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     

加性噪声对激光一级相变类比的影响

从单模激光场的增益－噪声模型出发,导出了激光场定态强度分布函数,研究了定态分布函数的极值点随加性噪声、乘性噪声和注入信号的变化情况。结果表明,乘性噪声是使激光系统出现一级相变类比的关键因素,注入信号使相变行为减弱,而加性噪声却使得定态分布中极值点的数量和位置出现来回跳跃式变化。     

Noise conversion from pump to the passively mode-locked fiber lasers at 1.5 μm

We characterize the noise conversion from the pump relative intensity noise (RIN) to the RIN and phase noise of passively mode-locked lasers at 1.5 μm. Two mode locking mechanisms, nonlinear polarization rotation (NPR) and semiconductor saturable absorber mirror (SESAM), are compared for noise conversion for the first time. It is found that the RIN and the phase noise of both types of lasers are dominated by the noise converted from the pump RIN and thus, can be predicted with the measured pump RIN and noise conversion ratios. The SESAM laser is found to show an excess noise conversion from the laser RIN to the laser phase noise due to the slow saturable absorber effect.     

Power spectra and spatial pattern dynamics of a ring laser

Experimental measurements of power spectra of a single longitudinal and transverse mode ring dye laser are presented that reveal the critical slowing down of the laser near threshold. External pump noise serves as a probe of the frequency response of the dye laser. Detailed comparisons of the spectral characteristics with computer simulations and an approximate analytic theory are given. The dynamics of spatial pattern formation in a multimode dye laser is examined through measurements of first-passage-time distributions. A comparison of the experiments with computer simulations based on a simple theoretical model of the two-mode laser shows qualitative agreement. These measurements indicate that there are a variety of complex phenomena associated with the transverse mode pattern formation dynamics that need to be addressed theoretically and studied further experimentally.     

双模环型激光增益噪声模型的非线性效应

讨论了一个双模环型激光增益噪声模型，其中考虑了完全饱和效应且乘法噪声由增益系数涨落引起。在共振及两模具有相同泵参数时，获得了光强联合定态分布的精确解析表达式。通过与现有的双模激光摸型（其中乘法噪声由损失系数涨落引起）的比较，发现乘法噪声系数的非线性效应减弱了乘法噪声给激光光强统计性质带来的反常特性，并且这种减弱随着乘法噪声增强或损失系数减小而愈加明显。     

Theoretical Analysis of the Critical Phenomena of a Brillouin Laser

The critical phenomena of a Brillouin laser are analyzed theoretically. The results show that the behavior of a Brillouin laser in the threshold region is a second-order phase transition. The critical point of the phase transition is the gain threshold of the Brillouin laser, and the order parameter is the amplitude of the Stokes component in stimulated Brillouin scattering. The critical slow-down phenomenon and the typical characteristics in phase transition are demonstrated. Further work on the combination of nonlinear optics and phase transition in the Brillouin laser may lead to a new view and findings that could be significant for both fields.     

Temperature dependent nonlinear response of quantum cascade structures

Current response and gain spectrum of a terahertz quantum cascade laser is analyzed at different temperatures by a nonequilibrium Green’s functions approach. The simulations are compared to recent results of time domain spectroscopy. Being able to retrieve higher harmonics of the response function, nonlinear phenomena in quantum cascade lasers are studied theoretically. For different temperatures, gain is simulated under operating conditions and related to the intensity inside the cavity, showing the degradation of performance with temperature. Resolving the electron densities in energy shows the breakdown of inversion at high intensities.     

Nonlinear analysis of wiggler taper, node competition, andspace-charge effects for a 280-GHz free electron laser

The nonlinear characteristics of a 280-GHz free electron laser (FEL) are simulated by numerical computation. The three-dimensional set of coupled nonlinear differential equations is solved for a set of TE and TM modes valid for the high gain Compton regime. The use of a nonlinear taper for efficiency enhancement, the sensitivity of gain to competing mode power levels, space-charge effects, and the effect of electron beam source distributions on gain and efficiency are examined for a 10-MeV, 3-kA beam. It is found that the nonlinear taper greatly enhances the gain and efficiency and makes the saturation power levels relatively insensitive to the competing mode power levels. The efficiency is increased to 48% by means of a nonlinear taper in which the 3-D and wiggler-averaged codes are compared and the effects of space charge are found to reduce the efficiency to a level of 32%. The effect of beam quality in terms of the four volume phase space is examined and found to have an observable effect at this wavelength     

横向受激布里渊散射的抑制

 从非线性光学的耦合波理论出发，结合流体力学的连续性方程，建立了光学元件中窄带泵浦的横向受激布里渊散射的二维理论模型，并在此基础上，利用数值模拟考察泵浦光带宽增加对受激散射过程的影响。研究表明:在一定的条件下，当泵浦光带宽略大于布里渊线宽时，受激散射过程的Stokes增益将显著降低；带宽越大，Stokes增益降低得越多；当带宽大于20GHz时，可以抑制横向受激布里渊散射带来的不良影响。另外，当带宽一定时，调制频率的改变也会影响受激散射过程，可以通过数值模拟确定最佳的调制频率。     

Laser intracavity absorption spectroscopy

Emission spectra of multimode lasers are very sensitive to spectrally selective extinction in their cavity. This phenomenon allows the quantitative measurement of absorption. The sensitivity of measurements of intracavity absorption grows with the laser pulse duration. The ultimate sensitivity obtained with a cw laser is set by various perturbations of the light coherence, such as quantum noise, Rayleigh scattering, four-wave mixing by population pulsations, and stimulated Brillouin scattering. It depends on the particular laser type used, and on its operative parameters, for example pump power, cavity loss, cavity length, and length of the gain medium. Nonlinear mode-coupling dominates the dynamics of lasers that feature a thin gain medium, such as dye lasers, whereas Rayleigh scattering is more important in lasers with a long gain medium, such as doped fibre lasers, or the Ti:sapphire laser. The highest sensitivity so far has been obtained with a cw dye laser. It corresponds to 70000 km effective length of the absorption path. The ultimate spectral resolution is determined by the spectral width of mode emission, which is 0.7 Hz in this dye laser. High sensitivity and high temporal and spectral resolution allow various practical applications of laser intracavity spectroscopy, such as measurements and simulations of atmospheric absorption, molecular and atomic spectroscopy, process control, isotope separation, study of free radicals and chemical reactions, combustion diagnostics, spectroscopy of excited states and nonlinear processes, measurements of gain and of spectrally narrow light emission. Intracavity absorption in single-mode lasers shows enhanced sensitivity as well, although not as high as in multimode lasers. Received: 10 May 1999 / Published online: 29 July 1999     

Suppressing laser phase noise in an optomechanical system

We propose a scheme to suppress the laser phase noise without increasing the optomechanical single-photon coupling strength.In the scheme,the parametric amplification terms,created by Kerr and Duffing nonlinearities,can restrain laser phase noise and strengthen the effective optomechanical coupling,respectively.Interestingly,decreasing laser phase noise leads to increasing thermal noise,which is inhibited by bringing in a broadband-squeezed vacuum environment.To reflect the superiority of the scheme,we simulate quantum memory and stationary optomechanical entanglement as examples,and the corresponding numerical results demonstrate that the laser phase noise is extremely suppressed.Our method can pave the way for studying other quantum phenomena.     

高功率激光驱动器中小尺度自聚焦和噪声模型

 建立了一套线性的近似分析方法，研究高功率激光驱动器中强激光传输的小尺度自聚焦效应和相位噪声对光束传输和光束质量的影响，给出了系统噪声强度、B积分值与光束近场调制对比度之间的定量关系。研究表明,为保证输出光束质量，即近场调制对比度小于给定值，系统内的噪声强度必须符合一定的谱分布。     

远程干涉型光纤传感系统的非线性相位噪声分析

以远程干涉型光纤传感系统为背景, 研究了系统非线性相位噪声构成, 对各构成要素的具体影响进行了详细分析和综合评价, 简要讨论了噪声抑制方案. 研究表明, 系统相位噪声主要包括强度噪声转化而来的相位噪声、非线性效应引起激光 线宽展宽导致的相位噪声以及自相位调制和交叉相位调制引入的相位噪声. 受激布里渊散射和四波混频可引入强度噪声并转化为相位噪声, 对于探测带宽较窄的光纤传感系统, 四波混频引入的该部分噪声往往可以忽略. 受激布里渊散射、四波混频和调制不稳定性都可引起激光线宽展宽从而造成相位噪声的增大. 当系统信道数目较多时, 交叉相位调制对相位噪声的贡献不可忽略. 所得结论对远程干涉型光纤传感系统的实际应用具有重要的指导意义.     

A model for noise processes in semiconductor laser amplifiers, part 1: the travelling-wave semiconductor laser amplifier

A new model for the noise processes in a travelling-wave semiconductor laser amplifier is presented. This model is based on applying perturbation techniques to the basic travelling-wave rate equations to deduce the noise rate equations. These equations are then used to calculate the power spectral densities of the intensity, electron density and phase noises introduced into a single signal mode propagating through the amplifier. The model can be applied to any gain profile within the amplifier, ranging from unsaturated to completely saturated. Furthermore, in contrast to most other semiconductor laser amplifier models, this model does not require the homogenization of the photon field over the length of the device.     

Saturation Effects in Mode competition Effects of a Two mode Laser with Multiplicative Noise

１ＩｎｔｒｏｄｕｃｔｉｏｎＴｗｏｍｏｄｅｌａｓｅｒｓ（ＴＭＬ）ｈａｖｅｂｅｎｔｈｅｓｕｂｊｅｃｔｏｆｅｘｔｅｎｓｉｖｅｉｎｔｅｒｅｓｔｉｎｒｅｃｅｎｔｙｅａｒｓ．Ｍｏｄｅｃｏｍｐｏｔｉｔｉｏｎｅｆｅｃｔｉｓｏｎｅｏｆｔｈｅｉｍｐｏｒｔａｎｔｐｒｏ...     

Mitigation of phase noise in dispersion compensated quasi-linear optical transmission systems: Analysis

We theoretically investigate the phase noise in quasi-linear optical transmission systems and study the mitigation of phase noise by properly choosing periodic dispersion compensation and amplification. Variational method is used to deduce the analytical formula for calculating the phase fluctuations of a Gaussian pulse. The analytical predictions are then checked against direct simulations by numerically solving the nonlinear Schrödinger equation. We find that stronger dispersion compensation maps can be used to reduce phase noise and it can be further mitigated by modifying the dispersion map appropriately. It is also found that shorter amplifier spacing yields lower phase noise. We also explore the effect of pre-, post- and bi-end dispersion compensation configurations on phase noise with full compensation and check the reduction of phase noise along the fiber link.     

Coherence and saturation properties of second-harmonic generation with a nonlinear crystal inside the laser cavity

The basic equations for second-harmonic generation including noise are derived for the case that the nonlinear crystal is put inside the laser cavity. A realistic model of a (detuned) laser with two-level atoms in single-mode operation is taken using the nonlinear theory of laser noise which describes the laser saturation effects, the phase diffusion and the intensity fluctuations. The reaction of the second-harmonic field on the fundamental field is taken into account as well as the reaction of the fundamental field on the laser. The nonlinear crystal is described by microscopic anharmonic oscillator equations (without introducing nonlinear susceptibilities by perturbation theory). The saturation of the polarization of the nonlinear medium is taken into account exactly with the only assumption that the influence of third and higher harmonics should be small. The electromagnetic field is described semiclassically by stochastic equations. In all equations, the damping is introduced simultaneously with Markoffian fluctuating forces by coupling to heatbaths. The equations are solved exactly in the stationary state without noise (the time dependent solution including noise will be presented in a subsequent paper). The most important saturation effect is a frequency shift which depends on the laser intensity.     

自混频激光理论模型及应用

建立了在同一块非线性激光晶体上实现自混频激光的理论模型。该模型计入了具有任意腰斑大小的泵浦光和腔内基频光的空间分布,并将该模型应用到NYAB和Nd:GdCOB的自混频蓝光实验。理论分析预测和证实了一些实验结果,同时,讨论和总结了提高自混频激光输出效率的途径。