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.     

Dynamics of the spatial spectrum of a self-focusing optical wave in a nonlinear medium

A new nonlinear equation for the dynamics of the spatial spectrum of a self-focusing monochromatic wave in a medium with cubic nonlinearity is derived in the nonparaxial approximation. The formation of optical beams with cross section on the order of a wavelength is considered. Backward self-reflection is found to be the fundamental cause for the limitation of optical self-focusing     

激光自聚焦和成丝模拟中的并行计算方法

已编制完成三维非线性流体力学与激光传播耦合并行模拟程序,用以研究高强度激光在稀疏等离子体中的自聚焦和成丝不稳定性形成机制.介绍该三维并行程序中所使用的数值方法和并行算法.     

Structural features of the self-action dynamics of ultrashort electromagnetic pulses

Self-focusing dynamics of electromagnetic pulses of arbitrary duration is analyzed numerically and analytically. The wave-field evolution is considered by the wave equation in the reflectionless approximation under quite general assumptions about the dispersion of the medium. Methods for qualitative investigation of the self-focusing dynamics of quasimonochromatic radiation are generalized to the case of wave packets with the length of a few oscillation periods. In particular, sufficient conditions for collapse and many other integral relations are obtained by the momentum method. A self-similar-type transformation is used to show that new structural features are primarily associated with the nonlinear dispersion of the medium (with the dependence of the group velocity of a wave packet on its amplitude). Numerical analysis confirms that the self-focusing of radiation is preceded by an increase in the steepness of the longitudinal profile.     

Wave collapse in plasmas and fluids

This lecture is a review of recent results (obtained mainly by the author and his co-authors) in the wave collapse theory with applications to plasma physics, fluid dynamics and nonlinear optics as well. The main attention in the review is paid to the qualitative reasons of the wave collapse and to the exact methods based on the integral estimations. Both approaches are applied to both the nonlinear Schrodinger equation and the two-dimensional generalized Benjamin-Ono equation which describes self-focusing of low-frequency oscillations in the boundary layer. (c) 1996 American Institute of Physics.     

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。     

在稀薄等离子体中激光传播的相对论自聚焦

讨论超强、超短脉冲激光在稀薄等离子体中传播过程的某些性质;用二维快速傅立叶变换求解波动方程.相对论自聚焦的基本方程包括非线性源项和衍射的影响.由于有质动力和相对论的影响,使等离子体的频率降低,从而使折射指数发生改变,影响激光在等离子体中的传播.在入射激光功率(p)超过临界功率(p_c)时,激光在传播过程中产生自聚焦;反之,激光在传播过程中逐渐衰减,不产生自聚焦.     

Effect of rippled laser beam on excitation of ion acoustic wave

Growth of a radially symmetrical ripple, superimposed on a Gaussian laser beam in collisional unmagnetised plasma is investigated. From numerical computation, it is observed that self-focusing of main beam as well as ripple determine the growth dynamics of ripple with the distance of propagation. The effect of growing ripple on excitation of ion acoustic wave (IAW) has also been studied.     

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.     

超高光束质量研究

提出了边界波具有π跃变性质的假说，作为惠更斯—菲涅耳原理的补充。根据该假说，在腔外和腔内实现了一系列新光束。重要的是，实现了等效光束质量因子小于１的新光束ＣＯ２激光器。这可看作是可控非线性自聚焦的结果。     

Self-focusing of laser radiation in cluster plasma

The self-focusing of laser radiation in plasma with ionized gaseous clusters is studied both analytically and numerically. An electrodynamic model is proposed for cluster plasma in a field of ultrashort laser pulse. The radiation self-action dynamics are studied using the equation for wave-field envelope with allowance for the electronic nonlinearity of the expanded plasma bunches and the group-velocity dispersion in a nanodispersive medium. It is shown that, for a laser power exceeding the self-focusing critical power, the wave-field self-compression occurs in a medium with dispersion of any type (normal, anomalous, or combined). Due to the strong dependence of the characteristic nonlinear field on the size of ionized cluster, the corresponding processes develop faster than in a homogeneous medium and give rise to the ultrashort pulses.     

Effect of pulse slippage on density transition-based resonant third-harmonic generation of short-pulse laser in plasma

The resonant third-harmonic generation of a self-focusing laser in plasma with a density transition was investigated. Because of self-focusing of the fundamental laser pulse, a transverse intensity gradient was created, which generated a plasma wave at the fundamental wave frequency. Phase matching was satisfied by using a Wiggler magnetic field, which provided additional angular momentum to the third-harmonic photon to make the process resonant. An enhancement was observed in the resonant third-harmonic generation of an intense short-pulse laser in plasma embedded with a magnetic Wiggler with a density transition. A plasma density ramp played an important role in the self-focusing, enhancing the third-harmonic generation in plasma. We also examined the effect of the Wiggler magnetic field on the pulse slippage of the third-harmonic pulse in plasma. The pulse slippage was due to the group-velocity mismatch between the fundamental and third-harmonic pulses.     

Catastrophic collapse of ultrashort pulses

We investigate theoretically the self-focusing dynamics of an ultrashort laser pulse both near and above the threshold at which the pulse effectively undergoes catastrophic collapse. We find that, as a result of space-time focusing and self-steepening, an "optical shock" wave forms inside the medium that gives rise to a broad blueshifted pedestal in the transmitted pulse spectrum. Our results are in good agreement with the primary features observed in experiments and thus provide a theoretical understanding for the underlying process that gives rise to "white-light" generation.     

Multiple fragmentation of wave packets in a nonlinear medium with normal dispersion of the group velocity

The features of the dynamics of the self-ffects of the wave field are considered for the case when the dynamics is described by the nonlinear Schrodinger equation (NSE) with a hyperbolic spatial operator. An analytical investigation of the characteristic regimes of the self-effects is carried out; these regimes are due to the spatial competition of the self-focusing compression of the wave packet in one direction and its defocusing in another. The initial distributions of the wave field are analyzed with the goal of using them in a numerical modeling for illustration of the features of the self-effects. It is shown that three stages can be discerned in the evolution of the localized distributions: self-focusing filamentation of the wave field in the transverse direction, and compression and subsequent fragmentation in the defocusing (longitudinal) direction. The strongest non-uniformities are excited in the self-similar collapse of the wave field to hyperbolas (to the characteristic curves of the hyperbolic operator of the NSE). The stabilization of the development of the fragmentation instability is discussed separately.     

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.     

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.     

Nonsteady-state self-interaction in a medium with striction nonlinearity

An analytic and numerical investigation is made of the self-focusing of a wave beam allowing for the inertia of the nonlinear response of the medium described by an acoustic type of equation. Some characteristics of the dynamics of self-interaction of the wave fields are analyzed in the paraxial optics approximation and the self-similar structures and space-time instability of a plane wave are considered. The stages of instability buildup, structure formation, and the establishment of a steady state are studied numerically.     

Self-focusing of femtosecond diffraction-resistant vortex beams in water

We report experiments on self-focusing of femtosecond diffraction-resistant vortex beams in water. These beams are higher-order Bessel beams with weak azimuthal modulation of the transverse intensity patterns. The modulation overrides the self-focusing dynamics and results in the formation of regular bottlelike filament distributions. The peak-power thresholds for filamentation, at a particular distance, are relatively accurately estimated by the adaptation of the Marburger formula derived earlier for Gaussian beams. The nonlinear conversion of the incident conical waves into the localized spatial wave packets propagating near the beam axis is observed.     

The structural features of wave collapse in medium with normal group velocity dispersion

The dynamic characteristics of self-action in three-dimensional wave packets described by the nonlinear Schrödinger equation with a hyperbolic space operator were studied analytically and numerically. The class of the initial wave field distributions for which self-focusing effects predominated over dispersion spreading and caused the arising of wave collapses was considered. The collapse of tubular wave packets was shown to be accompanied by packet shape changes during its contraction to the axis of the system. The nonlinear stabilization of collapses resulted in wave field fragmentation in the longitudinal direction followed by the expansion of the bunches thus formed along the axis. The dynamics of collapses was numerically studied taking into account medium nonlinearity saturation and nonlinear dissipation.     

Group velocity dispersion effect on the collapse of femtosecond laser pulses in air: a revised form for Marburger's law

The influence of group velocity dispersion(GVD) on the self-focusing of femtosecond laser pulses is investigated by numerically solving the extended nonlinear Schr?dinger equation. By introducing the GVD length LGVDinto the semi-empirical, self-focusing formula proposed by Marburger, a revised one is proposed, which can not only well explain the influence of GVD on the collapse distance, but also is in good agreement with the numerical results, making the self-focusing formula applicable for more cases.