises is negative can SR occur in the dependence of SNR upon the quantum noise intensity and pump noise intensity, while when the correlation coefficient between both noises is positive, it shows monotonically.     

Stochastic resonance in a single-mode laser driven by frequency modulated signal and coloured noises

By adding frequency modulated signals to the intensity equation of gain--noise model of the single-mode laser driven by two coloured noises which are correlated, this paper uses the linear approximation method to calculate the power spectrum and signal-to-noise ratio (SNR) of the laser intensity. The results show that the SNR appears typical stochastic resonance with the variation of intensity of the pump noise and quantum noise. As the amplitude of a modulated signal has effects on the SNR, it shows suppression, monotone increasing, stochastic resonance, and multiple stochastic resonance with the variation of the frequency of a carrier signal and modulated signal.     

Effects of signal modulation and coloured cross-correlation of coloured noises on the diffusion of a harmonic oscillator

The diffusion in a harmonic oscillator driven by coloured noises $\xi(t)$ and $\eta(t)$ with coloured cross-correlation in which one of the noises is modulated by a biased periodic signal is investigated. The exact expression of diffusion coefficient d as a function of noise parameter, signal parameter, and oscillator frequency is derived. The findings in this paper are as follows. 1) The curves of d versus noise intensity D and d versus noises cross-correlation time $\tau_3$ exist as two different phases. The transition between the two phases arises from the change of the cross-correlation coefficient $\lambda$ of the two Ornstein--Uhlenbeck (O-U) noises. 2) Changing the value of $\tau_3$, the curves of d versus Q, the intensity of colored noise that is modulated by the signal, can transform from a phase having a minimum to a monotonic phase. 3) Changing the value of signal amplitude A, d versus Q curves can transform from a phase having a minimum to a monotonic phase. The above-mentioned results demonstrate that a like noise-induced transition appears in the model.