Allowable propagation of short pulse laser beam in a plasma channel and electromagnetic solitary waves

Nonparaxial and nonlinear propagation of a short intense laser beam in a parabolic plasma channel is analyzed by means of the variational method and nonlinear dynamics. The beam propagation properties are classified by five kinds of behaviors. In particularly, the electromagnetic solitary wave for finite pulse laser is found beside the other four propagation cases including beam periodically oscillating with defocussing and focusing amplitude, constant spot size, beam catastrophic focusing. It is also found that the laser pulse can be allowed to propagate in the plasma channel only when a certain relation for laser parameters and plasma channel parameters is satisfied. For the solitary wave, it may provide an effective way to obtain ultra-short laser pulse.     

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.     

Single-focusing regime of propagation of femtosecond light packets when self-focused in a condensed medium

Numerical simulations are used to investigate the propagation of tightly focused megawatt femtosecond light packets in a nonlinear condensed medium in the single-focusing regime. A plasma is shown to be generated in a small region whose length and diameter increase with power in the single-focusing regime of propagation of a femtosecond light packet in a transparent dielectric. The limiting electron density in the microplasma formation region is virtually independent of the laser pulse power but increases with numerical aperture of the focusing optics. At a fixed femtosecond pulse power exceeding the critical self-focusing power, the transmission of light by a dielectric layer decreases with increasing numerical aperture of the focusing optics.     

Nonlinear propagation of an intense Laguerre–Gaussian laser pulse in a plasma channel

The nonlinear propagation of an intense Laguerre–Gaussian(LG) laser pulse in a parabolic preformed plasma channel is analyzed by means of the variational method. The evolution equation of the spot size is derived including the effects of relativistic self-focusing, preformed channel focusing, and ponderomotive self-channeling. The parametric conditions of the LG laser pulse and plasma channel for propagating with constant spot size, periodically focusing and defocusing oscillation,catastrophic focusing, and solitary waves are obtained. Compared with the laser pulse with fundamental Gaussian(FG)mode, it is found that the effect of vacuum diffraction is reduced by half and the effects of relativistic and wakefield focusing are decreased by a quarter due to the hollow transverse intensity profile of the LG laser pulse, while the effect of channel focusing is the same order of magnitude with that of the FG laser pulse. Thus, the matched condition for the intense LG laser pulse with constant spot size is released obviously, while the parameters of the laser and plasma for the existence of solitary waves nearly coincide with those of the FG laser pulse.     

用信息熵描述非线性光传输的研究

结合光束传输的薛定谔形式理论，基于量子机制的信息熵被用来描述非线性光传输，理论推导和数值模拟结果表明：信息熵及其对光传输方向的变化率可以表征光脉冲的压缩或展宽或光束的聚焦与发散，用信息熵表征非线性光传输优于对用脉（束）宽，二阶矩表征。     

Exact solution to the problem of nonlinear pulse propagation through random layered media and its connection with number triangles

An energy pulse refers to a spatially compact energy bundle. In nonlinear pulse propagation, the nonlinearity of the relevant dynamical equations could lead to pulse propagation that is nondispersive or weakly dispersive in space and time. Nonlinear pulse propagation through layered media with widely varying pulse transmission properties is not wave-like and a problem of broad interest in many areas such as optics, geophysics, atmospheric physics and ocean sciences. We study nonlinear pulse propagation through a semi-infinite sequence of layers where the layers can have arbitrary energy transmission properties. By assuming that the layers are rigid, we are able to develop exact expressions for the backscattered energy received at the surface layer. The present study is likely to be relevant in the context of energy transport through soil and similar complex media. Our study reveals a surprising connection between the problem of pulse propagation and the number patterns in the well known Pascal’s and Catalan’s triangles and hence provides an analytic benchmark in a challenging problem of broad interest. We close with comments on the relationship between this study and the vast body of literature on the problem of wave localization in disordered systems.     

Propagation properties of the beam generated by Gaussian mirror resonator passing through a paraxial ABCD optical system

By expanding a hard aperture function into a finite sum of complex Gaussian functions, approximate propagation formula is derived in the situation that the beam generated by Gaussian mirror resonator passes through a paraxial ABCD optical system with an annular aperture. The corresponding forms for a circular aperture and a circular black screen are also given. Some numerical simulations are shown to illustrate propagation properties and focusing properties of the beam passing through a paraxial ABCD optical system with the three different kinds of aperture.     

Growth of Raman-Stokes waves in focused pump beams

A theoretical analysis of the process of forward and backward Raman-Stokes pulse growth in a focused pump beam is presented. The position of the peak of the Stokes pulse duration build-up is determined as a function of the focusing lens. Numerical integration of the propagation equations shows strong modulation in the backward Stokes wave and high efficiency     

声表面波在圆弧处反射及透射的数值研究*

为了研究直达表面波在圆弧过渡面处传播性能的变化,采用有限元方法模拟了热弹机制下,线性脉冲激光辐照金属铝块表面时激发的表面波在近表面传播过程中,在不同曲率半径的圆弧处发生的反射及透射现象,建立了圆弧半径与反射表面波以及透射表面波时域信号特征之间的联系。计算结果表明:曲率半径与表面波中心波长的数值关系对表面波在圆弧处的传播有显著的影响;同时证明了根据透射表面波信号的到达时间可以反演圆弧半径的大小,为之后利用表面波信号定量检测材料表面圆弧凹痕的深度提供了理论依据。     

Effects of Higher-Order Relativistic Nonlinearity and Wakefield During a Moderately Intense Laser Pulse Propagation in a Plasma Channel

Using a variational approach, the propagation of a moderately intense laser pulse in a parabolic preformed plasma channel is investigated. The effects of higher-order relativistic nonlinearity (HRN) and wakefield are included. The effect of HRN serves as an additional defocusing mechanism and has the same order of magnitude in the spot size as that of the transverse wakefield (TWF). The effect of longitudinal wakefield is much larger than those of HRN and TWF for an intense laser pulse with the pulse length equaling the plasma wavelength. The catastrophic focusing of the laser spot size would be prevented in the present of HRN and then it varies with periodic focusing oscillations.     

水下强声波脉冲负压的产生和空化气泡运动

首先利用高速摄影和压力传感器测量的方法, 对曲面反射式水下强声波脉冲的传播和聚焦过程进行了实验研究.实验研究发现, 椭球面反射罩在起到汇聚声能的作用的同时也将使得强声波脉冲在传播过程中形成负压区, 并由此而引发近场声传播通道上空化气泡群的产生. 在实验结果的基础上, 进一步利用基于Kirchhoff衍射定理的声传播模型和大振幅条件下的QX气泡运动方程, 对强声波脉冲负压区的形成原因及空化气泡的运动过程进行了数值计算和分析. 研究结果表明, 在焦前区, 源于反射罩内表面的"尾波"和出口处的"边缘波"在传播过程中将形成反射波中的负压区; 在焦后区, 源于反射罩顶点的"中心波"在传播过程中将形成反射波中的负压区. 在反射波作用下, 空化气泡体现出了"正压区受压缩并振荡, 负压区膨胀"的运动特点. 在反射波之后, 空化气泡将出现成长、坍缩和回弹等典型的物理过程. 研究结果对曲面反射式水下强声波传播物理规律的认识具有实际意义.     

Effects of Relativistic and Ponderomotive Nonlinearities on an Intense Laser Pulse Propagation in a Plasma Channel

The optical guiding of a moderately intense laser pulse in a parabolic preformed plasma channel is analyzed by means of the variational method.Relativistic,ponderomotive and their coupling nonlinearities are included.The conditions for periodic defocusing and focusing,as well as constant spot size propagation are given.It is found that the laser focusing is released by the coupling of relativistic and ponderomotive nonlinearities.     

Effects of Higher-Order Relativistic Nonlinearity and Wakefield During a Moderately Intense Laser Pulse Propagation in a Plasma Channel

Using a variational approach,the propagation of a moderately intense laser pulse in a parabolic preformed plasma channel is investigated.The effects of higher-order relativistic nonlinearity (HRN) and wakefield are included.The effect of HRN serves as an additional defocusing mechanism and has the same order of magnitude in the spot size as that of the transverse wakefield (TWF).The effect of longitudinal wakefield is much larger than those of HRN and TWF for an intense laser pulse with the pulse length equaling the plasma wavelength.The catastrophic focusing of the laser spot size would be prevented in the present of HRN and then it varies with periodic focusing oscillations.     

各阶克尔非线性折射率对强激光大气传输的影响

用数值方法研究了各阶克尔非线性折射系数对强激光传输的影响,结果显示第7阶克尔非线性系数和第9阶克尔非线性系数协同影响激光传输,当第7阶克尔效应起作用时,忽略第9阶克尔效应的作用会导致光强随传输距离震荡剧烈,传输非常不稳定。要得到稳定传输需要第7阶克尔非线性系数和第9阶克尔非线性系数同时起作用或同时不起作用。在自聚焦阶段第3阶非线性折射率对折射率改变起主要作用,在稳定光丝传输阶段第7阶克尔非线性系数,第9阶克尔非线性系数起主要作用。第5阶克尔系数在整个传输过程中对折射率的改变一直比较小。     

Three Dimensional Laser Simulation Code on a Desktop Personal Computer

We present a new simulation code able to simulate the entire propagation of laser pulse, from the amplifiers level up to the focusing stage. This algorithm has some new characteristics that we intend to present. It computes the three-dimensional optical propagation equation using no approximation other than its picosecond expression. The stability has been carefully studied so that it can be applied to any geometry. This is a great improvement since, up to now only cylindrical geometry was accessible for accuracy. In this paper we also present a method using Fast Fourier Transform able to evaluate with a high accuracy, Fresnel’s distribution of a focused laser pulse. The advantages provided by our algorithm are its rapidity and its high physical understanding of the focusing phenomena.     

Finite element simulation of wave propagation in an axisymmetric bar

An accurate solution for high-frequency pulse propagation in an axisymmetric elastic bar is obtained using a new finite element technique that yields accurate non-oscillatory solutions for wave propagation problems in solids. The solution of the problem is very important for the understanding of dynamics experiments in the split Hopkinson pressure bar (SHPB). In contrast to known approaches, no additional assumptions are necessary for the accurate solution of the considered problem. The new solution helps to elucidate the complicated distribution of parameters during high-frequency pulse propagation down the bar as well as to estimate the applicability of the traditional dispersion correction used in the literature for the analysis of wave propagation in a finite bar. Due to the dimensionless formulation of the problem, the numerical results obtained depend on Poisson's ratio, the length of the bar and the pulse frequency, and are independent of Young's modulus, the density and the radius of the bar.     

Spatiotemporal transformation of a focused femtosecond pulse in the absence of self-focusing

The spatiotemporal transformation of a focused femtosecond pulse in fused silica at power much less than the critical power for self-focusing was numerically studied. We found that the pulse experiences unusual spatiotemporal reshaping, such as refocusing of the near-axis portion of the defocused pulse tail, even when the self-focusing effect was not taken into the calculation. Further studies revealed that a tubelike spatiotemporal distribution of the plasma is formed during pulse propagation and that it plays a decisive role in the transformations of the pulse. In addition, the tubelike plasma was found to exist universally under different external focusing conditions if the input pulse had sufficient power.     

Ionization focusing of a short intense laser pulse and generation of wake plasma waves

The propagation of a short intense laser pulse is studied in a gas taking into account the ionization of gas atoms by the high-frequency electromagnetic field of the pulse. The conditions are found under which the ionization structures produced by the laser pulse cause the pulse focusing accompanied by a substantial increase in its intensity. It is shown that the leading edge of the pulse is subjected to ionization refraction at the ionization front, the temporal profile of the pulse becoming steeper. This results in the efficient generation of a wake wave at the ionization front, which is amplified during the development of self-modulation instability. The amplitude of the wake plasma wave achieves a substantial value already at small paths of the pulse in matter (smaller than the diffraction length of the pulse).     

Correction of dispersion distortion of femtosecond pulses by using the non-planar surface of diffractive optical elements

Peculiarities of propagation of femtosecond pulses through a focusing diffractive optical element(DOE)are considered.It is shown that the time delay between the pulse and phase wavefronts can be decreased by fabricating the DOE on the optimal curvilinear surface.