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).     

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.     

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.     

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.     

Steady-State Analysis of Two Single-Mode Dye Laser Models with Multiplicative Colored Model

In this paper, a unified expansion theory that can be simultaneously applied to both large and small correlation times developed by Gang HU is established and applied to the systems driven by multiplicative colored noise. The stationary intensity probabilities are calculated for colored gain-noise and colored-loss-noise models. Comparing with the predictions of the best Fokker-Planck equation and the unified colored-noise approximation for the stationary intensity probability of the two models, it is found that the results of the unified expansion theory are in better agreement with simulations and experimental results than those of the best Fokker-Planck equation approximation and the unified colored-noise approximation.     

Intensity Correlation Function of a Single-Mode Laser Driven by Colored Cross-Correlation Noises in Modulation of a Bias Signal

By using the linear approximation method, the intensity correlation function is calculated for a single-mode laser modulated by a bias signal and driven by colored pump and quantum noises with colored cross-correlation. We found that, when the correlation time between the two noises is very short, the behavior of the intensity correlation function versus the time, in addition to decreasing monotonously, also exhibits several cases, such as one maximum, one minimum, and two extrema. When the correlation time between the two noises is very long, the behavior of the intensity correlation function exhibits oscillation and the envelope is similar to the case of short cross-correlation time.     

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.     

基于金刚石色心自旋磁共振效应的微位移测量方法

基于压电陶瓷精密微位移系统的扫描探测技术是目前精密测量仪器进行微纳区域/结构性能测试的核心系统,但压电陶瓷材料存在迟滞、非线性问题,限制了对微位移分辨能力的提升.本文以金刚石氮空位色心为敏感单元,利用电子自旋效应对磁场强度的高分辨敏感机理,结合永磁体周围不同位置对应的磁场强度变化关系,提出了一种基于金刚石氮空位色心电子自旋敏感机理的微位移检测方法.通过建立电子自旋效应与微位移的关联模型,搭建了相应的微位移测量系统.经实验验证,该系统对微位移测试的灵敏度为16.67 V/mm,检测分辨率达到60 nm,实现了对微位移的高分辨率测量.并通过理论分析,该系统的微位移测量分辨率可进一步提升至亚纳米级水平,为新型微位移测量技术提供了发展方向和研究思路.     

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 io when the noise correlation coefficient λ is positive; and there exists minimum （i.e., suppression） in the T-io curve when λ is negative. And whenλ is zero, T increases monotonously with increasing io. Furthermore, the curve of T upon the signal frequency Ω is also studied. Our study shows that no matter what the value of λ is, there exists minimum （i.e., suppression） in the T-Ω curve.     

Influence of Noise on Time Evolution of Intensity Correlation Function

Using the linear approximation method, we have studied how the correlation function C（t） of the laser intensity changes with time in the loss-noise model of the single-mode laser driven by the colored pump noise with signal modulation and the quantum noise with cross-correlation between the real and imaginary parts. We have found that when the pump noise self-correlation time T changes, （i） in the case of r 〈〈 1, the C（t） vs. t curve experiences a changing process from the monotonous descending to monotonous rise, and finally to the appearance of a maximum; （ii） in the case of r 〉〉 1, the curve only exhibits periodically surging with descending envelope. When r 〈〈 i and T does not change, with the increase of the pump noise intensity P, the curve experiences a repeated changing process, that is, from the monotonous descending to the appearance of a maximum, then to monotonous rise, and finally to the appearance of a maximum again. With the increase of the quantum noise intensity O,, the curve experiences a changing process from the monotonous rise to the appearance of a maximum, and finally to the monotonous descending. The increase of the quantum noise with cross-correlation between the real and imaginary parts will lead to the fall of the whole curve, but not affect the form of the time evolution of C（t）.