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     

非傍轴矢量光束二阶矩的发散特性

基于非傍轴矢量光束横截面上光强的精确表示和矢量二阶矩理论,应用严格的角谱表示的矢量衍射理论,对任意非傍轴矢量衍射光束的传输进行了系统的研究.给出了光束的束宽、横向发散角的积分表达式,论证了非傍轴矢量光束二阶矩的发散特性.对非傍轴矢量光束的束宽、发散角的定义及一些相关的问题进行了分析和讨论. 关键词： 矢量衍射理论 光束传输 矢量二阶矩 发散特性     

非傍轴矢量高斯光束的传输

运用非傍轴光束传输的矢量矩理论，对非傍轴矢量高斯光束的传输特性进行了系统的研究.结果表明，基于二阶矩定义的横向光束宽度在光束传播过程中满足简单的双曲线变化规律，并且给出了光束传输因子的解析表达式.就高度非傍轴情形，进一步给出了简洁的计算公式，在高斯光源线度趋向零的极限情形下，横向的最大发散角为90°.同时，还推广到了傍轴情形，得到了与原有傍轴公式稍有区别的结果，而且光束传输因子始终保持略大于1最后，对非傍轴矢量高斯光束和非傍轴标量高斯光束的传输进行了比较，结果显示对于线度在两个波长范围之内的高斯光源发散 关键词： 矢量高斯光束 光束传输 非傍轴 二阶矩     

截断非傍轴标量高斯光束的传输特性

基于精确光强定义下非傍轴标量光束的二阶矩理论,计算了不同束腰及光阑孔径条件下截断非傍轴标量高斯光束的束腰半径、远场发散角以及质量因子等光束传输特性,并将截断非傍轴标量高斯光束与自由高斯光束和平面波圆孔衍射光束进行了比较.数值计算表明截断参量的不同对截断高斯光束的传输特性影响很大.当R2ω0时,截断高斯光束与高斯光束在自由空间传输特性趋于一致,因此在精确光强定义下,对于非傍轴标量光束来说,当光阑孔径大于2倍束腰时,可以不考虑光阑对高斯光束的衍射作用.当R0.3ω0时,截断高斯光束传输特性趋于平面波通过圆孔的衍射曲线.因此,在这种情况下,可以将高斯光束作为平面波处理.只有当光阑孔径介于0.3倍束腰和2倍束腰之间时,需要同时考虑光阑孔径和高斯束腰对衍射的影响.     

光场的非傍轴性对光谱移动和光谱开关的影响

利用瑞利衍射积分公式，推导出多色高斯光束被硬边光阑衍射后光谱的解析公式，傍轴近似的光谱公式可作为特例得到.着重研究了束腰宽度与中心波长之比w₀/λ₀和截断参数δ对光谱移动和光谱开关的影响.结果表明，只有当w₀/λ₀和δ满足一定条件时，傍轴近似结果才与非傍轴结果一致.光场的非傍轴性会引起光谱移动不同和产生光谱开关的临界位置变化. 关键词： 非傍轴光场 高斯光束 光谱移动 光谱开关     

大气湍流中光束束宽扩展和角扩展的比较研究

以厄米-双曲余弦-高斯（H-ChG）光束为例,对H-ChG光束通过大气湍流传输时的束宽扩展和角扩展做了详细研究.用相对束宽和相对角扩展代替束宽和角扩展来研究湍流对光束影响的灵敏程度.研究表明,折射率结构常数C²_n越小,光束束宽扩展和角扩展越小.有较大阶数m,n,较小参数Ω₀和束腰宽度w₀ H-ChG光束的角扩展受湍流影响较小.当传输距离足够远时,这一结论对H-ChG光束的束宽扩展也成立.当传输距离不长时,对H-ChG光束相对束宽随Ω₀和w₀的变化规律做了分析.用数值计算例做了说明,并对结果的正确性做了物理解释.厄米-高斯,双曲余弦高斯和高斯光束在大气湍流中的扩展可作为H-ChG光束的特例来处理. 关键词： 束宽扩展和角扩展 大气湍流 厄米-双曲余弦-高斯光束     

湍流对离轴列阵高斯光束相干与非相干合成的影响

研究了湍流对离轴列阵高斯光束相干与非相干合成的影响.推导出了相干合成光束的传输方程.采用二阶矩束宽、桶中功率和参数β作为光束质量评价参数比较了离轴列阵高斯光束通过湍流大气的相干与非相干合成,并对主要结果给予了合理的物理解释.研究表明：一方面,不论是相干合成还是非相干合成,湍流都使得合成光束扩展、峰值光强下降,并且子光束数越多,合成光束受湍流影响就越小.另一方面,非相干合成光束较相干合成光束受到湍流的影响要小. 关键词： 相干与非相干合成 湍流大气 离轴列阵高斯光束     

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。     

光束质量与光束质量因子

应用标量光场光强的传统定义 ,推导了具有轴对称性的傍轴标量光束的光强二阶矩的传输规律。在此基础上 ,给出了光束的束腰半径、远场发散角及光束质量因子M2 ,并证明了光束质量因子M2 1。应用标量光场光强的精确定义 ,计算了非傍轴标量高斯光束的质量因子 ,结果表明 :当ω0 λ时 ,光束质量因子M2 可以小于 1,并随光束的束腰半径趋于零而趋向于零 ;ω0 >λ时 ,高斯光束的质量因子M2 非常接近于 1,且随光束束腰半径的增大迅速趋向于 1。此外 ,文章还对一些相关的问题进行了讨论。     

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     

Propagation characteristics of TM Gaussian beam

The propagation characteristics of TM polarized Gaussian beam, which is the rigorous solution of an eigenfunction problem for a confocal resonator, have been investigated using the nonparaxial vectorial moment theory of light beam propagation. The analytical expressions of the beam propagation factors are given by means of Fourier transform. Both the transversal second-order moment beam widths follow a simple hyperbolic variational law. For nonparaxial case, however, beam has different propagating features in the two transversal directions. As to paraxial case, its propagation approximately reduces to that of scalar Gaussian beam TEM₀₀ mode.     

Nonparaxial propagation of a super-Lorentz－Gauss SLG01 mode beam

Based on the vectorial Rayleigh--Sommerfeld integral formulae, this paper derives the analytical nonparaxial propagation equation of a super-Lorentz--Gauss (SLG) SLG₀₁ mode beam in free space. The far field expression and the scalar paraxial result are treated with special cases of the general formulae. According to the obtained analytical representation, the nonparaxial propagation properties of the SLG₀₁ mode beam are illustrated and analysed with numerical examples. This research provides an approach to investigate the propagation of the SLG₀₁ mode beam within the framework of the nonparaxial regime.     

非傍轴光束的光束质量因子．I．定义

在考虑了时间平均能流密度的矢量特性的情况下，用修正后的光强公式重新给出了非傍轴标量光场光强二阶矩的表达式。在此基础上，在忽略了瞬逝波的近似下证明了：对于在自由空间稳态传输的单色标量光场来说，其横截面上的光强二阶矩随轴坐标ｚ的变化成抛物线性变化。并进一步把傍轴光束的Ｍ２因子概念拓展到了非傍轴的标量光束。此外，还对一些相关的问题进行了讨论。     

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.     

Vectorial Nonparaxial Four-Petal Gaussian Beams and Their Propagation in Free Space

The vectorial nonparaxial four-petal Gaussian beam （FPGB） is introduced. The closed-form propagation expressions for the free-space propagation of FPGBs are derived and their more general applicable advantages are illustrated analytically and numerically. Some special interesting cases, in particular the paraxial one, are discussed. It is found that the parameter f = 1/kwo with the k being the wave number and wo being the waist width plays a crucial role in determining the nonparaxiallity of FPGBs. For small values of the f parameter the paraxial approximation is allowable. In the nonparaxial regime the beam order n additionally affects the vectorial and nonparaxial behaviour of FPGBs.     

Propagation of vectorial nonparaxial Gaussian beams through an annular aperture

Starting from the vectorial Rayleigh diffraction integrals, the nonparaxial propagation of vectorial Gaussian beams through an annular aperture is studied. The analytical propagation expressions are derived, which permit us to treat the on-axis field and far field of vectorial nonparaxial Gaussian beams diffracted at the annular aperture, the nonparaxial diffraction at a circular aperture and a circular disc as our special cases in a unified way. The validity of our treatment is confirmed by direct numerical integration of the Rayleigh formulae. It is shown that the f-parameter and annular obscuration affect the beam nonparaxiality in the case of diffraction at the annular aperture.     

The beam quality of nonparaxial Hermite-sine-Gaussian beam

Based on the theory of the second intensity moment of nonparaxial scalar beam and the method of angular spectrum, the expressions for the far-field divergence angle, waist width and M² factor of nonparaxial Hermite-sine-Gaussian (HSiG) beams are derived. Calculation and analysis show the dependence of the far-field divergence angle of nonparaxial HSiG beams on the parameter w₀/λ, as well as on order m, And it with even and odd orders approach 73.898° and 63.435° as w₀/λ → 0. With increasing order m and the parameter w₀/λ, the waist width increase monotonously, which is same as paraxial case. But nonparaxial M² factor is different from paraxial case, it cannot only less than 1, but also approach 0 as w₀/λ → 0.