真空中强激光加速电子的研究
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摘要
随着超短超强激光技术的进展，基于强激光场的新型电子加速器已成为强场物理中一个研究热点，并提出了多种用强激光加速电子的模型。电子加速的最终目的是把电子加速到GeV或TeV的能量，这需要超强激光场与粒子的相互作用。如此强的激光场在实验室可通过把激光束聚焦到非常小的空间尺寸(几个微米)而得到，其聚焦后的光斑尺寸可以与波长相比拟，在此情况下，傍轴标量理论不再有效，激光束的矢量性和非傍轴性必须考虑。
首先介绍了精确描述电磁场的一些常用方法，包括矢量瑞利-索末菲积分法、角谱法、微扰级数法等。阐述了激光场与粒子的两种相互作用模型：有质动势模型和相对论电子的动力学模型。在此基础上本文进行的主要创新性工作有：
基于矢量瑞利-索末菲积分研究了非傍轴近似下平面波通过薄透镜微光阑系统的聚焦和衍射特性，得出了轴上场分布的精确解析表达式及R＞＞λ时的场的一般解析表达式，所得结果可用于处理远场、傍轴场、轴上场以及无光阑情况。在光阑尺寸与波长相比拟或强聚焦时，矢量非傍轴方法应该被使用。
在考虑光束的部分相干性、矢量性和非傍轴性的基础上引入了部分相干矢量非傍轴ChG光束的概念，基于一般的矢量瑞利．索末菲积分理论，首次得出了部分相干矢量非傍轴ChG光束在自由空间中传输的交叉谱密度和场强解析表示式。完全相干矢量非傍轴ChG光束，矢量非傍轴GSM光束及它们相应的标量傍轴近似和远场结果可作为我们一般结果的特殊情况而得到。部分相干矢量非傍轴ChG光束的矢量性和非傍轴性主要有f和f_σ参数决定，但是离心参数也影响光束的矢量性和非傍轴行为。当f和f_σ参数非常小时，标量傍轴近似成立。一般的矢量瑞利-索末菲积分是一个非常有用的工具，不仅可以应用于矢量非傍轴GSM光束，也可用于其它的部分相干矢量非傍轴光束，表现出了一般可用的优点。部分相干矢量非傍轴ChG光束在自由空间中传输也可用Wingner分布函数矩阵方法处理得到相同的结果，这两种方法是等价的。
根据横向电场和纵向电场的关系，得出了拉盖尔-高斯(LG)的纵向电场解析表达式。首次研究了真空中拉盖尔-高斯光束加速电子的有关物理问题。研究表明只有模指数为p和ι=1的拉盖尔-高斯激光束有非0的轴上纵向电场，可用于加速轴上运动电子。y方向偏振的横向电场不能产生纵向电场分量，圆偏振与x方向偏振的拉盖尔-高斯激光束加速轴上运动的电子有相同的效果。讨论了轴上光场的相速度，群速度，电子滑动距离及轴上加速电位，电子能量增益等物理特征。轴上加速电场的相速度总是大于光速c。轴上加速电位与传输距离有关，且随着模指数p的增大而出现振荡。电子能量增益△W依赖于激光束的束腰宽度w_0，模指数P和激光场的初始相位φ_0。电子与激光场在有限作用距离范围内若满足一定条件，可使电子能量增益最大化。
研究了真空中线偏振和圆偏振BG光束加速电子的的一般特征。研究表明只有模指数n=1的贝塞尔-高斯激光束有非0的纵向电场可用于加速轴上电子。轴上加速场的相速度总是大于光速c。电子能量增益△W依赖于激光束的束腰宽度w_0，初始相位φ_0、波数k及其横向分量α。对于圆偏振的BG，△W还依赖于偏振角θ。当偏振角θ=0时，演化为线偏振贝塞尔激光束的有关结果。在激光功率一定的条件下，电子滑动距离z_s随w_0的增加，最大能量增益△W随w_0减小而增加。
在求得圆对称同频率交叉拉盖尔-高斯激光束总的横向和纵向电场解析表达式的基础上，首次提出和研究了用交叉拉盖尔-高斯激光束对电子加速的有关物理问题。研究表明两激光束的初始相位差在加速电子中起至关重要的作用。若两激光束的初始相位差π，总的轴上横向电场和磁场消失，而总的纵向电场达到量大值，加速电子最有效。电子滑动距离z_s随着模指数p的减小和w_0的增大而增大；对于固定的激光功率P，电子最大能量增益△W随着激光束束腰宽度w_0和模指数p的减小而增大。
研究了真空中用交叉贝塞尔激光束和贝塞尔-高斯激光束加速电子一般特征。得出了交叉贝塞尔和贝塞尔-高斯激光束总的横向和纵向电场、电子滑动距离，轴上加速电位及能量增益的解析表示式。研究表明只有0阶和1阶交叉贝塞尔激光束和贝塞尔-高斯激光束有非0的纵向电场分量，在两激光束初始相位差为π时，轴上纵向电场达到最大化可有效地用于加速电子。讨论了电子能量增益最大化的条件。并将交叉贝塞尔激光束与单贝塞尔激光束加速电子情况进行了比较，在z_s作用范围内用交叉贝塞尔光束加速电子可以获得更大的能量增益和加速梯度。
利用微扰级数法得到了强聚焦TEM_(1,0)模厄米—高斯激光场包含参数f高阶修正项场的解析表达式，在此基础上首次研究了强聚焦场中电子的动力学特征。数值计算表明当电子离轴入射时，强聚焦TEM_(1,0)模H-G激光场中包含f~3的高阶修正项是必要的，并且高于f~3的修正项可能会导致电子能量增益发散。强激光场中电子能量增益AW与激光束参数(激光输出功率P，激光束的束腰宽度w_0，激光场初始相位ψ_0)和电子初始入射参数(初始入射角θ，初始入射能量γ_0)有关，电子在强激光场中运动轨道上场的非对称性是导致电子能量增益的原因。如果电子的初始入射能量过低，电子接近激光束的强场区域会被反射，初始能量过高，电子将会在很短时间内穿过激光束的强场区；这都导致电子小能量增益或没有能量增益。激光场的初始相位通过改变激光场而影响电子的能量增益。电子共轴入射可作为电子离轴入射的特殊情况，在此情况下场表示中f的高次修正项对电子能量增益影响甚微可以忽略。合适地选择激光参数和电子入射参数可使电子能量增益最大化，最大化能量增益可达到GeV加速能级。
本论文研究成果对真空激光加速器的设计和应用具有一定的指导意义。目前强激光加速电子的理论和应用研究正处于一个快速发展阶段，但仍有许多问题有待于深入研究。
Considerable attention has focused on the possibility of using high-powerful laser beams to directly accelerate electrons in vacuum because of the rapid development in ultrashort high-power laser technology. Several methods to accelerate electrons by using laser beams have been proposed, and the main features of laser-accelerated electrons have been reviewed. The ultimate goal of electron acceleration is obviously to reach GeV or even TeV energies, a task that requires the use of interaction between laser fields of extremely high intensity with particles. Such intensities may be produced in the laboratory by focusing over extremely small spatial dimensions, typically a few microns. The very small spot size of laser beams is comparable with the wavelength, for which the paraxial theory is invalid and vectoriality, nonparaxiality of laser beams have to been considered.
First, some basic methods to the exact solution of electromagnetic field are introduced, including the vectoral Rayleigh-Sommerfeld diffraction integrals, angular spectrum representation, perturbation power series method, etc. The models of laser particle are expatiated, including the ponderomotive potential and the relativistic electron dynamics. Based on the above theory and methods, the main results obtained in this dissertation are as follows:
Starting from the vectorial Rayleigh-Sommerfeld diffraction integrals approach, the focusing and diffraction properties of plane wave propagating through a thin lens followed by a small circular aperture have been studied beyond the paraxial regime. A strict analytical expression for the axial field distribution of plane waves has been derived. Under the condition that R>>λ, the analytical field expressions have been deduced, which permit us to treat the far-field, paraxial field, axial field expressions and the expressions without lens as special cases of our general result. The vectorial approach should be used if the aperture dimension is comparable with the wavelength, or the focusing is strong.
The concept of partially coherent vectorial nonparaxial ChG beams has been introduced, where the partial coherence, vectorial property and nonparaxiality of ChG beams have been all taken into consideration. Based on the generalized vectorial Rayleigh diffraction integrals, the closed-form propagation expressions for the cross-spectral density matrix and intensity of partially coherent vectorial nonparaxial ChG beams in free space have been derived. The fully coherent vectorial nonparaxial ChG beams, vectorial nonparaxial GSM beams, and their corresponding scalar paraxial and far-field results have been obtained and treated as special cases of our general expressions. The vectorial property and nonparaxiality of partially coherent ChG beams are mainly determined by the f and f_σparameters, but the decentered parameter also affects their behavior. Only for small values of f and f_σparameters the scalar paraxial approach is allowable. In addition, the generalized vectorial Rayleigh diffraction integrals are a useful tool and applicable not only to vectorial nonparaxial GSM beams, but also to other types of partially coherent vectorial nonparaxial beams like ChG ones, showing general applicable advantages. The propagation of partially coherent vectorial nonparaxial ChG beams can be treated by using the Wigner distribution function matrix and the same results will be obtained because the two approaches are equivalent.
Using the relations between the transverse and longitudinal electric-field components, the analytical expression of longitudinal electric field of the LG beam has been derived. The general physical characteristics of acceleration electrons by using LG are studied. It is shown that only the longitudinal electric field of the LG beam with mode indices p and l=1 can be used to accelerate electrons. The linearly-and circularly-polarized LG beams with mode indices p and l=1 play the same role in laser electron acceleration because there is not axial longitudinal electric field of polarized LG beams in y direction. Some physical characteristics, such as phase and group velocities of the axial optical field, the slippage distance, accelerating potential, and energy gain of electrons etc., are discussed. The phase velocity of electric field on the axis is greater than the light velocity c in vacuum. The accelerating potential oscillates with mode index p increasing. The energy gain is dependent on the waist width w_0, mode index p, and the initial phaseφ_0. A finite energy gainΔW takes place over a finite interaction range and is maximized when some conditions are satisfied.
The general features of the direct acceleration of electrons by using linearly and circularly polarized BG beams in vacuum have been studied. The linearly and circularly polarized BG beams of order n=1 have non-zero axial electric field on axis and can be used to accelerate electrons. The phase velocity of electric field on the axis is greater than the light velocity c in vacuum. The energy gainΔW depends on the waist width w_0, wave number k and its transversal componentα, acceleration distance z_0 and initial phaseφ_0. For circularly polarized BG beams,ΔW is additionally dependent on the angleθ. If lettingθ=0, the results for accelerating field, accelerating potential, energy gain of circularly polarized BG beams reduce to those of linearly polarized BG beams. For a fixed laser power, z_s increases with w_0 increasing andΔW_(max) increases with w_0 decreasing.
The direct acceleration of electrons by using two linearly polarized and circularly symmetric crossed LG beams with equal frequency is proposed and studied. The resulting transverse and longitudinal electric fields have been derived. The initial phase difference plays a key role. For two linearly polarized crossed LG beams with a phase difference ofπ-rad the resulting axial transverse electric field, axial transverse and longitudinal magnetic fields disappear, and the resulting longitudinal electric field reaches a maximum, which can be used to effectively accelerate electrons in vacuum. The slippage distance z_s increases with mode index p decreasing and waist width w_0 increasing. For a fixed laser power, the maximum energy gainΔW_(max) increases with p and w_0 decreasing.
The general characteristics of accelerating electrons by using two polarized crossed BG and Bessel beams with equal frequency has been studied and the analytical expressions for the resulting transverse and longitudinal electric fields of two crossed BG and Bessel beams, the slippage distance z_s, accelerating potential and energy gainΔW have been derived. Two crossed BG or Bessel beams of the same order (w=0 or n=1) have a nonzero resultant longitudinal electric-field in the z-axis and can be used, in principle, to accelerate electrons. The initial phase difference plays a crucial role. For two linearly polarized crossed BG or Bessel beams with aπ-rad phase difference, the resultant transverse electric field vanishes, and there exists the non-zero resultant longitudinal field in the z-axis, which can be maximized and used to accelerate electrons. The conditions that the energy gain is maximized have been discussed. In comparison with the case of a single Bessel beam, the larger energy gain and accelerating gradient can be achieved in the interaction distance z_s by using two crossed Bessel beams.
Based on the method of the perturbation series expansion, the higher-order field corrections of TEM_(1,0)-mode H-G beams are derived, and used to study the electron acceleration by a tightly focused H-G beam. The illustrative numerical calculation results show that for the off-axis injection the field contributions of the terms up to order f~3 have to be included, and the terms higher than the order f~3 may result in a divergent energy gain. In the interaction of the electron and TEM_(1,0)-mode H-G beam the injection parameters including the injection energyγ_0 and the injection angleθand laser parameters including laser power P, the waist width w_0, and the initial phaseψ_0 both affect the energy gainΔW. The asymmetry of the transverse and longitudinal electric-field components along the electron trajectories results in the electron acceleration. For the small injection energyγ_0 the energy gainΔW is very small due to the reflection of electrons and for the large injection energyγ_0ΔW decreases because electrons penetrate through the LEM_(1,0)-mode H-G beam over a short time. The initial phaseψ_0 which alters the field distribution affects the final energy gain. The electron on-axis injection can be treated as a special case. For such a case the higher-order corrections can be neglected and the result is consistent with the previous one. The energy gain can be optimized to achieve the GeV energy gain by a suitable choice of injection parameters and the injection parameters.
The results obtained in this dissertation may be useful for design and application of electron acceleration. Currently, the theory and application in high-laser acceleration electron are in rapid development. However, there are many problems which deserve a further and deep study.
首先介绍了精确描述电磁场的一些常用方法，包括矢量瑞利-索末菲积分法、角谱法、微扰级数法等。阐述了激光场与粒子的两种相互作用模型：有质动势模型和相对论电子的动力学模型。在此基础上本文进行的主要创新性工作有：
基于矢量瑞利-索末菲积分研究了非傍轴近似下平面波通过薄透镜微光阑系统的聚焦和衍射特性，得出了轴上场分布的精确解析表达式及R＞＞λ时的场的一般解析表达式，所得结果可用于处理远场、傍轴场、轴上场以及无光阑情况。在光阑尺寸与波长相比拟或强聚焦时，矢量非傍轴方法应该被使用。
在考虑光束的部分相干性、矢量性和非傍轴性的基础上引入了部分相干矢量非傍轴ChG光束的概念，基于一般的矢量瑞利．索末菲积分理论，首次得出了部分相干矢量非傍轴ChG光束在自由空间中传输的交叉谱密度和场强解析表示式。完全相干矢量非傍轴ChG光束，矢量非傍轴GSM光束及它们相应的标量傍轴近似和远场结果可作为我们一般结果的特殊情况而得到。部分相干矢量非傍轴ChG光束的矢量性和非傍轴性主要有f和f_σ参数决定，但是离心参数也影响光束的矢量性和非傍轴行为。当f和f_σ参数非常小时，标量傍轴近似成立。一般的矢量瑞利-索末菲积分是一个非常有用的工具，不仅可以应用于矢量非傍轴GSM光束，也可用于其它的部分相干矢量非傍轴光束，表现出了一般可用的优点。部分相干矢量非傍轴ChG光束在自由空间中传输也可用Wingner分布函数矩阵方法处理得到相同的结果，这两种方法是等价的。
根据横向电场和纵向电场的关系，得出了拉盖尔-高斯(LG)的纵向电场解析表达式。首次研究了真空中拉盖尔-高斯光束加速电子的有关物理问题。研究表明只有模指数为p和ι=1的拉盖尔-高斯激光束有非0的轴上纵向电场，可用于加速轴上运动电子。y方向偏振的横向电场不能产生纵向电场分量，圆偏振与x方向偏振的拉盖尔-高斯激光束加速轴上运动的电子有相同的效果。讨论了轴上光场的相速度，群速度，电子滑动距离及轴上加速电位，电子能量增益等物理特征。轴上加速电场的相速度总是大于光速c。轴上加速电位与传输距离有关，且随着模指数p的增大而出现振荡。电子能量增益△W依赖于激光束的束腰宽度w_0，模指数P和激光场的初始相位φ_0。电子与激光场在有限作用距离范围内若满足一定条件，可使电子能量增益最大化。
研究了真空中线偏振和圆偏振BG光束加速电子的的一般特征。研究表明只有模指数n=1的贝塞尔-高斯激光束有非0的纵向电场可用于加速轴上电子。轴上加速场的相速度总是大于光速c。电子能量增益△W依赖于激光束的束腰宽度w_0，初始相位φ_0、波数k及其横向分量α。对于圆偏振的BG，△W还依赖于偏振角θ。当偏振角θ=0时，演化为线偏振贝塞尔激光束的有关结果。在激光功率一定的条件下，电子滑动距离z_s随w_0的增加，最大能量增益△W随w_0减小而增加。
在求得圆对称同频率交叉拉盖尔-高斯激光束总的横向和纵向电场解析表达式的基础上，首次提出和研究了用交叉拉盖尔-高斯激光束对电子加速的有关物理问题。研究表明两激光束的初始相位差在加速电子中起至关重要的作用。若两激光束的初始相位差π，总的轴上横向电场和磁场消失，而总的纵向电场达到量大值，加速电子最有效。电子滑动距离z_s随着模指数p的减小和w_0的增大而增大；对于固定的激光功率P，电子最大能量增益△W随着激光束束腰宽度w_0和模指数p的减小而增大。
研究了真空中用交叉贝塞尔激光束和贝塞尔-高斯激光束加速电子一般特征。得出了交叉贝塞尔和贝塞尔-高斯激光束总的横向和纵向电场、电子滑动距离，轴上加速电位及能量增益的解析表示式。研究表明只有0阶和1阶交叉贝塞尔激光束和贝塞尔-高斯激光束有非0的纵向电场分量，在两激光束初始相位差为π时，轴上纵向电场达到最大化可有效地用于加速电子。讨论了电子能量增益最大化的条件。并将交叉贝塞尔激光束与单贝塞尔激光束加速电子情况进行了比较，在z_s作用范围内用交叉贝塞尔光束加速电子可以获得更大的能量增益和加速梯度。
利用微扰级数法得到了强聚焦TEM_(1,0)模厄米—高斯激光场包含参数f高阶修正项场的解析表达式，在此基础上首次研究了强聚焦场中电子的动力学特征。数值计算表明当电子离轴入射时，强聚焦TEM_(1,0)模H-G激光场中包含f~3的高阶修正项是必要的，并且高于f~3的修正项可能会导致电子能量增益发散。强激光场中电子能量增益AW与激光束参数(激光输出功率P，激光束的束腰宽度w_0，激光场初始相位ψ_0)和电子初始入射参数(初始入射角θ，初始入射能量γ_0)有关，电子在强激光场中运动轨道上场的非对称性是导致电子能量增益的原因。如果电子的初始入射能量过低，电子接近激光束的强场区域会被反射，初始能量过高，电子将会在很短时间内穿过激光束的强场区；这都导致电子小能量增益或没有能量增益。激光场的初始相位通过改变激光场而影响电子的能量增益。电子共轴入射可作为电子离轴入射的特殊情况，在此情况下场表示中f的高次修正项对电子能量增益影响甚微可以忽略。合适地选择激光参数和电子入射参数可使电子能量增益最大化，最大化能量增益可达到GeV加速能级。
本论文研究成果对真空激光加速器的设计和应用具有一定的指导意义。目前强激光加速电子的理论和应用研究正处于一个快速发展阶段，但仍有许多问题有待于深入研究。
Considerable attention has focused on the possibility of using high-powerful laser beams to directly accelerate electrons in vacuum because of the rapid development in ultrashort high-power laser technology. Several methods to accelerate electrons by using laser beams have been proposed, and the main features of laser-accelerated electrons have been reviewed. The ultimate goal of electron acceleration is obviously to reach GeV or even TeV energies, a task that requires the use of interaction between laser fields of extremely high intensity with particles. Such intensities may be produced in the laboratory by focusing over extremely small spatial dimensions, typically a few microns. The very small spot size of laser beams is comparable with the wavelength, for which the paraxial theory is invalid and vectoriality, nonparaxiality of laser beams have to been considered.
First, some basic methods to the exact solution of electromagnetic field are introduced, including the vectoral Rayleigh-Sommerfeld diffraction integrals, angular spectrum representation, perturbation power series method, etc. The models of laser particle are expatiated, including the ponderomotive potential and the relativistic electron dynamics. Based on the above theory and methods, the main results obtained in this dissertation are as follows:
Starting from the vectorial Rayleigh-Sommerfeld diffraction integrals approach, the focusing and diffraction properties of plane wave propagating through a thin lens followed by a small circular aperture have been studied beyond the paraxial regime. A strict analytical expression for the axial field distribution of plane waves has been derived. Under the condition that R>>λ, the analytical field expressions have been deduced, which permit us to treat the far-field, paraxial field, axial field expressions and the expressions without lens as special cases of our general result. The vectorial approach should be used if the aperture dimension is comparable with the wavelength, or the focusing is strong.
The concept of partially coherent vectorial nonparaxial ChG beams has been introduced, where the partial coherence, vectorial property and nonparaxiality of ChG beams have been all taken into consideration. Based on the generalized vectorial Rayleigh diffraction integrals, the closed-form propagation expressions for the cross-spectral density matrix and intensity of partially coherent vectorial nonparaxial ChG beams in free space have been derived. The fully coherent vectorial nonparaxial ChG beams, vectorial nonparaxial GSM beams, and their corresponding scalar paraxial and far-field results have been obtained and treated as special cases of our general expressions. The vectorial property and nonparaxiality of partially coherent ChG beams are mainly determined by the f and f_σparameters, but the decentered parameter also affects their behavior. Only for small values of f and f_σparameters the scalar paraxial approach is allowable. In addition, the generalized vectorial Rayleigh diffraction integrals are a useful tool and applicable not only to vectorial nonparaxial GSM beams, but also to other types of partially coherent vectorial nonparaxial beams like ChG ones, showing general applicable advantages. The propagation of partially coherent vectorial nonparaxial ChG beams can be treated by using the Wigner distribution function matrix and the same results will be obtained because the two approaches are equivalent.
Using the relations between the transverse and longitudinal electric-field components, the analytical expression of longitudinal electric field of the LG beam has been derived. The general physical characteristics of acceleration electrons by using LG are studied. It is shown that only the longitudinal electric field of the LG beam with mode indices p and l=1 can be used to accelerate electrons. The linearly-and circularly-polarized LG beams with mode indices p and l=1 play the same role in laser electron acceleration because there is not axial longitudinal electric field of polarized LG beams in y direction. Some physical characteristics, such as phase and group velocities of the axial optical field, the slippage distance, accelerating potential, and energy gain of electrons etc., are discussed. The phase velocity of electric field on the axis is greater than the light velocity c in vacuum. The accelerating potential oscillates with mode index p increasing. The energy gain is dependent on the waist width w_0, mode index p, and the initial phaseφ_0. A finite energy gainΔW takes place over a finite interaction range and is maximized when some conditions are satisfied.
The general features of the direct acceleration of electrons by using linearly and circularly polarized BG beams in vacuum have been studied. The linearly and circularly polarized BG beams of order n=1 have non-zero axial electric field on axis and can be used to accelerate electrons. The phase velocity of electric field on the axis is greater than the light velocity c in vacuum. The energy gainΔW depends on the waist width w_0, wave number k and its transversal componentα, acceleration distance z_0 and initial phaseφ_0. For circularly polarized BG beams,ΔW is additionally dependent on the angleθ. If lettingθ=0, the results for accelerating field, accelerating potential, energy gain of circularly polarized BG beams reduce to those of linearly polarized BG beams. For a fixed laser power, z_s increases with w_0 increasing andΔW_(max) increases with w_0 decreasing.
The direct acceleration of electrons by using two linearly polarized and circularly symmetric crossed LG beams with equal frequency is proposed and studied. The resulting transverse and longitudinal electric fields have been derived. The initial phase difference plays a key role. For two linearly polarized crossed LG beams with a phase difference ofπ-rad the resulting axial transverse electric field, axial transverse and longitudinal magnetic fields disappear, and the resulting longitudinal electric field reaches a maximum, which can be used to effectively accelerate electrons in vacuum. The slippage distance z_s increases with mode index p decreasing and waist width w_0 increasing. For a fixed laser power, the maximum energy gainΔW_(max) increases with p and w_0 decreasing.
The general characteristics of accelerating electrons by using two polarized crossed BG and Bessel beams with equal frequency has been studied and the analytical expressions for the resulting transverse and longitudinal electric fields of two crossed BG and Bessel beams, the slippage distance z_s, accelerating potential and energy gainΔW have been derived. Two crossed BG or Bessel beams of the same order (w=0 or n=1) have a nonzero resultant longitudinal electric-field in the z-axis and can be used, in principle, to accelerate electrons. The initial phase difference plays a crucial role. For two linearly polarized crossed BG or Bessel beams with aπ-rad phase difference, the resultant transverse electric field vanishes, and there exists the non-zero resultant longitudinal field in the z-axis, which can be maximized and used to accelerate electrons. The conditions that the energy gain is maximized have been discussed. In comparison with the case of a single Bessel beam, the larger energy gain and accelerating gradient can be achieved in the interaction distance z_s by using two crossed Bessel beams.
Based on the method of the perturbation series expansion, the higher-order field corrections of TEM_(1,0)-mode H-G beams are derived, and used to study the electron acceleration by a tightly focused H-G beam. The illustrative numerical calculation results show that for the off-axis injection the field contributions of the terms up to order f~3 have to be included, and the terms higher than the order f~3 may result in a divergent energy gain. In the interaction of the electron and TEM_(1,0)-mode H-G beam the injection parameters including the injection energyγ_0 and the injection angleθand laser parameters including laser power P, the waist width w_0, and the initial phaseψ_0 both affect the energy gainΔW. The asymmetry of the transverse and longitudinal electric-field components along the electron trajectories results in the electron acceleration. For the small injection energyγ_0 the energy gainΔW is very small due to the reflection of electrons and for the large injection energyγ_0ΔW decreases because electrons penetrate through the LEM_(1,0)-mode H-G beam over a short time. The initial phaseψ_0 which alters the field distribution affects the final energy gain. The electron on-axis injection can be treated as a special case. For such a case the higher-order corrections can be neglected and the result is consistent with the previous one. The energy gain can be optimized to achieve the GeV energy gain by a suitable choice of injection parameters and the injection parameters.
The results obtained in this dissertation may be useful for design and application of electron acceleration. Currently, the theory and application in high-laser acceleration electron are in rapid development. However, there are many problems which deserve a further and deep study.
引文
1．张闯．粒子加速器的回顾与展望《核科学与工程》21(2001)39-44
2.McMillan E M. The Synchrotron—A Proposed High Energy Particle Accelerator. Phys. Rev. 68 (1945) 143-144.
3.Courant E D, Livingston M S et al. The Strong-Focusing Synchroton—A New High Energy Accelerator. Phys. Rev. 88 (1952) 1190-1196.
4.Channell P J. Laser acceleration of particles. AIP Conf. No. 91 (New York).
5.Pardy M. The quantum field theory of laser acceleration. Physics Letters A 3 (1998) 223-8.
6.Fedorov M V, Goreslavsky S P, Letokhov V S. Ponderomotive forces and stimulated Compton scattering of free electrons in a laser field. Phys. gev. E 55, (1997) 1015-1027.
7. Hartemann F V, Kerman A K. Classical Theory of Nonlinear Compton Scattering. Phys. Rev. Lett. 76 (1996) 624-627.
8. Quesnel B, P Mora. Theory and simulation of the interaction of ultraintense laser pulses with electrons in vacuum. Phys. Rev. E 58 (1998) 3719-3732.
9. Hafizi B, Ganguly A K, Ting A, et al. Analysis of Gaussian beam and Bessel beam driven laser accelerators. Phys. Rev. E 60 (1999) 4779-4792.
10. Edighoffer J A, Kimura W D, et al. Free-electron interactions with light using the inverse Cerenkov effect. IEEE J. Quantum Electronics, 17(1981)1507-14.
11. Kimura W D, Kim G H, Romea R D, et al. Laser Acceleration of Relativistic Electrons Using the Inverse Cherenkov Effect. Phys. Rev. Lett. 74 (1995) 546-549.
12. Lee S, Katsouleas T, Hemker R, et al. Simulations of a meter-long plasma wakefield accelerator. Phys. Rev. E 61 (2000) 7014-7021.
13. Rundquist A R, LeBlance S P, Gaul E W, et al. Optimization of laser wakefield acceleration. AIP Conference Proceedings. 569 (2001) 177-82.
14. Serbeto A, Rios L A, Shukla P K. Neutrino-driven wakefield plasma accelerator. Phys. Plasmas 9 (2002) 4406.
15. Pisin C, Tajima T, Takahashi Y. Plasma wakefield acceleration for ultrahigh-energy cosmic rays. Phys. Rev. Lett. 89 (2002) 975-977.
16. Lotov K V, Blowout regimes of plasma wakefield acceleration Phys. Rev. E 69 (2004) 046405-1-13
17. Altmark A M, Kanareykin A D, Sheinman I L. Tunable wakefield dielectric-filled accelerating structure. Tech. Phy. 76 (2005) 87-95.
18. Kuzntsov S V. Wakefield acceleration of noumonoenergetic electron bunches. Plasma Phys. Reports 32 (2006) 282-91.
19. Kalmykov S Y, Gorbunov L M, Mora P. Injection, trapping, and acceleration of electrons in a three-dimensional nonlinear laser wakefield. Phys. Plasmas 13 (2006) 113102-1-11.
20. Cai S Y, Bhattacharjee A. Inverse-free-electron-laser beat-wave accelerator. Phys. Rev. A 42 (1990) 4853-61.
21. Fishrer A, Gallardo J, Sandweiss J, et al. Inverse free electron laser accelerator AIP Conference Proceedings. 279 (1993) 299-318.
22.Maroli C, Petrillo V, Bonifacio R. Plasma-based inverse free-electron laser for high-gradient acceleration of electrons. Phys. Rev. Lett. 76 (1996) 3578-81.
23.Harteman F V, Baldis H A, Freeman R R, et al. The chirped-pulse inverse free-electron laser: A high-gradient vacuum laser accelerator. Phys. Plasmas. 6 (1999) 4104-10.
24.Yoder R B, Marshall T C, Hirshfield J L. Energy-gain measurements from a microwave inverse free-electron-laser accelerator. Phys. Rev. Lett. 86 (2001) 1765-8.
25.Musumeci P, Tochitsky S Y, et al. High energy gain of trapped electrons in a tapered, diffraction-dominated inverse-free-electron laser. Phys. Rev. Lett. 94 (2005) 154801/1-4.
26.Mirzanejhad S, Sohbatzadeh F, et al. Electron bunch acceleration in an inverse free-electron laser with a helical magnetic wiggler and axial guide field. Phys. Plasmas 13 (2006) 123105.
27.Tanq C M, pranqle P S, Sudan R N. Dynamics of space-charge waves in the laser beat wave accelerator. Phys. Fluids. 28 (1985)1974-83.
28.Amiranoff F, Bernard D, et al. Electron acceleration in Nd-laser plasma beat-wave experiments. Physica Scripta Volume T 63 (1996) 126-35.
29.Hafizi B, Ting A, et al. Vacuum beat wave acceleration. Phys.Rev. E 55 (1997) 5924-33.
30.Salamin Y I, Keitel C H. Analysis of electron acceleration in a vacuum beat wave. J. Phys. B 33 (2000) 5057-76.
31.Tochitsky S Y, Narang R, et al. Enhanced acceleration of injected electrons in a laser-beat-wave-induced plasma channel. Phys.Rev.Lett. 92 (2004) 095004/1-4.
32.Salamin Y I. Single-electron dynamics in a tightly focused laser beat wave: acceleration in vacuum. J. Phys. B 38 (2005)4095-110.
33.Richard H M. Electron Scattering by an Intense Polarized Photon Field Phys. Rev. Lett. 10 (1963)75-77
34．王加祥，霍裕昆，冯量．锥形光场对电子的加速效应．物理学报 45(1998)1264-11．
35.Esarey E, Sprangle P, Krall J. Laser acceleration of electron in vacuum. Phys. Rev. E 52 (1995) 5443-5453.
36.Salamin Y I, Keitel C H. Subcycle high electron acceleration by crossed laser beams. Appl. Phys. Lett. 77 (2000) 1082-1084.
37.Sprangle P, Esarey E, et al. Vacuum laser acceleration. Opt. Commun. 124 (1996) 69-73.
38．王平晓，孔青，霍裕昆．激光在真空中加速电子．物理 36(2007)32-38．
39.Tajima T, Dawson J M. Laser Electron Accelerator. Phys. Rev. Lett. 43 (1979) 267-270.
40．陈民，盛政明，马燕云，张杰．台面型电子加速器—激光尾波场加速器．物理 35(2006)1016-1027．
41.Plettner T, Bver R L, et al. Visible-Laser Acceleration of Relativistic Electrons in a Semi-Infinite Vacuum. Phys. Rev. Lett. 95 (2005) 134801.
42.Huang Y C, Byer R L. A proposed high-gradient laser-driven electron accelerator using crossed cylindrical laser focusing. Appl.Phys. Lett. 69 (1996) 2175-7.
43.Steinhauer L C, Kimura W D. A new approach for laser particle acceleration in vacuum. J.Appl.Phys.72 (1992) 3237-45.
44.Hartemann F V, Fochs S N, et al. Nonlinear ponderomotive scattering of relativistic electrons by an intense laser field at focus. Phys. Rev. E 51 (1995) 4833-4843.
45.Yu Wei, Yu M Y, Ma J X, et al. Ponderomotive acceleration of electrons at the focus of high intensity lasers. Phys. Rev. E 61 (2000) R2220-R2223.
46.Wang J X, Ho Y K, et al. Electron capture and violent acceleration by an extra-intense laser beam. Phys. Rev. E 58 (1998) 6575-6577.
47.Palmer R B. Interaction of relativistic particles and free electromagnetic waves in the presence of a static helical magnet. J. Appl. Phys. 43 (1972) 3014-23.
48.Scheid W, Hora H. On electron acceleration by plane transverse electromagnetic pulses in vacuum. Laser and Particle Beams 7 (1989) 315-32.
49.Rau B, Tajima T, Hojo H. Coherent Electron Acceleration by Subcycle Laser Pulses. Phys. Rev. Lett. 78 (1997) 3310-3313.
50.Sinqh K P. Electron acceleration by a chirped short intense laser pulse in vacuum. Appt. Phys. Lett. 87(2005) 254102.
51.Kawata S, Maruyama T, et al. Inverse-bremsstrahlung electron acceleration. Phys. Rev. Lett. 66 (1991) 2072-2075.
52.Li Y T, Sheng Z M, et al. Demonstration of bulk acceleration of ions in ultraintense laser interactions with low-density foams. Phys. Rev. E 72 (2005) 066404.
53.Li Y T, Yuan X H, et al. Observation of a fast electron beam emitted along the surface of a target irradiated by intense femtosecond laser pulses. Phys. Rev. Lett. 96 (2006) 165003.
54. Sheng Z M, Mima K, et al. Efficient acceleration of electrons with counterpropagating intense laser pulses in vacuum and underdense plasma. Phys. Rev. E 69 (2004) 016407.
55. Dong Q L, Sheng Z M, Yu M Y, Zhang J. Optimization of ion acceleration in the interaction of intense femtosecond laser pulses with ultrathin foils. Phys. Rev. E 68 (2003) 026408.
56. Li Y T, Zhang J, et al. Spatial distribution of high-energy electron emission from water plasmas produced by femtosecond laser pulses. Phys. Rev. Lett. 90 (2003) 165002.
57. Yu Wei, Chen Z Y, Yu M Y, et al. Electron acceleration and high-order harmonic generation by an intense short pulse laser in a magnetic field. Phys. Rev. E 66 (2002) 036406.
58. Yu Wei, Xu H, He F, et al. Direct acceleration of solid-density plasma bunch by ultraintense laser. Phys. Rev. E 72 (2005) 046401.
59. He F, Yu Wei, et al. Ponderomotive acceleration of electrons by a tightly focused intense laser beam. Phys. Rev. E 68 (2003) 046407.
60. Yu Wei, Bychenkov V, Sentoku Y, et al. Electron Acceleration by a Short Relativistic Laser Pulse at the Front of Solid Targets. Phys. Rev. Lett. 85(2000) 570-573.
61. Du C G, Li S Q. Dephasing time of a positron accelerated by a laser pulse. Chin. Phys. 11 (2002) 375-04.
62. Liu S, Guo H, et al. Direct acceleration of electrons using single Hermite-Gaussian beam and Bessel beam in vacuum. Phys. Lett. A 324 (2004)104-113.
63. Bochove E J, Moore G T, Scully M O. Acceleration of particles by an asymmetric Hermite-Gayssian laser beam. Phys. Rev. A 46 (1992) 6640-6653.
64. Esarey E, Pilloff M. Trapping and acceleration in nonlinear plasma waves.Phys.Plasmas 2 (1995) 1432-6.
65．曹娜．一种新型加速器的特性研究．2003 复旦大学博士学位论文．
66. McDonald K T. Laser Acceleration of Partices , Eds ,C. Joshi and T. Katsouleas , A IP Conf. 130 (AIP ,New York ,1985) 23.
67. McDonald K T, Chen P , et al. Proc. Workshop on Beam-Beam and Beam-Radiation Interaction High Intensity and Non21inear Effects (World Scientific ,Singapore) (1992) 127.
68. Bula C, McDonald K T, et al. Observation of Nonlinear Effects in Compton Scattering. Phys. Rev. Lett. 76 (1996) 3116-3119.
69. KibbleT W B. Mutual Refraction of Electrons and Photons. Phys. Rev. 150 (1966) 1060-1069.
70. Kong Q, Ho Y K, et al. Electron dynamics characteristics in high-intensity laser fields. Applied Physics B 74 (2002) 517-520.
71. Ho Y K, Wang J X, et al. Electron scattering by an intense continuous laser, beam Phys. Lett. A 220 (1996) 189-193
72. Wang J X, Ho Y K, et al. Nonlinear compton effect and electron inelastic scattering by an intense stationary laser beam. Phys.Lett. A 231 (1997) 139-143
73. Wang J X, Y K Ho et al. Inelastic electron scattering by an intense laser beam of the Hermite-Gaussian (0, 1) mode. Phys.Lett. A 234(1997) 415-418
74. Wang P X, Ho Y K, et al. Vacuum electron acceleration by an intense laser. Appl. Phys. Lett. 78 (2001) 2253-2255
75. Zhu L J, Ho Y K, et al. Violent acceleration of electrons by an ultra-intense pulsed laser beam. Phys.Lett. A 248 (1998) 319-324.
76. Malka G, Lefebvre E. Experimental Observation of Electrons Accelerated in Vacuum to Relativistic Energies by a High-Intensity Laser. Phys. Rev. Lett. 78 (1997) 3314-3317.
77. Bucksbaum P H, Bashkansky M, McIlrath T J. Scattering of electrons by intense coherent light. Phys. Rev. Lett. 58 (1987) 349-352.
78. Monot P, Auguste T, LompréL A, et al. Energy measurements of electrons submitted to an ultrastrong laser field. Phys. Rev. Lett. 70 (1993) 1232-1235.
79. Moore C I, Knauer J P. Observation of the Transition from Thomson to Compton Scattering in Multiphoton Interactions with Low-Energy Electrons. Phys. Rev. Lett. 74 (1995) 2439.
80. Moore C I,et al. Observation of the Transition from Thomson to Compton Scattering in Multiphoton Interactions with Low-Energy Electrons. Phys. Rev. Left. 74 (1995) 2439-2442
81. Hartemann F V, Fochs S N, Le Sage G P, et al. Nonlinear ponderomotive scattering of relativistic electrons by an intense laser field at focus. Phys. Rev. E 51 (1995) 4833.
82. Kimura W D, et al. First staging of two laser accelerators. Phys. Rev. Lett. 86 (2001) 4041.
83. Kimura W D, et al. Demonstration of High-Trapping Efficiency and Narrow Energy Spread in a Laser-Driven Accelerator. Phys. Rev. Lett. 92 (2004) 054801-1-4
84. Musumeci P, Tochitsky S Y, et al. High Energy Gain of Trapped Electrons in a Tapered, Diffraction-DominatedInverse-Free-Electron Laser Phys. Rev. Lett. 94 (2005) 154801-4
1．孟绍贤．超强场激光物理学．物理学进展．19(1999)236-269
2.Lax M, Louisell W H, et al. From Maxwell to paraxial wave optics. Phys Rev. 11 (1975) 1365-1370.
3.Salamin Y I, Keitel C H. Electron acceleration by a tightly focused laser beam. Phys. Rev.Lett. 85 (2002) 095005-4.
4.Rhodes D R. On the stored energy of planar apertures. IEEE Trans Antennas Propag.. AP-14 (1996) 676～683.
5.Rhodes D R. On a fundamental principle in the theory of planar antennas. Proc IEEE 52 (1964) 1013-1021.
6.Chen C G, Konkola P T, Ferrera J, et al. Analyses of vector Ganssian beam propagation and the validity of paraxial and spherical approximations. J Opt Soc Am A. 19 (2002) 404～412.
7.Carter W H. Electromagnetic field of a Gaussian beam with an elliptical cross section. J Opt Soc Am. 62 (1972) 1195-1201.
8.Mandel L, Wolf E. Optical coherence and quantum optics. Cambridge university press (1995) 109-125.
9.Bernardini A E. The stationary phase condition applicability to the study of tunnel effect. Mod Phys Lett B. 19 (2005) 883～888.
10.Born M, Wolf E. Principles of Optics. 4th ed. (Pergamon, New York, 1970). p.754.
11.Duan K L, Lü B D. Nonparaxial analysis of far-field properties of Gaussian beams diffracted by an aperture. Opt Expr. 11 (2003) 1474-1480.
12.Agrawal G P, Pattanayak D N. Gaussian beam propagation beyond the paraxial approximation. J opt Soc Am. 69 (1979) 575-578.
13.Luneburg R K. Mathematical Theory of optics (University of California Press, Berkeley, Calif., 1966).
14.Duan K L, Lü B D. Propagation properties of vectorial elliptical Gaussian beams beyond the paraxial approximation. Opt & Laser Tech. 36 (2004) 489-496.
15.Duan K L, Lü B D. Vectorial Nonparaxial Propagation Equation of Elliptical Gaussian Beams in the Presence of a Rectangular Aperture. J Opt Soc Am A. 21 (2004) 1613-1620.
16.Duan K L, Lü B D. Propagation of Hermite- and Laguerre-Gaussian beams beyond the paraxial approximation. J Opt Soc Am A. 2005.22. 1976～1980
17.Laabs H, Friberg A T. Nonparaxial eigenmodes of stable resonators. IEEE J. Quan. Elect. 35 (1999) 198-207.
18．焦其祥，李书芳等 电磁场与电磁波．科学出版社．(2004)
19.Davis L W. Theory of electromagnetic beams. Phys Rev. 19 (1979) 1177-1179.
20.Salamin Y I, Mocken G R, Keitel C H. Electron scattering and acceleration by a tightly focused laser beam. Phys. Rev. STAB. 5 (2002) 101301
21.Salamin Y I, Keitel C H. Electron acceleration by a tightly focused laser beam. Phys. Rev. Lett. 88 (2002) 095005-4
22.Chen M, Sheng Z M, Zhang J. Optimal injection scheme for electron acceleration by a tightly focused laser beam. Chin. Phys. 14 (2005) 1407-06.
23．段开椋，吕百达．非傍轴光束级数修正解的有效性，中国激光．31 (2004)432-436
24.Wünsche A. Transition from the paraxial approximation to exact solutions of the wave equation and application to Gaussian beams. J Opt Soc Am A. 9 (1992) 765～774.
25.Cao Q, Deng X. Corrections to the paraxial approximation of an arbitrary free-propagation beam. J Opt Soc Am A. 15 (1998) 1144～1148.
26.Heyman E, L B Felsen. Gaussian beam and pulsed-beam dynamics: complex-source and complex-spectrum formulations within and beyond paraxial asymptotics. J Opt Soc Am A. 18 (2001) 1588-1611.
27.Kibble T W B. Refraction of Electron Beams by Intense Electromagnetic Waves. Phys. Rev. Lett. 16 (1966) 1054-1056.
28.McDonald K T. Laser Acceleration of Partices, Eds ,C. Joshi and T. Katsouleas, A IP Conf. 130 (AIP ,New York, 1985) 23.
29.McDonald K T, Chen P, et al. Proc. Workshop on Beam-Beam and Beam-Radiation Interaction High Intensity and Non2linear Effects (World Scientific, Singapore) (1992) 127.
30.Bula C, McDonald K T, et al. Observation of Nonlinear Effects in Compton Scattering. Phys. Rev. Lett. 76 (1996) 3116-3119.
31.KibbleT W B. Mutual Refraction of Electrons and Photons. Phys. Rev. 150 (1966) 1060-1069.
32. Kong Q, Ho Y K, et al. Electron dynamics, characteristics in high-intensity laser fields. Applied Physics B 74 (2002) 517-520.
33. Ho Y K, Wang J X, et al. Electron scattering by an intense continuous laser beam Phys. Lett. A 220 (1996) 189-193
34. Wang J X, Ho Y K, et al. Nonlinear compton effect and electron inelastic scattering by an intense stationary laser beam. Phys.Lett. A 231 (1997) 139-143
35. Wang J X, Y K Ho et al. Inelastic electron scattering by an intense laser beam of the Hermite-Gaussian (0, 1) mode. Phys.Lett. A 234(1997) 415-418
36. Wang P X, Ho Y K, et al. Vacuum electron acceleration by an intense laser. Appl. Phys. Lett. 78 (2001) 2253-2255
37. Wang J X, Y K Ho, et al. Electron capture and violent acceleration by an extra-intense laser beam. Phys. Rev. E 58 (1998) 6575-6577.
38. Zhu L J, Ho Y K, et al. Violent acceleration of electrons by an ultra-intense pulsed laser beam. Phys.Lett. A 248 (1998) 319-324.
1. Lax M, Lousell W H and Mokinght W B. From Maxwell to paraxial wave optics. Phys. Rev. A 11 (1975) 1365-1370
2. Takenaka T, Yokota M and Fukumitsu. Propagation of light beams beyond the paraxial approximation. J. Opt, Soc. Am. A 2 (1985) 826-829
3. Wünsche A. Transition from the paraxial approximation to exact solution of the wave equation and application to Gaussian beams. J. Opt. Soc. Am. A 9 (1992) 765-774
4. Chen C G, Konkola P T, Ferrera J, Heilmann R K and Schattenburg M L. Analyses of vector Gaussian beam propagation and the validity of paraxial and spherical approximations. J. Opt. Soc. Am.A. 19 (2002) 404-412
5. Borghi R, Ciaffoni A and Sanfarsiero M. Exact axial electromagnetic field for vectorial Gaussian and flattened Gaussian boundary distributions. J. Opt. Soc. Am. A 19 (2002) 1207-1211
6. Zeng X, Liang C and An Y. Far-field propagation of an off-axis Gaussian wave. Appl. Opt. 38 (1999) 6253-6256
7. Duan K and Lü B. Vectorial Nonparaxial Propagation Equation of Elliptical Gaussian Beams in the Presence of a Rectangular Aperture. J. Opt. Soc Am A. 21 (2004) 1613-1620
8. Harvey J E and Krywonos A. Axial irradiance distribution throughout the whole space behind an annular aperture. Appl. opt. 41 (2002) 3790-3795
9. Marathay A S and McCalmont J F. On the usual approximation used in the Rayleigh-Sommerfeld diffraction theory. J. Opt. Soc. Am A .21 (2004) 510-516
10. Alessandro C, Bruno C and Porto P D. Analyses of vector Gaussian beam propagation and the validity of paraxial and spherical approximations. Opt. Commun., 202 (2002) 17-20
11. Tervo J and Turunen J. Angular spectrum representation of partially coherent electromagnetic fields. Opt. Commu. 209 (2002) 7-16
12. Duan K L and Lü B D. Partially coherent vectorial nonparaxial beams. J. Opt. Soc. Am A. 21 (2004) 1924-1932.
13. Zahid M and Zubairy M S Directionality of partially coherent Bessel-Gaussian beams Opt. Commun. 70 (1989) 361-364
14. Luneberg R K. Mathematical Theory of Optics, (University of California Press, Berkely and Los Angeles) (1964).
15. Duan K L and Lü B A. A comparison of the vectorial nonparaxial approach with Fresnel and Fraunhofer approximations. Optik. 115 (2004).218-222
16. Li Y and Wolf E: Focal shifts in diffracted converging spherical waves. Opt. Commun. 39 (1981) 211-215
17. Mandel L, Wolf E. Optical coherence and Quantum Optics, 1st edition (1995) Cambridge university press, New York 183
18. Tovar A A, Casperson L W Production and propagation of Hermite-sinusoidal-Gaussian laser beams. J. Opt. Soc. Am. A. 15 (1998) 2425-2432.
19. Lü B D, Ma H and Zhang B. Propagation properties of cosh-Gaussian beams Opt.Commun. 164 (1999) 165-170
20. Belafhal A and Ibnchaikh M. Propagation properties of Hermite-cosh-Gaussian laser beams. opt. Commun.186 (2000) 269-276
21. Duan K L, Lü B D. Partially coherent nonparaxial beams. Opt.Lett. 29 (2004) 800-802
22. Nemoto S. Nonparaxial Gaussian beams. Applied Optics 29 (1990) 1940
23. Turunen J, Tervonen E and Friberg A T. Acousto-optic control and modulation of optical coherence by electronically synthesized holographic gratings J. Appl.Phys. 67(1990) 49-59.
24. Tervonen E, Friberg A T and Turunen J. Gaussian Schell-model beams generated with synthetic acousto-optic holograms. J. Opt. Soc. Am A. 9 (1992) 796
25. Gradshteyn I S, Ryzhik I M. Table of Integrals, Series, and Products. 4th edition (1980) Academic press, New York 338
26. Duan K L and Lü B D. Wigner-distribution-function matrix and its application to partially coherent vectorial nonparaxial beams J. Opt. Soc. Am. B. 22 (2005)1585-93.
1.Perry M D and Mourou G. Terawatt to petawatt sub-picosecond laser. Science 264 (1994) 917-924
2.Perry M D, Pennington D, Stuart B C, et al. Petawatt laser pulses. Opt. Lett. 24(1999)160-162
3．朱鹏飞，钱列加等．基于“神光-Ⅱ”装置的飞秒拍瓦级光学参量啁啾脉冲放大的特性分 析与系统设计．物理学报 52(2003)587．
4．刘红军，陈国夫等．光学参量啁啾脉冲放大技术产生TW级激光脉冲系统的最优化设计．物理学报 50(2001)1717．
5.Murnance M M, Kapteyn H C, Rosen M D, et al. Ultrafast X-ray pulses from laser-produced plasmas. Science 251 (1991)531-536
6．何峰，余玮等．紧聚焦的飞秒激光脉冲在真空中对电子的加．物理学报 53(2004)165．
7. ScullyM O, Zubairy M S. Simple laser accelerator: optics and particle dynamics. Phys.Rev.A 44 (1991) 2656-2663
8. Esarey E, Sprangle P, Krall J. Laser acceleration of electrons in vacuum. Phys.Rev.E 52 (1995) 5443-5453.
9. Liu S, Guo H. Direct acceleration of electrons using single Hermite-Ganssian beam and Bessel beam in vacuum. Phys.Lett. A 324 (2004) 104-113
10. Sprangle P, Esarey E and Krall J. Laser driven electron acceleration in vacuum, gases, and plasmas. Phys.Plasmas. 3 (1996) 2183-2190
11. Haaland C M. Laser electron acceleration in vacuum. Opt. Commun. 114(1995) 280-284.
12. Sprangle P, Esarey E and Krall J. Vacuum laser acceleration. Opt.Commun. 124 (1996) 69-73
13. Salamin Y I and Keitel C H. Subcycle high electron acceleration by crossed laser beams. Appl..Phys.Lett. 77 (2000) 1082-1084
14. Gori F, Guattari G. Bessel-Gauss beam. Opt.Commun 64 (1987) 491-495.
15. Borghi R, Santarsiero M, Porras M A. Nonparaxial Bessel-Gauss beams. J.opt.Soc.Am .A 18 (2000) 1618-1626
16. Bagini V, Frezza F, Santarsiero M, et al. Generalized Bessel-Gauss beams. J. Mod..optics 43 (1995) 1155-1166
17. Lü B D. 2003 Laser optics, third ed. (Beijing: Higher Education Press) (in Chinese).
18. Lax M, Louisell W H, McKnight W B. From Maxwell to paraxial wave optics. Phys.Rev.A 11 (1975)1365
19. Born M, Wolfe 1989 Principles of Optics sixth ed. (corrected) Pergamon Oxford
20. Lawson J D 1975 Rutherford Laboratory Report No.RL-75-043 Lawson J D IEEE 1979 Trans.Nucl.Sci. NS-26 4217
21. Woodword P M 1947 J.Inst.Electr.Eng. 93 1554
22. Davis LW. Theory of electron electromagnetic beams. Phys.Rev.A 19 (1979) 1177-1179
1. Scully M O, Zubairy M S. Simple laser accelerator: optics and particle dynamics. Phys.Rev.A 44 (1991) 2656
2. Bochove E J, Moore G T, and Scully M O. Acceleration of particles by an asymmetric Hermite-Gaussian laser beam. Phys.Rev.A 46 (1992) 6640-6653
3.Esarey E, Sprangle P, Krall J. Laser acceleration of electrons in vacuum. Phys.Rev.E 52 (1995) 5443-5453.
4.Haaland C M. Laser electron acceleration in vacuum. Opt. Commun. 114 (1995) 280-284.
5.Sprangle P, Esarey E and Krall J. Vacuum laser acceleration. Opt.Commun 124 (1996) 69-73
6.Sprangle P, Esarey E and Krall J. Laser driven electron acceleration in vacuum, gases,and plasmas. Phys.Plasmas. 3 (1996) 2183-2190
7.Huang Y C, Zheng D, Tullock W M. Proposed structure for a crossed-laser beam,GeV per meter gradient, vacuum electron linear accelerator. Appl Phys. Lett. 68 (1996) 753.
8.Huang Y C, Byer R L. A proposed high-gradient laser-driven electron accelerator using crossed cylindrical laser focusing. Applied Physics Letters 69 (1996) 2175-7.
9.Huang Y C, Plettner T, Byer R L, Pantell RH, et al. Physics experiment for a laser-driven electron accelerator. Nucl. Instrum. Methods Phys. Res. A. 407 (1998) 316.
10.Salamin Y I, Keitel C H. Subcycle high electron acceleration by crossed laser beams. Applied Physics Letter 77 (2000) 1082-4
11.Salamin Y I, Mocken G R, Keitel C H. Relativistic electron dynamics in intense crossed laser beams: acceleration and Compton harmonics. Physical Review E 67 (2003) 16501-1-13
12.Mahmoud S T, Pandey H D, et al. Beat-wave excitation of electron plasma wave by cross-focusing of two intense laser beams. Journal of Plasma Physics 69 (2003) 45-58.
13.Gupta M K, Sharma R P, Gupta V L. Cross focusing of two laser beams and plasma wave excitation. Physics of Plasmas 12 (2005) 123101
14.Keitel C H, Keitel C H. Optimum conditions for electron acceleration using tightly focused laser beams. Laser Physics 13 (2003) 407-13
15.Shao L, Huo Y K, et al. Investigation of electron injection parameters in vacuum laser acceleration. Chin. Phys. Lett., 20 (2003)1251-3.
16．何峰，余玮等．紧聚焦的飞秒激光脉冲在真空中对电子的加．物理学报 53(2004)165．
17.Liu S, Guo H. Direct acceleration of electrons using single Hermite-Gaussian beam and Bessel beam in vacuum. Phys.Lett. A 324 (2004) 104-113
18.Li D, Imasaki K. Vacuum laser-driven acceleration by two slits-truncated Bessel beams. Appl. Phys. Lett. 87 (2005) 091106.
19. Li D, Imasaki K. Vacuum laser-driven acceleration by a slits-truncated Bessel beam. Appl. Phys. Lett. 86 (2005) 031110.
20. Durnin J. Exact solutions for nondiffracting beams: I. The scalar theory. J Opt Soc Am A 4 (1987) 65
21. Indebetouw G. Nondiffaction optical fields:some remarks on their analysis and synthesis J. Opt. Soc.Am. A 6 (1989)150-152.
22. Gori F, Guattari G. Bessel-Gauss beam. Opt.Commun. 64(1987) 491-495.
23. Rogel-Salazar J, New G H C, Chavez-Gerda S. Bessel-Gauss beam optical resonator. Opt. Commun. 190 (2001)117-122
24. Muys P, Vandamme E. Direct generation of Bessel beams. Appl Opt 41(2002) 6375.
25. Tsangaris C L, New G H C. Unstable Bessel beam resonator. Opt Commun 223 (2003) 233.
26. Bagini V, Frezza F, Santarsiero M, et al. Generalized Bessel-Gauss beams. J. Mod..Optics 43 (1995)1155-1166
27. Borghi R, Santarsiero M, Porras MA. Nonparaxial Bessel-Gauss beams .J.Opt.Soc.Am .A 18 (2000) 1618-1626
28. Siegman A E. Laser (Mill Valley, CA: University Science Press) (1986) 647
29. Lü B D 2003 Laser optics, third ed. (Beijing: Higher Education Press) (in Chinese).
30. Born M, Wolf E. Principles of optics. 7th (expanded) ed. Cambridge: Cambridge University Press 1999; p.16.
31. Lax M, Louisell W H, McKnight W B. From Maxwell to paraxial wave optics. Phys.Rev.A 11 (1975) 1365-1370
32. Lawson J D. Rutherford Laboratory Report 1975 No.RL-75-043 Lawson J D IEEE Trans.Nucl.Sci. 1979 NS-26 4217
33. Woodword P M J.Inst.Electr.Eng. 93 (1947) 1554
1. Zhu L J, Ho Y K, Wang J X, Kong Q. Violent acceleration of electrons by an ultra-intense pulsed laser beam. Phys.Lett.A. 248 (1998) 319-324.
2. He F, Yu W, Lu P, Xu H, Qian L, Shen B, Yuan X, Li R, and Xu Z. Ponderomotive acceleration of electrons by a tightly focused intense laser beam Phys. Rev. E 68 (2003) 046407
3. Malka G, Lefebvre E, Miquel J L. Experimental observation of electron accelerated in vacuum to relativistic energies by a high-intensity laser. Phys.Rev.Lett. 78 (1997) 3314-3317.
4. Malka G, Miquel J L. Experimental confirmation of ponderomotive-force electrons produced by an utrarelativistic pulse on a solid target. Phys.Rev.Lett. 77 (1996) 75-78.
5. Scully M O, Zubairy M S. Simple laser accelerator: optics and particle dynamics. Phys.Rev.A 44 (1991) 2656-2662
6. Bochove E J, Moore G T, and Scully M O. Acceleration of particles by an asymmetric Hermite-Gaussian laser beam Phys. Rev. A 46 (1992) 6640-6653.
7. Esarey E, Sprangle P, Krall J. Laser acceleration of electrons in vacuum. Phys.Rev.E 52 (1995) 5443-5453.
8. Zhu L J, Ho Y K, Wang J X, Kong Q. Violent acceleration of electrons by an ultra-intense pulsed laser beam. Phys.Lett.A 248 (1998) 319-324.
9. Wang J X, Ho Y K, Kong Q, Zhu L J, Feng L, Scheid S, and Hora H. Electron capture and violent acceleration by an extra-intense laser beam. Phys.Rev.E 58 (1998) 6375.
10. Wang J X, Ho Y K, Feng L, Kong Q, Wang P X, Yuan Z S, and Scheid W. High-intensity laser-induced electron acceleration in vacuum. Phys.Rev. E 60 (1999) 7473
11. Yousef I S, Faisal F H M, Keitel C H. Exact analysis of ultrahigh laser-induced acceleration of electrons by cyclotron autoresonance. Phys.Rev.A 62 (2000) 053809.
12. Kong Q, Ho Y K, Wang J X, Wang P X, Feng L, Yuan Z S. Conditions for electron capture by an ultraintense stationary laser beam. Phys.Rev. E 61 (2000) 1981.
13. Hirshfield J L, Wang C. Laser-driven electron cyclotron autoresonance accelerator with production of an optically chopped electron beam. Phys.Rev. E 61 (2000) 7252.
14. Yousef I S, Faisal F H M. Ultrahigh electron acceleration and Compton emission spectra in a superintense laser pulse and a uniform axial magnetic field. Phys.Rev.A 61 (2000) 043801.
15. Wang J X, Scheid W, Hoelss M, Ho Y K. Mechanism of electron violent acceleration by extra-intense lasers in vacuum. Phys.Lett.A. 280 (2001) 121-128.
16. Salamin Y I, Keitel C H. Electron acceleration by a tightly focused laser beam. Phys. Rev. Lett. 88 (2002) 095005
17. Salamin Y I, Mocken G R, Keitel C H.. Eelectron scattering and acceleration by a tightly focused laser beam. Phys.Rev. STAB. 5 (2002) 101301.
18. Salamin Y I. Relativistic electron dynamics in intense crossed laser beams: acceleration and Compton harmonics. Phys.Rev.E 67 (2003) 016501.
19. Liu S, Guo H, Tang H, Liu M. Direct acceleration of electron using single Hermite-Gaussian beam and Bessel beam in vacuum. Phys.Lett.A 324 (2004) 104-113.
20. Salamin Y I. Electron acceleration in a tightly-focrsed vacuum laser beat wave. Phys.Letts.A 335 (2005) 289-294.
21. Lax M, Louisell W H, Mcknight W B. From Maxwell to paraxial wave optics. Phys.Rev.A 11 (1975) 1365.
22. Laabs H. Propagation of Hermite-Gaussian-beams beyond the paraxial approximation. Opt.Commun. 147 (1998) 1-4.
23. Agrawal G P, Lax M. Free-space wave propagation beyond the paraxial approximation. Phys.Rev.A 27(1983) 1693-1695.
24. Chen C G, Konkola P T, Ferrera J, Herlmann R K and Schattenburg M L. Analyses of vector Gaussian beam propagation and the validity of paraxial and spherical approximations J.Opt.Soc.Am. A (2002) 19 404-412
25. Duan K, Wang B. and Lü B. Propagation of Hermite-Gaussian and Laguerre-Gaussian beams beyond the paraxial approximation J.Opt.Soc.Am. A 22 (2005) 1976-1980.
2.McMillan E M. The Synchrotron—A Proposed High Energy Particle Accelerator. Phys. Rev. 68 (1945) 143-144.
3.Courant E D, Livingston M S et al. The Strong-Focusing Synchroton—A New High Energy Accelerator. Phys. Rev. 88 (1952) 1190-1196.
4.Channell P J. Laser acceleration of particles. AIP Conf. No. 91 (New York).
5.Pardy M. The quantum field theory of laser acceleration. Physics Letters A 3 (1998) 223-8.
6.Fedorov M V, Goreslavsky S P, Letokhov V S. Ponderomotive forces and stimulated Compton scattering of free electrons in a laser field. Phys. gev. E 55, (1997) 1015-1027.
7. Hartemann F V, Kerman A K. Classical Theory of Nonlinear Compton Scattering. Phys. Rev. Lett. 76 (1996) 624-627.
8. Quesnel B, P Mora. Theory and simulation of the interaction of ultraintense laser pulses with electrons in vacuum. Phys. Rev. E 58 (1998) 3719-3732.
9. Hafizi B, Ganguly A K, Ting A, et al. Analysis of Gaussian beam and Bessel beam driven laser accelerators. Phys. Rev. E 60 (1999) 4779-4792.
10. Edighoffer J A, Kimura W D, et al. Free-electron interactions with light using the inverse Cerenkov effect. IEEE J. Quantum Electronics, 17(1981)1507-14.
11. Kimura W D, Kim G H, Romea R D, et al. Laser Acceleration of Relativistic Electrons Using the Inverse Cherenkov Effect. Phys. Rev. Lett. 74 (1995) 546-549.
12. Lee S, Katsouleas T, Hemker R, et al. Simulations of a meter-long plasma wakefield accelerator. Phys. Rev. E 61 (2000) 7014-7021.
13. Rundquist A R, LeBlance S P, Gaul E W, et al. Optimization of laser wakefield acceleration. AIP Conference Proceedings. 569 (2001) 177-82.
14. Serbeto A, Rios L A, Shukla P K. Neutrino-driven wakefield plasma accelerator. Phys. Plasmas 9 (2002) 4406.
15. Pisin C, Tajima T, Takahashi Y. Plasma wakefield acceleration for ultrahigh-energy cosmic rays. Phys. Rev. Lett. 89 (2002) 975-977.
16. Lotov K V, Blowout regimes of plasma wakefield acceleration Phys. Rev. E 69 (2004) 046405-1-13
17. Altmark A M, Kanareykin A D, Sheinman I L. Tunable wakefield dielectric-filled accelerating structure. Tech. Phy. 76 (2005) 87-95.
18. Kuzntsov S V. Wakefield acceleration of noumonoenergetic electron bunches. Plasma Phys. Reports 32 (2006) 282-91.
19. Kalmykov S Y, Gorbunov L M, Mora P. Injection, trapping, and acceleration of electrons in a three-dimensional nonlinear laser wakefield. Phys. Plasmas 13 (2006) 113102-1-11.
20. Cai S Y, Bhattacharjee A. Inverse-free-electron-laser beat-wave accelerator. Phys. Rev. A 42 (1990) 4853-61.
21. Fishrer A, Gallardo J, Sandweiss J, et al. Inverse free electron laser accelerator AIP Conference Proceedings. 279 (1993) 299-318.
22.Maroli C, Petrillo V, Bonifacio R. Plasma-based inverse free-electron laser for high-gradient acceleration of electrons. Phys. Rev. Lett. 76 (1996) 3578-81.
23.Harteman F V, Baldis H A, Freeman R R, et al. The chirped-pulse inverse free-electron laser: A high-gradient vacuum laser accelerator. Phys. Plasmas. 6 (1999) 4104-10.
24.Yoder R B, Marshall T C, Hirshfield J L. Energy-gain measurements from a microwave inverse free-electron-laser accelerator. Phys. Rev. Lett. 86 (2001) 1765-8.
25.Musumeci P, Tochitsky S Y, et al. High energy gain of trapped electrons in a tapered, diffraction-dominated inverse-free-electron laser. Phys. Rev. Lett. 94 (2005) 154801/1-4.
26.Mirzanejhad S, Sohbatzadeh F, et al. Electron bunch acceleration in an inverse free-electron laser with a helical magnetic wiggler and axial guide field. Phys. Plasmas 13 (2006) 123105.
27.Tanq C M, pranqle P S, Sudan R N. Dynamics of space-charge waves in the laser beat wave accelerator. Phys. Fluids. 28 (1985)1974-83.
28.Amiranoff F, Bernard D, et al. Electron acceleration in Nd-laser plasma beat-wave experiments. Physica Scripta Volume T 63 (1996) 126-35.
29.Hafizi B, Ting A, et al. Vacuum beat wave acceleration. Phys.Rev. E 55 (1997) 5924-33.
30.Salamin Y I, Keitel C H. Analysis of electron acceleration in a vacuum beat wave. J. Phys. B 33 (2000) 5057-76.
31.Tochitsky S Y, Narang R, et al. Enhanced acceleration of injected electrons in a laser-beat-wave-induced plasma channel. Phys.Rev.Lett. 92 (2004) 095004/1-4.
32.Salamin Y I. Single-electron dynamics in a tightly focused laser beat wave: acceleration in vacuum. J. Phys. B 38 (2005)4095-110.
33.Richard H M. Electron Scattering by an Intense Polarized Photon Field Phys. Rev. Lett. 10 (1963)75-77
34．王加祥，霍裕昆，冯量．锥形光场对电子的加速效应．物理学报 45(1998)1264-11．
35.Esarey E, Sprangle P, Krall J. Laser acceleration of electron in vacuum. Phys. Rev. E 52 (1995) 5443-5453.
36.Salamin Y I, Keitel C H. Subcycle high electron acceleration by crossed laser beams. Appl. Phys. Lett. 77 (2000) 1082-1084.
37.Sprangle P, Esarey E, et al. Vacuum laser acceleration. Opt. Commun. 124 (1996) 69-73.
38．王平晓，孔青，霍裕昆．激光在真空中加速电子．物理 36(2007)32-38．
39.Tajima T, Dawson J M. Laser Electron Accelerator. Phys. Rev. Lett. 43 (1979) 267-270.
40．陈民，盛政明，马燕云，张杰．台面型电子加速器—激光尾波场加速器．物理 35(2006)1016-1027．
41.Plettner T, Bver R L, et al. Visible-Laser Acceleration of Relativistic Electrons in a Semi-Infinite Vacuum. Phys. Rev. Lett. 95 (2005) 134801.
42.Huang Y C, Byer R L. A proposed high-gradient laser-driven electron accelerator using crossed cylindrical laser focusing. Appl.Phys. Lett. 69 (1996) 2175-7.
43.Steinhauer L C, Kimura W D. A new approach for laser particle acceleration in vacuum. J.Appl.Phys.72 (1992) 3237-45.
44.Hartemann F V, Fochs S N, et al. Nonlinear ponderomotive scattering of relativistic electrons by an intense laser field at focus. Phys. Rev. E 51 (1995) 4833-4843.
45.Yu Wei, Yu M Y, Ma J X, et al. Ponderomotive acceleration of electrons at the focus of high intensity lasers. Phys. Rev. E 61 (2000) R2220-R2223.
46.Wang J X, Ho Y K, et al. Electron capture and violent acceleration by an extra-intense laser beam. Phys. Rev. E 58 (1998) 6575-6577.
47.Palmer R B. Interaction of relativistic particles and free electromagnetic waves in the presence of a static helical magnet. J. Appl. Phys. 43 (1972) 3014-23.
48.Scheid W, Hora H. On electron acceleration by plane transverse electromagnetic pulses in vacuum. Laser and Particle Beams 7 (1989) 315-32.
49.Rau B, Tajima T, Hojo H. Coherent Electron Acceleration by Subcycle Laser Pulses. Phys. Rev. Lett. 78 (1997) 3310-3313.
50.Sinqh K P. Electron acceleration by a chirped short intense laser pulse in vacuum. Appt. Phys. Lett. 87(2005) 254102.
51.Kawata S, Maruyama T, et al. Inverse-bremsstrahlung electron acceleration. Phys. Rev. Lett. 66 (1991) 2072-2075.
52.Li Y T, Sheng Z M, et al. Demonstration of bulk acceleration of ions in ultraintense laser interactions with low-density foams. Phys. Rev. E 72 (2005) 066404.
53.Li Y T, Yuan X H, et al. Observation of a fast electron beam emitted along the surface of a target irradiated by intense femtosecond laser pulses. Phys. Rev. Lett. 96 (2006) 165003.
54. Sheng Z M, Mima K, et al. Efficient acceleration of electrons with counterpropagating intense laser pulses in vacuum and underdense plasma. Phys. Rev. E 69 (2004) 016407.
55. Dong Q L, Sheng Z M, Yu M Y, Zhang J. Optimization of ion acceleration in the interaction of intense femtosecond laser pulses with ultrathin foils. Phys. Rev. E 68 (2003) 026408.
56. Li Y T, Zhang J, et al. Spatial distribution of high-energy electron emission from water plasmas produced by femtosecond laser pulses. Phys. Rev. Lett. 90 (2003) 165002.
57. Yu Wei, Chen Z Y, Yu M Y, et al. Electron acceleration and high-order harmonic generation by an intense short pulse laser in a magnetic field. Phys. Rev. E 66 (2002) 036406.
58. Yu Wei, Xu H, He F, et al. Direct acceleration of solid-density plasma bunch by ultraintense laser. Phys. Rev. E 72 (2005) 046401.
59. He F, Yu Wei, et al. Ponderomotive acceleration of electrons by a tightly focused intense laser beam. Phys. Rev. E 68 (2003) 046407.
60. Yu Wei, Bychenkov V, Sentoku Y, et al. Electron Acceleration by a Short Relativistic Laser Pulse at the Front of Solid Targets. Phys. Rev. Lett. 85(2000) 570-573.
61. Du C G, Li S Q. Dephasing time of a positron accelerated by a laser pulse. Chin. Phys. 11 (2002) 375-04.
62. Liu S, Guo H, et al. Direct acceleration of electrons using single Hermite-Gaussian beam and Bessel beam in vacuum. Phys. Lett. A 324 (2004)104-113.
63. Bochove E J, Moore G T, Scully M O. Acceleration of particles by an asymmetric Hermite-Gayssian laser beam. Phys. Rev. A 46 (1992) 6640-6653.
64. Esarey E, Pilloff M. Trapping and acceleration in nonlinear plasma waves.Phys.Plasmas 2 (1995) 1432-6.
65．曹娜．一种新型加速器的特性研究．2003 复旦大学博士学位论文．
66. McDonald K T. Laser Acceleration of Partices , Eds ,C. Joshi and T. Katsouleas , A IP Conf. 130 (AIP ,New York ,1985) 23.
67. McDonald K T, Chen P , et al. Proc. Workshop on Beam-Beam and Beam-Radiation Interaction High Intensity and Non21inear Effects (World Scientific ,Singapore) (1992) 127.
68. Bula C, McDonald K T, et al. Observation of Nonlinear Effects in Compton Scattering. Phys. Rev. Lett. 76 (1996) 3116-3119.
69. KibbleT W B. Mutual Refraction of Electrons and Photons. Phys. Rev. 150 (1966) 1060-1069.
70. Kong Q, Ho Y K, et al. Electron dynamics characteristics in high-intensity laser fields. Applied Physics B 74 (2002) 517-520.
71. Ho Y K, Wang J X, et al. Electron scattering by an intense continuous laser, beam Phys. Lett. A 220 (1996) 189-193
72. Wang J X, Ho Y K, et al. Nonlinear compton effect and electron inelastic scattering by an intense stationary laser beam. Phys.Lett. A 231 (1997) 139-143
73. Wang J X, Y K Ho et al. Inelastic electron scattering by an intense laser beam of the Hermite-Gaussian (0, 1) mode. Phys.Lett. A 234(1997) 415-418
74. Wang P X, Ho Y K, et al. Vacuum electron acceleration by an intense laser. Appl. Phys. Lett. 78 (2001) 2253-2255
75. Zhu L J, Ho Y K, et al. Violent acceleration of electrons by an ultra-intense pulsed laser beam. Phys.Lett. A 248 (1998) 319-324.
76. Malka G, Lefebvre E. Experimental Observation of Electrons Accelerated in Vacuum to Relativistic Energies by a High-Intensity Laser. Phys. Rev. Lett. 78 (1997) 3314-3317.
77. Bucksbaum P H, Bashkansky M, McIlrath T J. Scattering of electrons by intense coherent light. Phys. Rev. Lett. 58 (1987) 349-352.
78. Monot P, Auguste T, LompréL A, et al. Energy measurements of electrons submitted to an ultrastrong laser field. Phys. Rev. Lett. 70 (1993) 1232-1235.
79. Moore C I, Knauer J P. Observation of the Transition from Thomson to Compton Scattering in Multiphoton Interactions with Low-Energy Electrons. Phys. Rev. Lett. 74 (1995) 2439.
80. Moore C I,et al. Observation of the Transition from Thomson to Compton Scattering in Multiphoton Interactions with Low-Energy Electrons. Phys. Rev. Left. 74 (1995) 2439-2442
81. Hartemann F V, Fochs S N, Le Sage G P, et al. Nonlinear ponderomotive scattering of relativistic electrons by an intense laser field at focus. Phys. Rev. E 51 (1995) 4833.
82. Kimura W D, et al. First staging of two laser accelerators. Phys. Rev. Lett. 86 (2001) 4041.
83. Kimura W D, et al. Demonstration of High-Trapping Efficiency and Narrow Energy Spread in a Laser-Driven Accelerator. Phys. Rev. Lett. 92 (2004) 054801-1-4
84. Musumeci P, Tochitsky S Y, et al. High Energy Gain of Trapped Electrons in a Tapered, Diffraction-DominatedInverse-Free-Electron Laser Phys. Rev. Lett. 94 (2005) 154801-4
1．孟绍贤．超强场激光物理学．物理学进展．19(1999)236-269
2.Lax M, Louisell W H, et al. From Maxwell to paraxial wave optics. Phys Rev. 11 (1975) 1365-1370.
3.Salamin Y I, Keitel C H. Electron acceleration by a tightly focused laser beam. Phys. Rev.Lett. 85 (2002) 095005-4.
4.Rhodes D R. On the stored energy of planar apertures. IEEE Trans Antennas Propag.. AP-14 (1996) 676～683.
5.Rhodes D R. On a fundamental principle in the theory of planar antennas. Proc IEEE 52 (1964) 1013-1021.
6.Chen C G, Konkola P T, Ferrera J, et al. Analyses of vector Ganssian beam propagation and the validity of paraxial and spherical approximations. J Opt Soc Am A. 19 (2002) 404～412.
7.Carter W H. Electromagnetic field of a Gaussian beam with an elliptical cross section. J Opt Soc Am. 62 (1972) 1195-1201.
8.Mandel L, Wolf E. Optical coherence and quantum optics. Cambridge university press (1995) 109-125.
9.Bernardini A E. The stationary phase condition applicability to the study of tunnel effect. Mod Phys Lett B. 19 (2005) 883～888.
10.Born M, Wolf E. Principles of Optics. 4th ed. (Pergamon, New York, 1970). p.754.
11.Duan K L, Lü B D. Nonparaxial analysis of far-field properties of Gaussian beams diffracted by an aperture. Opt Expr. 11 (2003) 1474-1480.
12.Agrawal G P, Pattanayak D N. Gaussian beam propagation beyond the paraxial approximation. J opt Soc Am. 69 (1979) 575-578.
13.Luneburg R K. Mathematical Theory of optics (University of California Press, Berkeley, Calif., 1966).
14.Duan K L, Lü B D. Propagation properties of vectorial elliptical Gaussian beams beyond the paraxial approximation. Opt & Laser Tech. 36 (2004) 489-496.
15.Duan K L, Lü B D. Vectorial Nonparaxial Propagation Equation of Elliptical Gaussian Beams in the Presence of a Rectangular Aperture. J Opt Soc Am A. 21 (2004) 1613-1620.
16.Duan K L, Lü B D. Propagation of Hermite- and Laguerre-Gaussian beams beyond the paraxial approximation. J Opt Soc Am A. 2005.22. 1976～1980
17.Laabs H, Friberg A T. Nonparaxial eigenmodes of stable resonators. IEEE J. Quan. Elect. 35 (1999) 198-207.
18．焦其祥，李书芳等 电磁场与电磁波．科学出版社．(2004)
19.Davis L W. Theory of electromagnetic beams. Phys Rev. 19 (1979) 1177-1179.
20.Salamin Y I, Mocken G R, Keitel C H. Electron scattering and acceleration by a tightly focused laser beam. Phys. Rev. STAB. 5 (2002) 101301
21.Salamin Y I, Keitel C H. Electron acceleration by a tightly focused laser beam. Phys. Rev. Lett. 88 (2002) 095005-4
22.Chen M, Sheng Z M, Zhang J. Optimal injection scheme for electron acceleration by a tightly focused laser beam. Chin. Phys. 14 (2005) 1407-06.
23．段开椋，吕百达．非傍轴光束级数修正解的有效性，中国激光．31 (2004)432-436
24.Wünsche A. Transition from the paraxial approximation to exact solutions of the wave equation and application to Gaussian beams. J Opt Soc Am A. 9 (1992) 765～774.
25.Cao Q, Deng X. Corrections to the paraxial approximation of an arbitrary free-propagation beam. J Opt Soc Am A. 15 (1998) 1144～1148.
26.Heyman E, L B Felsen. Gaussian beam and pulsed-beam dynamics: complex-source and complex-spectrum formulations within and beyond paraxial asymptotics. J Opt Soc Am A. 18 (2001) 1588-1611.
27.Kibble T W B. Refraction of Electron Beams by Intense Electromagnetic Waves. Phys. Rev. Lett. 16 (1966) 1054-1056.
28.McDonald K T. Laser Acceleration of Partices, Eds ,C. Joshi and T. Katsouleas, A IP Conf. 130 (AIP ,New York, 1985) 23.
29.McDonald K T, Chen P, et al. Proc. Workshop on Beam-Beam and Beam-Radiation Interaction High Intensity and Non2linear Effects (World Scientific, Singapore) (1992) 127.
30.Bula C, McDonald K T, et al. Observation of Nonlinear Effects in Compton Scattering. Phys. Rev. Lett. 76 (1996) 3116-3119.
31.KibbleT W B. Mutual Refraction of Electrons and Photons. Phys. Rev. 150 (1966) 1060-1069.
32. Kong Q, Ho Y K, et al. Electron dynamics, characteristics in high-intensity laser fields. Applied Physics B 74 (2002) 517-520.
33. Ho Y K, Wang J X, et al. Electron scattering by an intense continuous laser beam Phys. Lett. A 220 (1996) 189-193
34. Wang J X, Ho Y K, et al. Nonlinear compton effect and electron inelastic scattering by an intense stationary laser beam. Phys.Lett. A 231 (1997) 139-143
35. Wang J X, Y K Ho et al. Inelastic electron scattering by an intense laser beam of the Hermite-Gaussian (0, 1) mode. Phys.Lett. A 234(1997) 415-418
36. Wang P X, Ho Y K, et al. Vacuum electron acceleration by an intense laser. Appl. Phys. Lett. 78 (2001) 2253-2255
37. Wang J X, Y K Ho, et al. Electron capture and violent acceleration by an extra-intense laser beam. Phys. Rev. E 58 (1998) 6575-6577.
38. Zhu L J, Ho Y K, et al. Violent acceleration of electrons by an ultra-intense pulsed laser beam. Phys.Lett. A 248 (1998) 319-324.
1. Lax M, Lousell W H and Mokinght W B. From Maxwell to paraxial wave optics. Phys. Rev. A 11 (1975) 1365-1370
2. Takenaka T, Yokota M and Fukumitsu. Propagation of light beams beyond the paraxial approximation. J. Opt, Soc. Am. A 2 (1985) 826-829
3. Wünsche A. Transition from the paraxial approximation to exact solution of the wave equation and application to Gaussian beams. J. Opt. Soc. Am. A 9 (1992) 765-774
4. Chen C G, Konkola P T, Ferrera J, Heilmann R K and Schattenburg M L. Analyses of vector Gaussian beam propagation and the validity of paraxial and spherical approximations. J. Opt. Soc. Am.A. 19 (2002) 404-412
5. Borghi R, Ciaffoni A and Sanfarsiero M. Exact axial electromagnetic field for vectorial Gaussian and flattened Gaussian boundary distributions. J. Opt. Soc. Am. A 19 (2002) 1207-1211
6. Zeng X, Liang C and An Y. Far-field propagation of an off-axis Gaussian wave. Appl. Opt. 38 (1999) 6253-6256
7. Duan K and Lü B. Vectorial Nonparaxial Propagation Equation of Elliptical Gaussian Beams in the Presence of a Rectangular Aperture. J. Opt. Soc Am A. 21 (2004) 1613-1620
8. Harvey J E and Krywonos A. Axial irradiance distribution throughout the whole space behind an annular aperture. Appl. opt. 41 (2002) 3790-3795
9. Marathay A S and McCalmont J F. On the usual approximation used in the Rayleigh-Sommerfeld diffraction theory. J. Opt. Soc. Am A .21 (2004) 510-516
10. Alessandro C, Bruno C and Porto P D. Analyses of vector Gaussian beam propagation and the validity of paraxial and spherical approximations. Opt. Commun., 202 (2002) 17-20
11. Tervo J and Turunen J. Angular spectrum representation of partially coherent electromagnetic fields. Opt. Commu. 209 (2002) 7-16
12. Duan K L and Lü B D. Partially coherent vectorial nonparaxial beams. J. Opt. Soc. Am A. 21 (2004) 1924-1932.
13. Zahid M and Zubairy M S Directionality of partially coherent Bessel-Gaussian beams Opt. Commun. 70 (1989) 361-364
14. Luneberg R K. Mathematical Theory of Optics, (University of California Press, Berkely and Los Angeles) (1964).
15. Duan K L and Lü B A. A comparison of the vectorial nonparaxial approach with Fresnel and Fraunhofer approximations. Optik. 115 (2004).218-222
16. Li Y and Wolf E: Focal shifts in diffracted converging spherical waves. Opt. Commun. 39 (1981) 211-215
17. Mandel L, Wolf E. Optical coherence and Quantum Optics, 1st edition (1995) Cambridge university press, New York 183
18. Tovar A A, Casperson L W Production and propagation of Hermite-sinusoidal-Gaussian laser beams. J. Opt. Soc. Am. A. 15 (1998) 2425-2432.
19. Lü B D, Ma H and Zhang B. Propagation properties of cosh-Gaussian beams Opt.Commun. 164 (1999) 165-170
20. Belafhal A and Ibnchaikh M. Propagation properties of Hermite-cosh-Gaussian laser beams. opt. Commun.186 (2000) 269-276
21. Duan K L, Lü B D. Partially coherent nonparaxial beams. Opt.Lett. 29 (2004) 800-802
22. Nemoto S. Nonparaxial Gaussian beams. Applied Optics 29 (1990) 1940
23. Turunen J, Tervonen E and Friberg A T. Acousto-optic control and modulation of optical coherence by electronically synthesized holographic gratings J. Appl.Phys. 67(1990) 49-59.
24. Tervonen E, Friberg A T and Turunen J. Gaussian Schell-model beams generated with synthetic acousto-optic holograms. J. Opt. Soc. Am A. 9 (1992) 796
25. Gradshteyn I S, Ryzhik I M. Table of Integrals, Series, and Products. 4th edition (1980) Academic press, New York 338
26. Duan K L and Lü B D. Wigner-distribution-function matrix and its application to partially coherent vectorial nonparaxial beams J. Opt. Soc. Am. B. 22 (2005)1585-93.
1.Perry M D and Mourou G. Terawatt to petawatt sub-picosecond laser. Science 264 (1994) 917-924
2.Perry M D, Pennington D, Stuart B C, et al. Petawatt laser pulses. Opt. Lett. 24(1999)160-162
3．朱鹏飞，钱列加等．基于“神光-Ⅱ”装置的飞秒拍瓦级光学参量啁啾脉冲放大的特性分 析与系统设计．物理学报 52(2003)587．
4．刘红军，陈国夫等．光学参量啁啾脉冲放大技术产生TW级激光脉冲系统的最优化设计．物理学报 50(2001)1717．
5.Murnance M M, Kapteyn H C, Rosen M D, et al. Ultrafast X-ray pulses from laser-produced plasmas. Science 251 (1991)531-536
6．何峰，余玮等．紧聚焦的飞秒激光脉冲在真空中对电子的加．物理学报 53(2004)165．
7. ScullyM O, Zubairy M S. Simple laser accelerator: optics and particle dynamics. Phys.Rev.A 44 (1991) 2656-2663
8. Esarey E, Sprangle P, Krall J. Laser acceleration of electrons in vacuum. Phys.Rev.E 52 (1995) 5443-5453.
9. Liu S, Guo H. Direct acceleration of electrons using single Hermite-Ganssian beam and Bessel beam in vacuum. Phys.Lett. A 324 (2004) 104-113
10. Sprangle P, Esarey E and Krall J. Laser driven electron acceleration in vacuum, gases, and plasmas. Phys.Plasmas. 3 (1996) 2183-2190
11. Haaland C M. Laser electron acceleration in vacuum. Opt. Commun. 114(1995) 280-284.
12. Sprangle P, Esarey E and Krall J. Vacuum laser acceleration. Opt.Commun. 124 (1996) 69-73
13. Salamin Y I and Keitel C H. Subcycle high electron acceleration by crossed laser beams. Appl..Phys.Lett. 77 (2000) 1082-1084
14. Gori F, Guattari G. Bessel-Gauss beam. Opt.Commun 64 (1987) 491-495.
15. Borghi R, Santarsiero M, Porras M A. Nonparaxial Bessel-Gauss beams. J.opt.Soc.Am .A 18 (2000) 1618-1626
16. Bagini V, Frezza F, Santarsiero M, et al. Generalized Bessel-Gauss beams. J. Mod..optics 43 (1995) 1155-1166
17. Lü B D. 2003 Laser optics, third ed. (Beijing: Higher Education Press) (in Chinese).
18. Lax M, Louisell W H, McKnight W B. From Maxwell to paraxial wave optics. Phys.Rev.A 11 (1975)1365
19. Born M, Wolfe 1989 Principles of Optics sixth ed. (corrected) Pergamon Oxford
20. Lawson J D 1975 Rutherford Laboratory Report No.RL-75-043 Lawson J D IEEE 1979 Trans.Nucl.Sci. NS-26 4217
21. Woodword P M 1947 J.Inst.Electr.Eng. 93 1554
22. Davis LW. Theory of electron electromagnetic beams. Phys.Rev.A 19 (1979) 1177-1179
1. Scully M O, Zubairy M S. Simple laser accelerator: optics and particle dynamics. Phys.Rev.A 44 (1991) 2656
2. Bochove E J, Moore G T, and Scully M O. Acceleration of particles by an asymmetric Hermite-Gaussian laser beam. Phys.Rev.A 46 (1992) 6640-6653
3.Esarey E, Sprangle P, Krall J. Laser acceleration of electrons in vacuum. Phys.Rev.E 52 (1995) 5443-5453.
4.Haaland C M. Laser electron acceleration in vacuum. Opt. Commun. 114 (1995) 280-284.
5.Sprangle P, Esarey E and Krall J. Vacuum laser acceleration. Opt.Commun 124 (1996) 69-73
6.Sprangle P, Esarey E and Krall J. Laser driven electron acceleration in vacuum, gases,and plasmas. Phys.Plasmas. 3 (1996) 2183-2190
7.Huang Y C, Zheng D, Tullock W M. Proposed structure for a crossed-laser beam,GeV per meter gradient, vacuum electron linear accelerator. Appl Phys. Lett. 68 (1996) 753.
8.Huang Y C, Byer R L. A proposed high-gradient laser-driven electron accelerator using crossed cylindrical laser focusing. Applied Physics Letters 69 (1996) 2175-7.
9.Huang Y C, Plettner T, Byer R L, Pantell RH, et al. Physics experiment for a laser-driven electron accelerator. Nucl. Instrum. Methods Phys. Res. A. 407 (1998) 316.
10.Salamin Y I, Keitel C H. Subcycle high electron acceleration by crossed laser beams. Applied Physics Letter 77 (2000) 1082-4
11.Salamin Y I, Mocken G R, Keitel C H. Relativistic electron dynamics in intense crossed laser beams: acceleration and Compton harmonics. Physical Review E 67 (2003) 16501-1-13
12.Mahmoud S T, Pandey H D, et al. Beat-wave excitation of electron plasma wave by cross-focusing of two intense laser beams. Journal of Plasma Physics 69 (2003) 45-58.
13.Gupta M K, Sharma R P, Gupta V L. Cross focusing of two laser beams and plasma wave excitation. Physics of Plasmas 12 (2005) 123101
14.Keitel C H, Keitel C H. Optimum conditions for electron acceleration using tightly focused laser beams. Laser Physics 13 (2003) 407-13
15.Shao L, Huo Y K, et al. Investigation of electron injection parameters in vacuum laser acceleration. Chin. Phys. Lett., 20 (2003)1251-3.
16．何峰，余玮等．紧聚焦的飞秒激光脉冲在真空中对电子的加．物理学报 53(2004)165．
17.Liu S, Guo H. Direct acceleration of electrons using single Hermite-Gaussian beam and Bessel beam in vacuum. Phys.Lett. A 324 (2004) 104-113
18.Li D, Imasaki K. Vacuum laser-driven acceleration by two slits-truncated Bessel beams. Appl. Phys. Lett. 87 (2005) 091106.
19. Li D, Imasaki K. Vacuum laser-driven acceleration by a slits-truncated Bessel beam. Appl. Phys. Lett. 86 (2005) 031110.
20. Durnin J. Exact solutions for nondiffracting beams: I. The scalar theory. J Opt Soc Am A 4 (1987) 65
21. Indebetouw G. Nondiffaction optical fields:some remarks on their analysis and synthesis J. Opt. Soc.Am. A 6 (1989)150-152.
22. Gori F, Guattari G. Bessel-Gauss beam. Opt.Commun. 64(1987) 491-495.
23. Rogel-Salazar J, New G H C, Chavez-Gerda S. Bessel-Gauss beam optical resonator. Opt. Commun. 190 (2001)117-122
24. Muys P, Vandamme E. Direct generation of Bessel beams. Appl Opt 41(2002) 6375.
25. Tsangaris C L, New G H C. Unstable Bessel beam resonator. Opt Commun 223 (2003) 233.
26. Bagini V, Frezza F, Santarsiero M, et al. Generalized Bessel-Gauss beams. J. Mod..Optics 43 (1995)1155-1166
27. Borghi R, Santarsiero M, Porras MA. Nonparaxial Bessel-Gauss beams .J.Opt.Soc.Am .A 18 (2000) 1618-1626
28. Siegman A E. Laser (Mill Valley, CA: University Science Press) (1986) 647
29. Lü B D 2003 Laser optics, third ed. (Beijing: Higher Education Press) (in Chinese).
30. Born M, Wolf E. Principles of optics. 7th (expanded) ed. Cambridge: Cambridge University Press 1999; p.16.
31. Lax M, Louisell W H, McKnight W B. From Maxwell to paraxial wave optics. Phys.Rev.A 11 (1975) 1365-1370
32. Lawson J D. Rutherford Laboratory Report 1975 No.RL-75-043 Lawson J D IEEE Trans.Nucl.Sci. 1979 NS-26 4217
33. Woodword P M J.Inst.Electr.Eng. 93 (1947) 1554
1. Zhu L J, Ho Y K, Wang J X, Kong Q. Violent acceleration of electrons by an ultra-intense pulsed laser beam. Phys.Lett.A. 248 (1998) 319-324.
2. He F, Yu W, Lu P, Xu H, Qian L, Shen B, Yuan X, Li R, and Xu Z. Ponderomotive acceleration of electrons by a tightly focused intense laser beam Phys. Rev. E 68 (2003) 046407
3. Malka G, Lefebvre E, Miquel J L. Experimental observation of electron accelerated in vacuum to relativistic energies by a high-intensity laser. Phys.Rev.Lett. 78 (1997) 3314-3317.
4. Malka G, Miquel J L. Experimental confirmation of ponderomotive-force electrons produced by an utrarelativistic pulse on a solid target. Phys.Rev.Lett. 77 (1996) 75-78.
5. Scully M O, Zubairy M S. Simple laser accelerator: optics and particle dynamics. Phys.Rev.A 44 (1991) 2656-2662
6. Bochove E J, Moore G T, and Scully M O. Acceleration of particles by an asymmetric Hermite-Gaussian laser beam Phys. Rev. A 46 (1992) 6640-6653.
7. Esarey E, Sprangle P, Krall J. Laser acceleration of electrons in vacuum. Phys.Rev.E 52 (1995) 5443-5453.
8. Zhu L J, Ho Y K, Wang J X, Kong Q. Violent acceleration of electrons by an ultra-intense pulsed laser beam. Phys.Lett.A 248 (1998) 319-324.
9. Wang J X, Ho Y K, Kong Q, Zhu L J, Feng L, Scheid S, and Hora H. Electron capture and violent acceleration by an extra-intense laser beam. Phys.Rev.E 58 (1998) 6375.
10. Wang J X, Ho Y K, Feng L, Kong Q, Wang P X, Yuan Z S, and Scheid W. High-intensity laser-induced electron acceleration in vacuum. Phys.Rev. E 60 (1999) 7473
11. Yousef I S, Faisal F H M, Keitel C H. Exact analysis of ultrahigh laser-induced acceleration of electrons by cyclotron autoresonance. Phys.Rev.A 62 (2000) 053809.
12. Kong Q, Ho Y K, Wang J X, Wang P X, Feng L, Yuan Z S. Conditions for electron capture by an ultraintense stationary laser beam. Phys.Rev. E 61 (2000) 1981.
13. Hirshfield J L, Wang C. Laser-driven electron cyclotron autoresonance accelerator with production of an optically chopped electron beam. Phys.Rev. E 61 (2000) 7252.
14. Yousef I S, Faisal F H M. Ultrahigh electron acceleration and Compton emission spectra in a superintense laser pulse and a uniform axial magnetic field. Phys.Rev.A 61 (2000) 043801.
15. Wang J X, Scheid W, Hoelss M, Ho Y K. Mechanism of electron violent acceleration by extra-intense lasers in vacuum. Phys.Lett.A. 280 (2001) 121-128.
16. Salamin Y I, Keitel C H. Electron acceleration by a tightly focused laser beam. Phys. Rev. Lett. 88 (2002) 095005
17. Salamin Y I, Mocken G R, Keitel C H.. Eelectron scattering and acceleration by a tightly focused laser beam. Phys.Rev. STAB. 5 (2002) 101301.
18. Salamin Y I. Relativistic electron dynamics in intense crossed laser beams: acceleration and Compton harmonics. Phys.Rev.E 67 (2003) 016501.
19. Liu S, Guo H, Tang H, Liu M. Direct acceleration of electron using single Hermite-Gaussian beam and Bessel beam in vacuum. Phys.Lett.A 324 (2004) 104-113.
20. Salamin Y I. Electron acceleration in a tightly-focrsed vacuum laser beat wave. Phys.Letts.A 335 (2005) 289-294.
21. Lax M, Louisell W H, Mcknight W B. From Maxwell to paraxial wave optics. Phys.Rev.A 11 (1975) 1365.
22. Laabs H. Propagation of Hermite-Gaussian-beams beyond the paraxial approximation. Opt.Commun. 147 (1998) 1-4.
23. Agrawal G P, Lax M. Free-space wave propagation beyond the paraxial approximation. Phys.Rev.A 27(1983) 1693-1695.
24. Chen C G, Konkola P T, Ferrera J, Herlmann R K and Schattenburg M L. Analyses of vector Gaussian beam propagation and the validity of paraxial and spherical approximations J.Opt.Soc.Am. A (2002) 19 404-412
25. Duan K, Wang B. and Lü B. Propagation of Hermite-Gaussian and Laguerre-Gaussian beams beyond the paraxial approximation J.Opt.Soc.Am. A 22 (2005) 1976-1980.