Self-focusing in a plasma due to ponderomotive forces and relativistic effects

The propagation of intense laser pulses in a plasma is discussed in terms of a constant shape, paraxial ray approximation. Self-focusing due to ponderomotive forces and relativistic effects is investigated. It is found that the stationary self-focusing behaviour of each mechanism treated separately is similar, with several orders of magnitude difference in critical power. In stationary self-focusing due to the combined mechanisms, complete saturation of ponderomotive self-focusing prevents the occurrence of relativistic effects. Self-focusing lengths and minimum radii are given for a large range of beam powers. A characteristic focal spot radius is found which depends only on the plasma density.     

Quadruple Gaussian Laser Beam Profile Dynamics in Collisionless Magnetized Plasma

This paper presents an investigation of self-focusing of a quadruple Gaussian laser beam in collisionless magnetized plasma. The nonlinearity due to ponderomotive force which arises on account of nonuniform intensity distribution of the laser beam is considered. The nonlinear partial differential equation governing the evaluation of complex envelope in the slowly varying envelope approximation is solved using a paraxial formalism. The self-focusing mechanism in magnetized plasma, in the presence of self-compression mechanism will be analyzed in contrast to the case in which it is absent. It can be observed that, in case of ponderomotive nonlinearity, the self-compression mechanism obstructs the pulse self-focusing above a certain intensity value. The effect of an external magnetic field is to generate pulses with smaller spot size and shorter compression length. The lateral separation parameter and the initial intensity of the laser beam play a crucial role on focusing and compression parameters. Also, the three-dimensional analysis of pulse propagation is presented by coupling the self-focusing equation with the self-compression one.     

Nonparaxial propagation of soliton-like laser beams-pulses in media with saturable nonlinearity

The theoretical analysis of manifestations of nonparaxiality of propagation (in the plane transverse to the direction of propagation of radiation) of soliton-like beams-pulses in self-focusing media with electronic saturable nonlinearity is carried out. It is shown that, in formation of such structures by pulses of a comparatively small duration, a modulation of the radiation intensity arises, which can result in a fragmentation of the beam in the longitudinal direction. The number and depth of such "jags" are governed by the power of the nonparaxial beam.     

Self-compression of femtosecond pulses in argon with a power close to the self-focusing threshold

Self-compression of femtosecond pulses in noble gases with an input power close to the self-focusing threshold has been investigated experimentally and theoretically. It is demonstrated that either multiphoton ionization （MPI） or space-time focusing and self-steepening effects can induce pulse shortening, but they predominate at different beam intensities during the propagation. The latter effects play a key role in the final pulse self-compression. By choosing an appropriate focusing parameter, action distance of the space-time focusing and self-steepening effects can be lengthened, which can promote a shock pulse structure with a duration as short as two optical cycles. It is also found that, for our calculation cases in which an input pulse power is close to the self-focusing threshold, either group velocity dispersion （GVD） or multiphoton absorption （MPA） has a negligible influence on pulse characteristics in the propagation process.     

Lie-optics, geometrical phase and nonlinear dynamics of self-focusing and soliton evolution in a plasma

It is useful to state propagation laws for a self-focusing laser beam or a soliton in group-theoretical form to be called Lie-optical form for being able to predict self-focusing dynamics conveniently and amongst other things, the geometrical phase. It is shown that the propagation of the gaussian laser beam is governed by a rotation group in a non-absorbing medium and by the Lorentz group in an absorbing medium if the additional symmetry of paraxial propagation is imposed on the laser beam. This latter symmetry, however, needs care in its implementation because the electromagnetic wave of the laser sees a different refractive index profile than the laboratory observer in this approximation. It is explained how to estimate this non-Taylor paraxial power series approximation. The group theoretical laws so-stated are used to predict the geometrical or Berry phase of the laser beam by a technique developed by one of us elsewhere. The group-theoretical Lie-optic (or ABCD) laws are also useful in predicting the laser behavior in a more complex optical arrangement like in a laser cavity etc. The nonlinear dynamical consequences of these laws for long distance (or time) predictions are also dealt with. Ergodic dynamics of an ensemble of laser beams on the torus during absorptionless self-focusing is discussed in this context. From the point of view of new physics concepts, we introduce a stroboscopic invariant torus and a stroboscopic generating function in classical mechanics that is useful for long-distance predictions of absorptionless self-focusing.     

Quadruple Gaussian Laser Beam Profile Dynamics in Collisionless Magnetized Plasma

This paper presents an investigation of self-focusing of a quadruple Gaussian laser beam in collisionless magnetized plasma. The nonlinearity due to ponderomotive force which arises on account of nonuniform intensity distribution of the laser beam is considered. The nonlinear partial differential equation governing the evaluation of complex envelope in the slowly varying envelope approximation is solved using a paraxial formalism. The self-focusing mechanism in magnetized plasma, in the presence of self-compression mechanism will be analyzed in contrast to the case in which it is absent. It can be observed that, in case of ponderomotive nonlinearity, the self-compression mechanism obstructs the pulse self-focusing above a certain intensity value. The effect of an external magnetic field is to generate pulses with smaller spot size and shorter compression length. The lateral separation parameter and the initial intensity of the laser beam play a crucial role on focusing and compression parameters. Also, the three-dimensional analysis of pulse propagation is presented by coupling the self-focusing equation with the self-compression one.     

Self-focusing and defocusing of self-similar π pulses in an amplifying two-level medium

The effect of transverse perturbations on the propagation of electromagnetic π pulses in an amplifying two-level medium is studied. The cases of quasi-monochromatic and extremely short pulses are considered. The equations describing the behavior of the transverse size of the pulse during its propagation in the medium are derived. It is shown that, if the ratios of the diffraction length to the length of dispersion spreading are smaller than certain critical values, self-focusing regimes are realized for both types of pulses. Otherwise, at a finite distance, blowup of defocusing occurs, after which the amplified pulse propagates as if it is a one-dimensional pulse, with the velocity equal to the velocity of light in vacuum. Similarities and distinctions in the dynamics of propagation of extremely short and quasi-monochromatic pulses are indicated.     

大芯径石英光纤中皮秒脉冲激光的自聚焦

本文报道了对大芯径石英光纤中皮秒脉冲激光自聚焦现象的实验研究和理论分析.文中测量了自聚焦先场的近场光强轮廓,研究了自聚焦光场的时域和频域性质,并对环形自聚焦光场的成因进行了解释.     

Mode improvement of a femtosecond laser beam by the spatially self-focusing effect in solid material

The self-focusing effect of femtosecond pulses in a thin piece of BK7 glass is researched through experiment and calculation. The spatial-mode improvement of the femtosecond laser beam is observed. Against the incident pulse with spatial wings, a Gauss-like spatial mode is obtained due to the spatially self-focusing effect in a solid material. The femtosecond pulse propagation in the thin glass plate is analyzed by the amended propagation equation, and the theoretical result shows a qualitative agreement with the experimental result. According to the analysis, the mode improvement of the femtosecond laser beam is resulted from the combination with the self-focusing and dispersion effects in the solid material.     

飞秒强激光经氩气和氩团簇的传播

通过数值求解三维电场传播方程,理论模拟了飞秒强激光脉冲（50 fs,1016 w/cm2）在氩气和中等尺寸氩团簇中的传播效应.结果表明,飞秒强激光脉冲经氩气传播将发生频谱蓝移展宽和光束发散;而经中等尺寸氩团簇传播,则存在一定程度的自聚焦效应.     

Time-resolved measurements of self-focusing pulses in air

The spatial, spectral, and temporal properties of self-focusing 798-nm 100-fs pulses in air are experimentally measured with high-resolution, single-shot techniques at a set propagation distance of 10.91 m. The data, obtained with an initially collimated Gaussian beam, show significant evolution of spatial narrowing as well as temporal and spectral changes at intensities lower than those required for significant ionization of air.     

高功率激光在非均匀大气中传输的自聚焦效应研究进展

地基激光空间碎片清除和利用激光辐射把转换的太阳能从空间轨道输运到地面等应用中,不可避免地遇到高功率激光在非均匀大气中的传输问题。由于激光功率已远远超过大气非线性自聚焦临界功率,大气自聚焦效应是影响光束质量的一个重要物理因素。概述了近年来国内外高功率激光在非均匀大气中上行或下行传输的自聚焦效应研究进展,主要介绍了高功率激光在非均匀大气中的传输模型、理论基础、数值和解析研究方法,着重介绍了自聚焦效应对激光传输特性和光束质量的影响,并总结了优化靶面光束质量的方案。此外,还介绍了大气群速度色散效应和大气湍流效应等物理因素对激光光束质量的影响。最后,还提出了该领域值得进一步深入研究的一些问题。     

熔石英介质中强紫外激光自聚焦效应研究

 针对脉冲宽度约1 ns、波长为351 nm的三倍频紫外激光，定量分析了熔石英介质中的自聚焦长度、峰值光强与强紫外激光光束质量及环境条件等因素的关系，研究了产生紫外光非线性自聚焦效应的阈值条件。研究结果表明：在强紫外激光光束质量一定的前提下，可将B积分值定义为自聚焦的阈值条件;入射强紫外激光光束质量越差，在熔石英介质中产生自聚焦的阈值条件越低;即使对于空间分布均匀的理想光束，当空气中存在灰尘时，经过一段距离的传输后，在熔石英介质中将导致强紫外激光自聚焦效应的产生，且灰尘尺寸较大时的自聚焦效应较明显,自聚焦的阈值条件也相对较低。     

Kerr非线性介质中聚焦像散高斯光束的传输特性

当高功率激光通过Kerr非线性介质传输时,Kerr效应会严重影响激光的传输特性.实际应用中常遇到像散光束.迄今为止,像散光束传输特性的研究大都局限于在线性介质中的传输,而在非线性介质中传输的研究较少,且还未涉及像散激光束通过含光学系统的Kerr非线性介质传输变换的研究.本文主要研究Kerr效应对聚焦光束像散特性和焦移特性的影响,以及聚焦像散高斯光束的自聚焦焦距和光束焦点调控.在光束扩展情况下,推导出了聚焦像散高斯光束在Kerr非线性介质中传输的束宽、束腰位置和焦移的解析公式,研究表明:在自聚焦介质中,随着自聚焦作用增强(如光束功率增强),光束像散越强,但焦移越小;在自散焦介质中,随着自散焦作用增强(如光束功率增强),光束像散越弱,但焦移越大.另一方面,在光束自聚焦情况下,推导出了自聚焦焦距的解析公式,研究表明利用光束像散可以调控光束焦点个数.     

Effect of Critical Beam Radius on Self-focusing of cosh-Gaussian Laser Beams in Collisionless Magnetized Plasma

Effect of critical beam radius on self-focusing of cosh-Gaussian laser beams in collisionless magnetized plasma under ponderomotive nonlinearity forms the main core of present work. To investigate propagation dynamics of cosh-Gaussian laser beams in collisionless magnetized plasma, well established parabolic equation approach under WKB and paraxial approximations is employed. Our study is crucially pivoted on the concept of critical curve and subsequent determination of numerical interval for decentered parameter to sustain the competition between diffraction and self-focusing during the propagation of laser beam. Additionally, in the present study an interesting feature in the self-focusing region of the critical curve has been attempted for different values of decentered parameter.     

X and Y waves in the spatiotemporal Kerr dynamics of a self-guided light beam

The nonlinear stage of development of the spatiotemporal instability of the monochromatic Townes beam in a medium with self-focusing nonlinearity and normal dispersion is studied by analytical and numerical means. Small perturbations to the self-guided light beam are found to grow into two giant, splitting Y pulses featuring shock fronts on opposite sides. Each shocking pulse amplifies a co-propagating X wave, or dispersion- and diffraction-free linear wave mode of the medium, with super-broad spectrum.     

Effect of Critical Beam Radius on Self-focusing of cosh-Gaussian Laser Beams in Collisionless Magnetized Plasma

Effect of critical beam radius on self-focusing of cosh-Gaussian laser beams in collisionless magnetized plasma under ponderomotive nonlinearity forms the main core of present work. To investigate propagation dynamics of cosh-Gaussian laser beams in collisionless magnetized plasma, well established parabolic equation approach under WKB and paraxial approximations is employed. Our study is crucially pivoted on the concept of critical curve and subsequent determination of numerical interval for decentered parameter to sustain the competition between diffraction and self-focusing during the propagation of laser beam. Additionally, in the present study an interesting feature in the self-focusing region of the critical curve has been attempted for different values of decentered parameter.     

Breathing and beating dynamics of Gaussian beam in planar graded-index absorbing nonlinear waveguides

The spatial dynamics of laser beams in absorbing planar waveguides with a parabolic index profile in a saturable or cubic-quintic medium are calculated using the “collective variable approach” technique. In the absence of losses, we construct diagrams which define regions of self-focusing and self-diffractive beam propagation for both types of media. It is found that propagating pulses exhibit an oscillatory pattern, similar to breathing behavior in homogeneous media. If the incident pulse spatial profile and the center of the index profile are not aligned, the pulse oscillates around the index origin with a “beat” frequency that depends on the graded index. Both the breathing and the beat frequencies are also calculated for other graded-index profiles, such as those with additional higher-power terms, and are found to be extremely sensitive to the index profile. In media with linear and nonlinear absorption, we demonstrate the difference between the breathing behavior in graded-index and homogeneous waveguides.     

梯度折射率介质中高斯光束的非线性传输特性

 利用无像差自聚焦理论研究了梯度折射率非线性Kerr介质中高斯光束的传输特性,得到了高斯光束光斑半径和波面曲率半径的表达式。解析结果清楚地表明了衍射、自聚焦以及梯度折射率效应之间的竞争对高斯光束传输行为的影响。梯度折射率效应使光束自聚焦的距离缩短。