The influence of higher order contributions to the correlation function of the intensity fluctuation in a Laser near threshold

The influence of higher order contributions to the correlation function of the intensity fluctuation in a Laser near threshold is investigated by solving the Fokker-Planck equation. It is found that higher contributions have to be taken into account slightly above threshold, i.e. the noise spectrum of the intensity consists of several Lorentzian lines. It is shown that, to a good accuracy, one can introduce an effective Lorentzian line, the width of which is 25% larger than the width of the first Lorentzian line slightly above threshold.     

Photon statistics and autocorrelation of a multi-mode laser

The intensity fluctuation properties were experimentally studied for one mode among many oscillating longitudinal modes of an argon ion laser in a region sufficiently above threshold. The individual longitudinal mode fluctuated considerably even well above the threshold, while the laser intensity summed over all the longitudinal modes was observed stable. This fluctuation was found to be much larger than expected from the previous theoretical work by Arecchi and Ricca which did not consider the combination-tone polarization. The slowing-down and the increase of the fluctuation were observed when the excitation was lowered toward to its threshold value. The correlation time of the intensity fluctuation measured ranged from 0.7 μs to 20 μs depending on the oscillation condition.     

Correlation function of the amplitude and of the intensity fluctuation for a laser model near threshold

In extension of a preceding paper the correlation function of the amplitude and of the intensity fluctuation are calculated in the threshold region. The laser amplitude is treated as a classical random variable obeying a van der Pol equation with a noise term. In order to get correlation functions, the method of distribution functions is employed. The distribution functions are evaluated by the Fokker-Planck equation. The lowest eigensolutions of the Fokker-Planck equation are obtained approximately by a variational method.     

Steady-State Analysis of a Two-Mode Laser System with Cross-Correlation Between Real and Imaginary Parts of Quantum Noise

An inhomogeneously broadened two-mode laser system with cross-correlations between the real and imag- inary parts of quantum noise is considered. The Fokker-Planek equation of the system is derived by the phase-locking method. The steady-state probability distribution, the mean light intensity, the normalization autocorrelation function, and cross correlation function are calculated. The results indicate that： （i） The cross-correlation between the real and imaginary parts of quantum noise can cause the stationary probability distribution from one peak structure to two extrema structure when the laser system is operated above threshold; （ii） The cross-correlation between the real and imaginary parts of quantum noise enhance the light intensity fluctuation and decrease the laser output when the laser system is operated below or near threshold; （iii） The effect of the cross-correlation between the real and imaginary parts of quantum noise is very weak on the stationary properties when the laser system is operated far above threshold.     

Influence of fluctuations of a laser pump on the intensity correlation of resonance fluorescence radiation

The influence of fluctuations of a relatively weak laser pump on the intensity correlation of resonance fluorescence radiation is studied for a laser acting both below and above the threshold. Below the threshold the radiation of the laser is characterized by Gaussian properties causing non-factorization of the intensity correlation function. Above the threshold the laser shows non-linear filter properties and, therefore, the deviation of the exact intensity correlation function from its factorized value is small.     

单模激光系统输入信号后的稳态平均光强相对涨落

研究了具有实虚部间关联的量子噪声和抽运噪声驱动的单模激光系统输入信号后的统计性质,采用线性化近似方法计算了系统的稳态平均光强相对涨落,分析了量子噪声实虚部间关联系数、量子噪声强度、抽运噪声强度、输入信号振幅和频率、净增益等对稳态平均光强相对涨落的影响,发现在量子噪声实虚部间弱关联、小噪声、远离阚值、信号振幅不大和频率较高的条件下激光场的统计涨落较小。     

激光光强扰动对相干场成像降质影响理论研究

激光相干场成像系统发射多束激光,经大气传输对远程目标成像,大气湍流引起的激光束光强扰动是影响成像质量的一个关键因素.本文从湍流引起的激光束光强扰动对回波解调信号的影响关系入手,建立了激光回波光强扰动因子对相位闭合系数和成像频谱分量的降质传函理论模型;基于三光束激光相干场成像系统仿真验证了理论模型的有效性.研究表明激光相干场成像频谱分量和成像像质主要受三光束相位闭合求解算法中第二光束光强扰动影响.该研究揭示了激光回波光强扰动对成像像质的影响机理,对于分析大气湍流等引起的光强扰动降质效应和合理分配多光束光强稳定性以提高成像质量具有理论指导意义.     

Effects of light on cesium 6S-8S two-photon transition

This work presents a simple approach for determining the contribution of Lorentzian or Gaussian statistics by data fitting the spectrum to a Voigt profile. The fitting result shows that the Lorentzian width remains almost constant (∼1.51 MHz) and the Gaussian width increases (∼1.0-2.0 MHz) while changing the laser intensity or atomic density. The frequency shift associated with the cesium 6S-8S two-photon transition as a function of laser power is approximately ), agrees closely with the theoretical value. These results can be used to improve the optical secondary frequency standard in the near infrared region.     

Dynamical properties of total intensity fluctuation spectrum in two-mode Nd:YVO_4 microchip laser

We investigate the total intensity fluctuation spectrum of the two-longitudinal- mode Nd:YVO4microchip laser(ML).We find that low-frequency relaxation oscillation(RO) peaks still appear in the total intensity fluctuation spectrum, which is different from a previous research result that the low-frequency RO peaks exist in the spectrum of the individual mode but compensate for each other totally in the total intensity fluctuation spectrum. Taking the spatial hole-burning effect into account, one and two-mode rate equations for Nd:YVO4ML laser are established and studied. Based on the theoretical model, we find that when the gains and losses for two longitudinal models are different, a low-frequency RO peak will appear in the total intensity fluctuation spectrum, while when they share the same gain and loss, the total spectrum will behave like that of a single mode laser. Theoretical simulation results coincide with experimental results very well.     

Statistical fluctuations in a saturation laser model with correlated noises

We study the effects of correlations between quantum and pump noises on fluctuations of the laser intensity in a saturation laser model. An approximative Fokker--Planck equation and analytic expressions of the steady-state probability distribution function (SPD) of the laser system are derived. Based on the SPD, the normalized mean, the normalized variance, and the normalized skewness of the steady-state laser intensity are calculated numerically. The results indicate that (i) the correlation strength \lambda of correlated noises always enhances the fluctuation of laser intensity; (ii) the correlation time \tau of correlated noises strengthens the fluctuation of laser intensity for the below-threshold case but \tau weakens it for the above-threshold case.     

Computation of the statistical properties of laser light

In this paper a statistical ensemble of laser light is defined. The lasing field is treated as a classical variable, the spontaneous emission is considered phenomenally by using a random function. Special attention is paid to the transverse mode behaviour. To calculate the ensemble elements, an approach based on Fresnel integration has been developed. Theoretical investigations into some stripe stable resonators have been carried out. Some results for the intensity, the mode spectrum, the correlation between transverse modes, the beam quality, and the spectra of the intensity and the output power fluctuation are presented and discussed.     

An effect of curvature of rotating diffuse objects on the dynamics of speckles produced in the diffraction field

The time correlation function is analyzed of the speckel intensity fluctuation produced in the Fresnel diffraction field from a rotating diffuse object under illumination of a Gaussian laser beam. The dependence of the curvature radius of the rotating diffuse object on the time correlation length of the speckle intensity fluctuation is especially explored by taking into account the size of the detecting aperture. The theoretical results are confirmed experimentally for detecting apertures with various sizes. It is shown that a detecting aperture with an appropriate size is required. It becomes useful for determining the radius of curvature of the rotating diffuse object from measurements of the time correlation length of the speckle intensity fluctuation.     

Conductance noise spectrum of mesoscopic systems

We investigate the shape as well as the size- and temperature-dependence of the conductance noise spectrum of a small system containing electrons and both fixed and mobile scatterers. If the number of mobile scatterers within a phase-coherent region is sufficiently large, the temporal variation of the conductance can be viewed as a random walk process limited by the universal conductance fluctuations, resulting in a practically Lorentzian power spectrum. We discuss the conditions under which the noise spectrum of a system consisting of many phase-coherent regions is either Lorentzian or 1/f-like. The temperature-dependence of the power spectrum is determined by the hopping mechanism and the variation of the phase breaking length. As a function of temperature the spectrum satisfies power law scaling relations with exponents depending on the dimension and the temperature range; the spectral intensity can both increase and decrease with decreasing temperature.     

Correlation functions for a laser with saturable absorber near threshold

We study in the threshold region the relaxation times and the correlation functions of the field amplitude and of the intensity fluctuations for a solid-state laser containing a saturable absorber in the domain of the parameter space where bistability can occur. We show that the relaxation times display in a small domain above threshold a net-like structure which disappears in the polynomial approximation. The noise spectrum is nearly lorentzian only in a very small domain around the transition point and well above threshold. The line-width displays the well-known sharpening at and above threshold.Supported in part by the Polish Ministry of Science, Technology and Higher Education, Project M.R.I.7Chercheur qualifié F.N.R.S.     

Measurements of the fine structure of laser intensity correlations near threshold

The correlation function of the intensity fluctuations of a single mode laser in the threshold region has been measured with a fast digital correlator. The various exponential components have been separated for the first time, by exploiting the nonlinear characteristics of the correlator. The results are in quantitative agreement with the theoretical predictions.     

Spectral linewidths of two mode lasers

By application of quasilinear response theory the spectral linewidths of two mode lasers near their threshold are calculated. Use is made of an adaequate fluctuation-dissipation relation. The laser is described by a fluctuation Hamiltonian with intensity and phase coupling of the modes. Incidentally the two modes' intensity fluctuation linewidths (given earlier) are rederived, and a formerly given result on the detuned single mode laser is corrected. For the phase coupled two mode laser we find a third threshold between the photon thresholds and, for large pumping, a linewidth factor 1/2.     

二次谐波中的饱和效应和乘性噪声

研究了单模激光中产生的二次谐波的统计性质,用全饱和激光理论导出了二次谐波光子计数ｍ的几率分布函数、二次阶乘矩和三次阶矩的表达式,同实验值比较,理论与实验在阈值附近符合得很好。研究结果表明,激光场基波和二次谐波的涨落随空腔衰减常数的增大而减小;当激光场中含有乘性噪声时,乘性噪声增强基波的涨落,同时抑制二次谐波的涨落。     

全频域下窄线宽激光器光谱线宽的分析

窄线宽激光器的线宽表征方式通常采用延时自外差法测量技术。该技术是通过延时光纤差拍产生一个与待测激光线宽相关的洛伦兹频谱,因此该频谱只具有单一的线宽表现形式。为了能够观察到激光器的线宽和频率噪声在其傅里叶频率分布下的完整特性,报道了一种基于β算法计算窄线宽激光器线宽的方法。该方法是结合频率噪声中的白噪声和1/f噪声分别诱导不同激光线型的理论,从而确定激光线宽。首先,对β算法的基本原理进行了详细的分析说明。通过基于维纳-辛钦定理,分析了窄线宽激光器不同频率范围内的频率噪声和激光线宽的依赖关系。阐明了在截止频率趋于0和无穷大的两个范围条件时,激光频谱特性从高斯线型向洛伦兹线型演变。同时推导出使两种线型转换的截止频率表达式,并将其转换为频率噪声函数,该函数定义为β分子线。此时频率噪声分量中高斯线型的总和即为激光线宽计算公式;其次,对窄线宽激光器的频率噪声和激光线型进行数值仿真。将通过OEwaves公司的OE4000互相关零差相位/频率噪声自动测试系统测得的频率噪声谱密度,带入β算法理论公式中。结果显示：1/f噪声导致激光呈现高斯线型,线宽随截止频率的增加而增大。而白噪声将导致洛伦兹线型,线宽不再随截止频率而改变。此外,在低频区域,频率噪声电平远大于其傅里叶频率,噪声调制系数较高,该部分噪声可以决定线宽大小。因此,高斯线型区域对应的频率噪声的积分,即为待测激光器的线宽;在高频区域,频率噪声电平与其傅里叶频率相差较小,频率波动较快,噪声对线宽影响可以忽略。并且频率带宽在截止频率范围内,计算的线宽误差较小。最后,实验上运用β算法对RIO公司的1 550 nm低噪声窄线宽激光器的频率噪声功率谱密度进行积分计算,成功获得了其不同傅里叶频率分布下对应的激光线宽值。其中β分子线将频率噪声中的白噪声和1/f噪声分隔两部分：当频率噪声谱密度大于β分子线时,激光即为高斯线型,线宽随频率积分带宽的增加而减少;而频率噪声谱密度小于β分子线时,激光呈现洛伦兹线型,线宽为定值不再改变。同时为了对β算法进行实验验证,搭建了延迟光纤为50 km、移频频率为60 MHz的延时自外差法测量系统。对注入电流为110 mA的RIO 1 550 nm低噪声窄线宽激光器的线宽进行实验测量,测量结果表明激光线宽为1.8 kHz,与上述β算法中2.8 kHz的频率带宽积分结果一致。充分证明了此算法的准确性。β算法可以对任意类型的窄线宽激光器进行线宽表征,对窄线宽激光器的研究具有重要意义。     

Influence of Signal and Noise on Statistical Fluctuation of Single-Mode Laser System

On the basis of calculating the steady-state mean normalized intensity fluctuation of a signal-mode laser system driven by both colored pump noise with signal modulation and the quantum noise with cross-correlation between its real and imaginary parts, we analyze the influence of modulation signal, noise, and its correlation form on the statistical fluctuation of the laser system. We have found that when the amplitude of modulation signal weakens and its frequency quickens, the statistical fluctuation will reduce rapidly. The statistical fluctuation of the laser system can be restrained by reducing the intensity of pump noise and quantum noise. Moreover, with prolonging of colored cross-correlation time, the statistical fluctuation of laser system experiences a repeated changing process, that is, from decreasing to augmenting,then to decreasing, and finally to augmenting again. With the decreasing of the value of cross-correlation coefficient, the statistical fluctuation will decrease too. When the cross-correlation form between the real part and imaginary part of quantum noise is zero correlation, the statistical fluctuation of laser system has a minimum. Compared with the influence of intensity of pump noise, the influence of intensity of quantum noise on the statistical fluctuation is smaller.