增益(损耗)介质中高功率激光束的小尺度自聚焦理论研究

将Bespalov-Talanov理论推广到介质有增益(损耗)的情形,揭示了在介质有增益或损耗从而 光强随传输距离变化的情况下小尺度自聚焦的特性.主要是在一定的输入功率下,小尺度调 制增长的临界频率、最快增长频率及其对应的最大增益(B积分)均随介质增益或传输距离的 增大而增大;对于确定的输出功率,随介质增益的提高,B积分值变小,同时最快增长频率 向低频方向移动.利用局部能量守恒定律唯象地研究了增益和损耗对激光束成丝的影响,发 现增益使成丝距离延长而损耗使成丝距离缩短.讨论了介质增益和损耗对高功率激光放大器 设计的影响.尽量使激光器在小输入高增益状态下运行,可以从某种程度上抑制因小尺度自 聚焦而导致的介质破坏效应. 关键词： 自聚焦 成丝 强激光传输     

小尺度自聚焦理论的非傍轴修正

从原始的非傍轴传输方程出发,研究了光束的非傍轴效应对小尺度自聚焦现象的影响结果是,非傍轴效应对不稳定区间的截止频率没有影响,但使最快增长频率增大,最大增长率减小同时,由于非傍轴的影响出现了一个新的增益区间,在该区间里,增益远远大于在原区间里的增益,但是,随着背景光强的增大,增益迅速减小.     

发散光束小尺度自聚焦特性的研究

研究了发散光束的小尺度自聚焦效应。从非线性傍轴波动方程出发,利用坐标变换,推导出发散光束小尺度扰动的传输方程,进而得到小尺度扰动增长的临界频率、最大增长频率和相应B积分值的变化规律。研究了发散光束初始曲率半径对小尺度自聚焦效应的影响。结果表明,对于一定的传输距离,随着发散光束初始曲率半径的减小,小尺度扰动的最大增长频率减小,相应的最大增益减小,即B积分值也减小。对于一定的初始曲率半径,随着传输距离的增大,B积分值增长变缓,并最终停止。利用局部能量守恒定律研究了发散光束的成丝距离,发现小的初始曲率半径可以延长成丝距离。     

Small-scale Self-focusing of Intense Laser Beams in Nonlinear Media with Loss

1　Ｉｎｔｒｏｄｕｃｔｉｏｎ　　Ｉｔｉｓｗｅｌｌｋｎｏｗｎｔｈａｔｓｍａｌｌ ｓｃａｌｅｓｅｌｆ ｆｏｃｕｓｉｎｇ (ＳＳＳＦ)ｃａｎｃａｕｓｅｔｈｅｄｅｇｒａｄａｔｉｏｎａｎｄｂｒｅａｋｕｐｏｆｈｉｇｈｐｏｗｅｒｌａｓｅｒｂｅａｍｓｂｙａｍｐｌｉｆｙｉｎｇｓｍａｌｌ ｓｃａｌｅｂｅａｍｉｍｐｅｒｆｅｃｔｉｏｎｓ.Ｔｈｉｓｐｒｏｂｌｅｍｉｓｏｆｐｒａｃｔｉｃａｌｉｍｐｏｒｔａｎｃｅｂｅｃａｕｓｅｉｔｉｓｔｈｅｍａｉｎｆａｃｔｏｒｌｉｍｉｔｉｎｇｔｈｅｍａｘｉｍｕｍ ｐｏｗｅｒａｖａｉｌａｂｌｅｆｒｏｍａ…     

光纤中扰动的小信号增益

从非线性薛定谔方程出发,在小信号近似下,推导并求解了光纤中扰动相位和幅度的演化方程,利用得到的扰动相位及功率增益的表达式,研究了初相位和频率对传输过程中扰动增益的影响。研究表明：扰动的初相位对扰动增益的初值和初始阶段的演化规律有重要影响;取决于扰动初相位,任何一个频率的扰动增益都有可能达到一个共同的最大值;在被认为无调制不稳定的正色散区和扰动频率大于截止频率的负色散区,扰动增益随距离是振荡的;在被认为有调制不稳定的扰动频率小于截止频率的负色散区,频率相同而初相位不同的扰动增益将经历不同形式的演化后趋于同一正值。     

热晕小尺度不稳定性实验研究

本文报导了STRS不稳定性的模拟实验结果,研究了正弦强度分布的小尺度扰动源在热晕介质中传播的不稳定性发展情况,对不同扰动空间周期、不同光功率下小尺度不稳定性的增长做了一些实验研究,证实了激光在介质传播中,热晕将导致小尺度不稳定性的指数增长。     

介质的增益与损耗对高功率激光小尺度自聚焦的影响

 由光束在非线性介质中传输所满足的近轴波方程，应用Bespalov Talanov（BT）理论，导出了光束在两种介质中传输时，小尺度不稳定增长所遵循的微分方程。通过对比分析介质的增益和损耗对高功率激光的小尺度自聚焦行为的不同影响，得出了截止频率、最快增长频率、纹波的积分指数增益等特性随各参量的变化,求得了最大和最小的纹波增长的距离，以及介质的增益和损耗特性对成丝距离的影响。     

Study of nonlinear propagation of chirped optical pulses in laser amplifying medium

In chirped pulse amplification, the amplification of an optical pulse in laser amplifying medium is a very important link. After considering dispersion, Kerr nonlinear effect, gain distribution and loss of the medium, the physical model that the optical pulse propagates in the medium has been established, which is suitable for the general situation where the optical pulse propagates in the amplifying medium. Using a split-step Fourier method, the propagation state of a chirped optical pulse in the amplifying medium has been numerically simulated, and the influences of the gain dispersion of the medium and the frequency detuning of the pulse on the optical pulse have been discussed emphatically. The results show that, with the amplification and propagation of the ultrashort chirped pulse in the amplifying medium, gain saturation and Kerr nonlinear effect of the medium will cause distortion of the optical pulse. For the optical pulse with a wideband spectrum, gain dispersion will cause the gain narrowing effect, so it is equivalent to a loss mechanism. The frequency detuning of the optical pulse will cause distortion of the pulse, which can be used to weaken the impact of gain saturation, thus reshaping the optical pulse.     

Investigation of amplified spontaneous X-ray laser radiation using the equation for the transverse correlation function of the field

A physical model, based on the solution of the quasi-optics equation for the transverse correlation function (TCF) of the field amplitude, is developed for investigating the brightness, angular divergence, and spatial coherence of the amplified spontaneous emission in a laboratory X-ray laser. The model takes account of the spontaneous source of radiation, diffraction, regular refraction, regular amplification taking account of saturation, nonresonance absorption, scattering by small-scale fluctuations of the electron density and the gain, and scattering by random hose-like deviations of the extended plasma medium of the X-ray laser. It is established that the TCF method makes it possible to obtain the final result much more quickly than the basic Monte Carlo method for the parabolic equation for the field amplitude. As a result of the statistical linearization of the equation for the transverse correlation function in the presence of gain saturation, this method overestimates the absolute values of the average intensity of the amplified spontaneous radiation, but the maximum overestimation does not exceed 10%. It is found that fluctuations of the optical parameters of the medium of the X-ray laser degrade the quality of the amplified spontaneous radiation beam, and they are the analog of the nonresonance absorption from the standpoint of the effect on the brightness of the laser and therefore decrease the observed gain. For the characteristic conditions of an X-ray laser with a quasistationary generation scheme, the contribution of small-scale gain fluctuations and random hose-like deviations of the plasma filament of the laser to the scattering of the amplified spontaneous radiation is much smaller than the contribution of small-scale density fluctuations. Calculations of the amplified spontaneous radiation in an X-ray laser, which is produced by unilateral irradiation of a curved target and possesses an asymmetric plasma electron density profile in the gain zone, are performed. It is shown that in the gain saturation regime the coherence length and the coherent power of the amplified spontaneous radiation can be substantially increased, realizing in the gain zone a convex electron density profile instead of a typical concave profile. It is found that this improvement of the coherence occurs only under conditions such that the characteristic depth of the small-scale density fluctuations does not exceed several percent of the typical regular values of the density in the gain zone.     

Irreversible coupling by use of dissipative optics

The time reversibility of optical propagation impedes the definite performance of many optical devices, such as couplers, polarization converters, etc. We suggest a novel concept in which we use media with loss and gain, thus breaking the time-reversal characteristics, to achieve a unidirectional optical mode interference and coupling, which is a desirable feature for light-wave circuits. Using a matched periodic modulation of both the index of refraction and loss (gain) of the medium, we implement a spatially single sideband perturbation, which breaks the symmetry to allow only a unidirectional energy transfer from mode m to mode n of the optical structure. We elaborate on this phenomenon in coupling between two modes of a multimode optical waveguide.     

片状放大器中片间空气间隔对小尺度自聚焦的影响

从非线性Schr?dinger方程出发，根据线性的近似分析方法，通过把介质片厚度和片间空气间隔转化为线性与非线性传输距离比讨论了系统B积分值和空气间隔对非线性增益谱的影响.着重分析了激光介质片数以及B积分值和非线性增长率之间的关系，并讨论了增长率随B积分值与片数的变化规律.其他参量不变的情况下，片间空气间隔的增大，使增益谱向长波方向移动，而介质片数则对增益谱的最高增益和谱线位置都有影响.同时，对这一现象做了无空气间隔的等效模拟.     

高功率激光放大器中光束的成丝和B积分

研究了高功率激光放大器中光束的成丝问题,利用弗兰兹－诺德威克（Frantz-Nodvik)模型将准稳态波动议程推广到介质有饱和增益的情形,进而得到高功率激光放大器中小尺度调制的传输方程,在小信号增益和饱和增益情形下,分别得到了小尺度调制方程的精确解析解和数值解。结果表明,对于相同的输入光强,增益使小尺度调制增益谱的范围加宽,最快增长频率增高,最大增长率提高;同时,在放大介质中,小尺度调制的最快增长频率和最大增长率还随传输距离变化,增益饱和效应使小尺度调制的增长速度以及B积分的增长低于无饱和放大情形。     

Disturbing synchronization: Propagation of perturbations in networks of coupled oscillators

We study the response of an ensemble of synchronized phase oscillators to an external harmonic perturbation applied to one of the oscillators. Our main goal is to relate the propagation of the perturbation signal to the structure of the interaction network underlying the ensemble. The overall response of the system is resonant, exhibiting a maximum when the perturbation frequency coincides with the natural frequency of the phase oscillators. The individual response, on the other hand, can strongly depend on the distance to the place where the perturbation is applied. For small distances on a random network, the system behaves as a linear dissipative medium: the perturbation propagates at constant speed, while its amplitude decreases exponentially with the distance. For larger distances, the response saturates to an almost constant level. These different regimes can be analytically explained in terms of the length distribution of the paths that propagate the perturbation signal. We study the extension of these results to other interaction patterns, and show that essentially the same phenomena are observed in networks of chaotic oscillators.     

Modulational instability in systems with integrating nonlinearity

A new type of modulational instability for coherent as well as partially coherent light in systems with integrating nonlinearity caused by an irreversible process is investigated both experimentally and theoretically. In such systems plane waves never reach the stationary limit and exhibit a nontrivial time dependence resulting in new features of the modulational instability. For example, the modulational frequency of the nonexponentially increasing perturbation with maximum gain decreases while the wave is propagating. The threshold for vanishing modulational instability due to a finite degree of spatial coherence depends only on system parameters and not on the light intensity.     

基于螺旋波纹波导高增益高效率被动式压缩方法

 对一种改进型螺旋波纹波导实现高增益高效率被动式脉冲压缩进行了研究,并利用微扰理论求解出了该波导的损耗特性。结合波导的色散和损耗特性,设计了输入微波的频率调制形式。还对改进型螺旋波纹波导进行了模拟研究,在输入脉冲宽度为66 ns的条件下,得到了半高宽为1.9 ns的压缩脉冲,增益为21.2倍,脉冲宽度比为34.7倍,压缩效率为61%,这表明改进型螺旋波纹波导应用于被动式脉冲压缩具有高效率高增益特性。     

光纤中单光子传输方程的求解及分析

量子信息在光纤中传输时,会受到光纤损耗、色散、非线性效应等多因素的影响,将产生传输态的演化与能量转移.本文以单模光纤传输方程以及电磁场量子化理论为基础,对单模光纤中基模模场进行量子化处理,推导并建立了考虑损耗、色散、非线性效应后的单光子传输方程.基于微扰法对单光子非线性传输方程进行了求解,给出了稳定解存在的必要条件及其所满足的色散方程.深入讨论了广域光功率随微扰频率的变化关系,并且分析了光纤色散、非线性效应对解的影响.为量子光纤传输系统性能的深入研究奠定了理论基础.     

Modulational interactions in magnetised piezoelectric semiconductor plasmas

Based on hydrodynamic model of plasmas an analytical investigation of frequency modulational interaction between copropagating high frequency pump and acoustic mode and consequent amplification (steady-state and transient) of the modulated waves is carried out in a magnetised piezoelectric semiconductor medium. The phenomenon of modulational amplification is treated as four wave interaction process involving cubic nonlinearity of the medium. Gain constants, threshold-pump intensities and optimum-pulse duration for the onset of modulational instabilities are estimated. The analysis has been performed in non-dispersive regime of the acoustic mode, which is one of the preconditions for achieving an appreciable initial steady-state growth of the modulated signal wave. It is found that the transient gain constant diminishes very rapidly if one chooses the pump pulse duration beyond the maximum gain point. Moreover, the desired value of the gain can be obtained by adjusting intensity and pulse duration of the pump and doping concentration of the medium concerned. Received 12 August 1999 and Received in final form 17 December 1999     

Beam breakup and modulational instability in a bulk type I quadratic medium

The effect of a small modulation superimposed on a strip (1D) solitary wave propagating in a bulk quadratic medium was investigated both analytically and numerically near Type I phase matching. General, exact results were obtained. By using first order perturbation theory, we obtained the gain coefficient for the modulational instability and the modulation cut-off frequency and we investigated their dependence on various beam and material parameters. The wave evolves into a clean periodic sequence of solitary waves and does not reproduce the incident beam. We showed that the beam breakup observed experimentally is due entirely to noise induced modulational instability.     

Study of modulation instability in a temporally incoherent photorefractive ring resonator below the threshold with incoherent light

Modulation instability (MI) and evolution of pattern formation inside a passive non-linear photorefractive ring resonator having cavity-length longer than the coherence length of the light circulating in the resonating cavity has been theoretically analyzed. Dynamics of the system below the threshold conditions have also been analyzed, numerically using linear perturbation theory for the Kerr-type non-linearity. The process of modulation instability in a temporally incoherent cavity below the cavity threshold and the influence of various parameters such as the cavity-length, intensity feedback of the perturbed wave field, amplitude of the incoming beam and spatial frequency on the gain factor and the spatial spectral density have also been studied. For the perturbed wave field, it has been found that the growth rate of MI increases with increase in the intensity feedback as well as the spatial frequency. It has also been found that increasing the intensity feedback of the perturbed wave field, for a given value of the spatial frequency, the spatial spectral density of the perturbation at the output of the non-linear medium increases with the shifting peak positions to the higher spatial frequency side.     

Hirota方程的怪波解及其传输特性研究

求出了高阶Hirota方程在可积条件下的一种精确呼吸子解,并基于此呼吸子解得到了Hirota方程的一种怪波解.在此怪波解的基础上研究了怪波的激发,发现对平面波进行周期性扰动可以激发怪波,对平面波进行高斯扰动可以更快地激发怪波,还可以直接在常数项上增加高斯扰动激发怪波.作为一个实例,采用分步傅里叶方法数值研究了在考虑自频移和拉曼增益时怪波的传输特性,自频移使怪波中心发生偏移,拉曼增益使得怪波分裂得更快,而且拉曼增益值越大怪波分裂得越快,但是拉曼增益对怪波的峰值强度没有明显影响.最后数值模拟了相邻怪波之间的相互作用特点,随着怪波之间距离的减小,怪波将合二为一,成为一束怪波,之后再分裂,并分析了拉曼增益和自频移对怪波相互作用的影响.