矢量效应对超短脉冲光束非傍轴传输的影响

从严格的矢量非傍轴传输方程出发,并通过傅里叶变换及角谱分析的方法,分析了在超短脉冲光束中,矢量效应对其在自由空间中的非傍轴传输的影响。结果表明,矢量效直对脉冲光束的标量傍轴解的修正有着重要的影响,当对脉冲光束进行非傍轴传输处理时,必须考虑它的矢量特性。基于上述分析,得到了支配超短脉冲光束传输的矢量非傍轴方程的一个完整积分解。从这个积分解出发,通过对电场进行泰勒级数展开的方法,得到了一种相对简单的方法,通过这种方法,可以从脉冲光束的已知标量傍轴解来求出矢量非傍轴波动方程的相对精确解。     

自由空间中超短脉冲光束的非傍轴效应分析

在应用时间与空间傅里叶变换的基础上, 运用泰勒展开的方法, 得出了一种对多周期超短脉冲光束进行非傍轴修正的方法, 并将其应用于脉冲高斯光束．与数值结果的比较表明, 对于束宽在波长量级的脉冲光束, 二阶修正已经很接近非傍轴精确解, 并在例子中观察到：由于超短脉冲光束中时空耦合效应的存在, 脉冲的时间分布将会影响修正的空间分布．     

矢量可控空心光束的非傍轴传输

提出了矢量可控空心光束概念,可控空心光束可以很好地描写中心光强不完全为零的圆对称窄心光束,具有可用多个参最米控制中央暗斑尺寸、形式简单易于分析、其传输变换特性更接近于实际等特点.利用矢量瑞利-索末菲衍射积分公式,导出了矢量可控空心光束的非傍轴传输解析公式,从所得结果可退化得到傍轴近似结果.利用导出的公式计算分析了矢量可控空心光束在自由空间的非傍轴传输特性,并与傍轴结果进行了比较分析.结果表明矢量可控空心光束在近场很好地保持其空心光场分布特性;参量f和传输距离决定了矢量可控空心光束的非傍轴特性.     

超短脉冲贝塞尔光束的非近轴效应对传输的影响

 对超短脉冲贝塞尔光束在近轴近似和非近轴情况下自由空间中的传输作了研究。结果表明，其空间波形在传输中保持贝塞尔形状不变，不受非近轴效应影响；然而当空间参数较大时，非近轴效应影响超短脉冲贝塞尔光束的时间波形。     

矢量非傍轴离轴高斯光束的传输

基于矢量瑞利-索末菲衍射积分公式，得出了波动方程的一个解，它代表矢量非傍轴离轴高斯光束，其在自由空间的传输方程表示为解析的结果.矢量非傍轴离轴高斯光束的轴上和远场公式，矢量非傍轴高斯光束的传输方程，以及傍轴的结果都可作为一般表达式的特例而得出.研究表明，f参数对光束的非傍轴特性有重要影响，而离心参数也影响非傍轴行为.与共轴情况不同的是，对离轴情况，在y方向存在场的纵向分量. 关键词： 激光光学 矢量非傍轴离轴高斯光束 瑞利-索末菲衍射积分 f参数 离轴参数     

超短脉冲贝塞尔光束的非近轴效应对传输的影响

对超短脉冲贝塞尔光束在近轴近似和非近轴情况下自由空间中的传输作了研究。结果表明,其空间波形在传输中保持贝塞尔形状不变,不受非近轴效应影响;然而当空间参数较大时,非近轴效应影响超短脉冲贝塞尔光束的时间波形。     

超短脉冲径向偏振光束的解析解及时空耦合效应

从超短脉冲光束的傍轴传输方程出发, 运用傅里叶变换和相关数学算符的对易性, 得到了超短脉冲径向偏振光束的解析表达式.该解可适用于任意脉冲驱动的径向偏振光束. 基于该解析表达式并结合具体例子,讨论了超短脉冲径向偏振光束在自由空间中的传输性质. 结果表明, 在传输过程中时空耦合主要体现在光束边沿的脉冲延迟. 这一效应导致了脉冲不同时间位置处横向光强分布随传输的变化, 以及脉冲前后沿关于束腰的不对称性. 本文的方法同样适用于得到超短脉冲方位角偏振光束的解析解和传输性质.     

超短脉冲径向偏振光束的解析解及时空耦合效应

从超短脉冲光束的傍轴传输方程出发,运用傅里叶变换和相关数学算符的对易性,得到了超短脉冲径向偏振光束的解析表达式,该解可适用于任意脉冲驱动的径向偏振光束.基于该解析表达式并结合具体例子,讨论了超短脉冲径向偏振光束在自由空间中的传输性质.结果表明,在传输过程中时空耦合主要体现在光束边沿的脉冲延迟.这一效应导致了脉冲不同时间位置处横向光强分布随传输的变化,以及脉冲前后沿关于束腰的不对称性.本文的方法同样适用于得到超短脉冲方位角偏振光束的解析解和传输性质.     

激光物理

TN241 2004031707 矢量效应对超短脉冲光束非傍轴传输的影响=Influenceof vectorial effect on the non-paraxial propagation of ultrashort pulsed beam in free space[刊,中]/陆大全(华南师范大学传输光学实验室.广东,广州(510631)),胡巍…∥光学学报.—2004,24(1).—52-56     

矢量非傍轴厄米-拉盖尔-高斯光束的光束质量

基于矢量Rayleigh-Sommerfeld衍射积分，推导出矢量非傍轴圆偏振厄米-拉盖尔-高斯(HLG)光束的远场解析表达式.矢量非傍轴圆偏振高斯光束可作为一般公式的特例给出.将桶中功率(PIB)概念推广到非傍轴范畴，用以描述矢量非傍轴光束的远场光束质量，其中光强用时间平均坡印廷矢量的z分量取代.数值计算和分析表明，矢量非傍轴HLG光束的PIB不仅与束腰宽度与波长之比w₀/λ有关，而且还与α参数，模指数n和m以及所取桶的尺寸有关. 关键词： 矢量非傍轴厄米-拉盖尔-高斯光束 矢量Rayleigh-Sommerfeld衍射积分 桶中功率     

A comparison of the vectorial nonparaxial approach with Fresnel and Fraunhofer approximations

Based on the vectorial Rayleigh diffraction integrals, a nonparaxial propagation equation of vectorial plane waves diffracted at a circular aperture is derived. The nonparaxial far-field expression, Fresnel and Fraunhofer diffraction formulae are given and treated as special cases of our general expression. The theoretical formulation permits us to study and compare the transversal and axial intensity distributions of diffracted plane waves both analytically and numerically. Illustrative numerical examples are given. It is shown that the vectorial nonparaxial approach has to be used if the aperture size is comparable with or less than the wavelength, and the knowledge of both transversal and axial intensity distributions is required to provide a comprehensive comparison of the paraxial and nonparaxial results.     

Nonparaxial propagation of a vectorial apertured off-axis Lorentz beam

Based on the vectorial Rayleigh--Sommerfeld integral formula and the complex Gaussian expansion of the hard-edge aperture function, an analytical propagation expression for a nonparaxial vectorial off-axis Lorentz beam passing through a rectangular aperture is derived. The unapertured case, the far field expression and the scalar paraxial result are also presented as special cases of the general formulae, respectively. Some numerical examples are also given to show the propagation characteristics of a nonparaxial vectorial off-axis Lorentz beam through a rectangular aperture. It is indicated that the f parameter, the off-axis displacement and the truncation parameter all play an important role in determining nonparaxial propagation behaviour.     

非傍轴矢量拉盖尔-高斯光束的二阶矩表示

基于Porras提出的光传输的非傍轴矢量矩理论，推导出初始圆偏振的非傍轴矢量拉盖尔-高斯(LG)光束的特征参数，包括束宽、远场发散角和M²因子等的公式，并表示为级数求和形式.非傍轴矢量高斯光束公式作为特例给出.研究表明，基于二阶矩定义的束宽按双曲线规律传输，当w₀/λ→0(w₀为束宽，λ为波长)时，远场发散角θ趋于90°，大于非傍轴标量理论预示的值63.435°.非傍轴矢量LG光束的M²因子不仅与模指数p有关，而且还与w₀/λ有关.最后，对非傍轴矢量LG光束和非傍轴标量LG光束的传输作了比较，结果表明在w₀/λ较小时，矢量效应对远场发散角的影响十分显著.对θ→90°引起的问题和非傍轴矢量矩理论的适用范围，以及解决问题的可能途径作了分析和讨论. 关键词： 非傍轴矢量拉盖尔-高斯光束 圆偏振 非傍轴矢量矩理论 光束参数     

矢量非傍轴双曲余弦-高斯光束

 引入了矢量非傍轴双曲余弦-高斯(ChG)光束概念。使用矢量瑞利-索末菲衍射积分公式推导出了矢量非傍轴ChG光束在自由空间传输的解析公式。矢量非傍轴ChG光束轴上和远场的解析式以及傍轴结果作为一般传输公式的特例给出。研究表明,对矢量非傍轴ChG光束,其非傍轴性主要由f参数决定,但偏心参数会影响其横向光强剖面形状和非傍轴行为。     

Vectorial Hermite--Laguerre--Gaussian beams beyond the paraxial approximation

Starting from the vectorial Rayleigh--Sommerfeld integrals, the free-space propagation expressions for vectorial Hermite--Laguerre--Gaussian (HLG) beams beyond the paraxial approximation are derived. The far-field expressions and the scalar paraxial results are given as special cases of our general expressions. The intensity distributions of vectorial nonparaxial HLG beams are studied and illustrated with numerical examples.     

Vectorial partially coherent flat-topped beams and their nonparaxial propagation

The concept of vectorial partially coherent flat-topped beams is proposed, and their nonparaxial propagation in free space is studied in detail. Based on the vector Rayleigh diffraction integral formulae, the analytical propagation expressions for the cross-spectral density matrix of the polarized vectorial nonparaxial partially coherent flat-topped beams are derived and applied to study the nonparaxial propagation properties of vectorial partially coherent flat-topped beams. The effect of propagation parameters on the intensity and the coherence property of the nonparaxial vectorial partially coherent flat-topped beam is illustrated and analyzed comparatively with the corresponding paraxial results.     

Propagation of vectorial apertured cosh-Gaussian beams beyond the paraxial approximation

By using the vectorial Rayleigh-Sommerfeld diffraction integrals, the propagation equation of vectorial nonparaxial cosh-Gaussian (ChG) beams in the presence of an aperture is derived and expressed in a closed form. The on-axis, far-field and paraxial cases are studied as special cases. Analytical results are illustrated with numerical examples.     

Space-angle distribution of the reflected charged particles adjusted for spin calculations

The efficiency of the proposed method of solution for the spin-considered highly anisotropic multiple scattering problem is based, following optics, upon the admission that the complete solution of the vectorial transport equation boundary problem is the superposition of the anisotropic and smooth parts, calculated separately. We use a vectorial small angle modification of the spherical harmonics method to evaluate the anisotropic part and the vectorial discrete ordinates method to obtain a smooth one. Some calculation examples for reflected radiation are given.