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。     

Partially coherent nonparaxial beams

The concept of a partially coherent nonparaxial beam is proposed. A closed-form expression for the propagation of nonparaxial Gaussian Schell model (GSM) beams in free space is derived and applied to study the propagation properties of nonparaxial GSM beams. It is shown that for partially coherent nonparaxial beams a new parameter f(sigma) has to be introduced, which together with the parameter f, determines the beam nonparaxiality.     

Transformation of nonparaxial Gaussian beams

Based on the vector theory of nonparaxial Gaussian beams, the paper presents a theory about the transformation of nonparaxial Gaussian beams after lens. The collimating characteristic and propagation properties are discussed in detail, and the collimating field after lens for the vector and scalar theory respectively is compared, and the quantitative difference is also derived.     

Exact transcendental equation for scalar modes of rectangular dielectric waveguides

Conclusion A Fourier operator method has been used to derive for the first time an exact closed-form eigenvalue equation for the scalar mode propagation constants of a buried rectangular dielectric waveguide. The new method has been implemented and the results used to determine the accuracy of the scalar finite-difference approach. It is hoped that the exact results obtained here may assist in the validation of the accuracy of the other numerical and semi-analytical methods.     

非傍轴高斯光束传输特性的研究

基于非傍轴矢量光束横截面上光强的严格定义〈S_z〉,采用桶中功率定义光束的束宽、远场发散角以及M²因子. 以非傍轴矢量高斯光束为例,对光束的传输特性进行了详细的理论分析和数值计算,并与非傍轴标量理论的结果进行了比较分析. 研究表明,光源半宽ω₀/Λ<1时,传输特性的矢量描述与非傍轴标量描述有显著差别,随着ω₀/Λ的增大,两者趋于一致,并逐步过渡到 关键词： 非傍轴高斯光束 桶中功率 束宽 发散角     

Scalar field of nonparaxial Gaussian beams

A family of closed-form expressions for the scalar field of strongly focused Gaussian beams in oblate spheroidal coordinates is given. The solutions satisfy the wave equation and are free from singularities. The lowest-order solution in the far field closely matches the energy density produced by a sine-condition, high-aperture lens illuminated by a paraxial Gaussian beam. At the large waist limit the solution reduces to the paraxial Gaussian beam form. The solution is equivalent to the spherical wave of a combined complex point source and sink but has the advantage of being more directly interpretatable.     

Partially coherent nonparaxial modified Bessel--Gauss beams

The concept of partially coherent nonparaxial modified Bessel--Gauss (MBG) beams is proposed. Based on the generalized Rayleigh-Sommerfeld diffraction integral, the analytical propagation equations of nonparaxial MBG beams in free space are derived and analysed, and some special cases are discussed. In particular, under the paraxial approximation our results reduce to the corresponding paraxial ones. Numerical calculation examples are given to illustrate the dependence of intensity and spectral degree of coherence on the beam order $m$, \textit{$\xi $} and $f$ parameters, and to compare the difference between the paraxial and nonparaxial results.     

Predict acoustic field of vibrating beams by Helmholtz integral equation and BEM

New method of predicting the acoustic field radiation of vibratingbodies is presented.It is based on the Helmholtz integral equation and bounda-ry element method and applicable to the use of computers.The acoustic field ofthe cantilever beams has been calculated and measured.Test results haveproved the effectiveness of the predicting method.     

非傍轴矢量高斯光束的光强表示

基于瑞利-索末菲衍射积分,未使用任何近似,对非傍轴矢量光束的两种光强表示式,即传统光强公式和时间平均坡印廷矢量的z分量进行了研究。对非傍轴矢量高斯光束详细数值计算结果的比较表明,两种表示式之间的差异,即两者的相对误差与束腰宽度及传输距离和波长的比值有关。对非傍轴矢量高斯光束,若传输距离与波长的比值为10,束腰宽度与波长的比值大于等于0.8,则最大相对误差不到1.5%。因此,传统光强公式是可用的。     

非傍轴矢量异常空心光束的传输特性

 将Cai提出的异常空心光束的理论模型推广到非傍轴范畴,推导出非傍轴矢量异常空心光束传输的解析表达式,用以研究它在自由空间中的传输特性。研究表明,异常空心光束在传输过程中光束形状会发生变化。与高斯光束不同,非傍轴异常空心光束傍轴近似成立条件依赖于传输距离,这与异常空心光束光强分布随传输距离的变化有关。非傍轴异常空心光束远场的光束质量可用桶中功率来描述,桶中功率随f参数(波长与束腰宽度的比值)的增大而减小。     

非傍轴矢量高斯光束的光强表示

 基于瑞利-索末菲衍射积分,未使用任何近似,对非傍轴矢量光束的两种光强表示式,即传统光强公式和时间平均坡印廷矢量的z分量进行了研究。对非傍轴矢量高斯光束详细数值计算结果的比较表明,两种表示式之间的差异,即两者的相对误差与束腰宽度及传输距离和波长的比值有关。对非傍轴矢量高斯光束,若传输距离与波长的比值为10,束腰宽度与波长的比值大于等于0.8,则最大相对误差不到1.5%。因此,传统光强公式是可用的。     

Orbital angular momentum and nonparaxial light beams

The simple relationship between total angular momentum and energy and the seemingly natural separation of the angular momentum into spin and orbital components in the paraxial approximation, are investigated for a general nonparaxial form of monochromatic beam with near cylindrical symmetry.     

Generation of linear and nonlinear nonparaxial accelerating beams

We study linear and nonlinear self-accelerating beams propagating along circular trajectories beyond the paraxial approximation. Such nonparaxial accelerating beams are exact solutions of the Helmholtz equation, preserving their shapes during propagation even under nonlinearity. We generate experimentally and observe directly these large-angle bending beams in colloidal suspensions of polystyrene nanoparticles.     

非傍轴双曲余弦-高斯脉冲电磁光束远场特性

利用矢量瑞利-索末菲衍射积分公式,推导出了非傍轴部分空间相干部分光谱相干双曲余弦-高斯(ChG)脉冲电磁光束在自由空间传输时交叉谱密度矩阵的远场解析公式,并用来表示脉冲电磁光束的光谱密度(光强)和偏振度。结果表明,对非傍轴远场部分空间相干部分光谱相干ChG脉冲电磁光束,其非傍轴性主要由参数f, f决定,而离心参数、脉冲宽度和时间相干长度影响其非傍轴行为。非傍轴部分空间相干部分光谱相干高斯-谢尔模型脉冲电磁光束的远场传输可作为特例处理。     

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     

非傍轴截断平顶光束的质量因子

 使用功率密度的二阶矩方法和Li提出的平顶光束模型,推导出了非傍轴截断平顶光束的束腰宽度、远场发散角和光束质量因子的解析表达式。计算结果表明：非傍轴截断平顶光束的质量因子不仅与截断参数、光束阶数有关,而且与初始束腰宽度和波长之比有关;当截断参数趋近于0时,远场发散角趋于渐近值63.435°;对于光束阶数为1和截断参数趋于无穷大的特例,计算结果分别退化为非傍轴截断高斯光束和非傍轴无截断平顶光束的结果;功率密度的二阶矩方法可用于截断光束,并克服了光束质量因子的发散困难。     

截断非傍轴双曲余弦-高斯光束的远场特性

基于瑞利-索末菲衍射积分公式,推导出截断非傍轴双曲余弦-高斯光束在自由空间传输的解析表示式,分析了一些特例,并引入非傍轴范畴的桶中功率概念,用以描述非傍轴光束的远场光束质量。结果表明:截断非傍轴双曲余弦-高斯光束的光强和桶中功率不仅与束腰宽度与波长之比、偏心参数及截断参数有关,而且桶中功率还与桶的尺寸有关。在一定的范围内,较大的束腰宽度与波长之比, 截断参数和较小的偏心参数使光束有更好的聚焦特性,表现出更好的光束质量。     

非傍轴双曲余弦-高斯脉冲电磁光束远场特性

利用矢量瑞利-索末菲衍射积分公式,推导出了非傍轴部分空间相干部分光谱相干双曲余弦-高斯(ChG)脉冲电磁光束在自由空间传输时交叉谱密度矩阵的远场解析公式,并用来表示脉冲电磁光束的光谱密度(光强)和偏振度。结果表明,对非傍轴远场部分空间相干部分光谱相干ChG脉冲电磁光束,其非傍轴性主要由参数f, f决定,而离心参数、脉冲宽度和时间相干长度影响其非傍轴行为。非傍轴部分空间相干部分光谱相干高斯-谢尔模型脉冲电磁光束的远场传输可作为特例处理。     

非傍轴贝塞尔-高斯光束在自由空间的传输

从瑞利-索末菲衍射积分出发,推导出任意阶非傍轴贝塞尔-高斯光束在自由空间传输的解析表达式.非傍轴贝塞尔光束和非傍轴高斯光束等的传输方程都可以作为本文一般结果的特例而得出.物理分析和数值计算表明,当高斯和贝塞尔部分的横向尺度与波长相比拟或小于波长时,应当用非傍轴方法处理.     

截断非傍轴双曲余弦-高斯光束的远场特性

基于瑞利-索末菲衍射积分公式,推导出截断非傍轴双曲余弦-高斯光束在自由空间传输的解析表示式,分析了一些特例,并引入非傍轴范畴的桶中功率概念,用以描述非傍轴光束的远场光束质量。结果表明:截断非傍轴双曲余弦-高斯光束的光强和桶中功率不仅与束腰宽度与波长之比、偏心参数及截断参数有关,而且桶中功率还与桶的尺寸有关。在一定的范围内,较大的束腰宽度与波长之比, 截断参数和较小的偏心参数使光束有更好的聚焦特性,表现出更好的光束质量。