Non-equiphase Hermite-Gaussian model of diode laser beams

A non-equiphase Hermite-Gaussian model is proposed to describe the field in the plane parallel to the junction of double-heterostructure (DH) diode laser beams. The analytical expression for the far field of DH diode laser beams is derived and used to compare the calculated intensity profiles with the measured and calculated values given by Nemoto and Zeng et al., showing a further improvement between the calculated and measured profiles by using the non-equiphase Hermite-Gaussian model.     

厄米-高斯光束的焦开关

考虑了由光阑和透镜组成的简单光学系统。研究表明，当厄米-高斯光束入射这一系统，在系统和光束参数满足一定条件时会出现称为焦开关的新现象。详细的数值计算和物理分析说明了厄米-高斯光束的焦开关特性。与已有的工作做了比较，并指出了焦开关可能的应用。     

Hermite-Gaussian beams with sinusoidal vortex phase modulation

In this Letter,vortex phase and sinusoidal phase modulations of Hermite-Gaussian beams are studied theoretically and experimentally.The coding method of the experiment is introduced in detail,and the evolution law of focus under different beam order(m,n) and topological charge(l) is given.In order to verify the accuracy of the generation experiment,the optical field distribution under sinusoidal vortex modulation is analyzed deeply.The relevant analysis and methods provided in this Letter have certain practical significance for the development of laser mode analysis,optical communication,and other fields.     

复宗量厄米-高斯光束的相干模表示

基于激光的相干模分解理论，讨论了复宗量厄米_高斯(EHG)光束的模相关和相干模表示，推导出EHG光束的模相关系数的解析表达式，并给出了一种只包含有限个模式的相干模表示. 在此基础上，根据EHG光束的模结构，分析了EHG光束和常规厄米_高斯(SHG)光束M²因子的差异. 关键词： 复宗量厄米_高斯(EHG)光束 相干模分解 2因子')" href="#">M²因子 模相关系数(MCCs)     

像散厄米-高斯光束的对称化和相关问题的研究

 从比较两种对称化光学系统出发，使用三柱透镜对称化光学系统对像散厄米高斯光束作了详细分析，研究表明：对称化光学系统的作用是将像散光束变换为对称化实宗量光束；并消去xy耦合项。这样，当光束继续在自由空间传输时，能保持其形状不变。然而，有xy耦合项的对称化复光束却不具有这种传输不变性。     

湍流大气中厄米-高斯光束M2因子的变化

 基于广义惠更斯-菲涅耳原理和Wigner分布函数二阶矩的定义,推导出直角坐标系下大气湍流中部分相干光的M²因子传输公式。以厄米-高斯（H-G）光束为例,给出了H-G光束通过大气湍流传输后M²因子的解析表达式,并采用Tatarskii谱,详细讨论了M²因子的主要影响因素。结果表明,M2因子主要由光束的束腰宽度、波长、光束阶数、大气湍流的折射率起伏结构常数和在湍流中传输距离决定。随着光束阶数、折射率起伏结构常数及传输距离的增大,M²因子明显增大,光束阶数越高,湍流对M²因子变化的影响越小。对于给定的传输距离,存在最佳初始束宽,使M2因子最小。     

自加速类贝塞尔-厄米-高斯光束的理论和实验研究

空间相位调制一直是设计新型自加速光束的重要方法.参照类贝塞尔光束产生的思路,从理论上提出了一种新型的自加速无衍射类贝塞尔-厄米-高斯光束,并从数值模拟和实验两个方面研究此光束沿不同轨道的演化.理论上通过对厄米-高斯光束进行相位调制,产生了不同模式的自加速类贝塞尔-厄米-高斯光束.采用分步傅里叶算法模拟了(0,1),(1,0),(1,1)和(1,2)阶类贝塞尔-厄米-高斯光束沿预设轨道的传输过程.采用计算全息和空间光调制技术在实验中观察了类贝塞尔-厄米-高斯光束沿预设轨道的传输,例如抛物、双曲、双曲正割和三维轨道.实验观察与理论结果符合得很好.实验验证了不同阶类贝塞尔-厄米-高斯光束的奇特光斑结构,验证了光束的非衍射特性及传输轨道的可控性,且理论模拟验证了光束的自修复特性.作为此前研究的类贝塞尔光束的一般形式,本文所得到的光束可用于构造出更加新型实用的光束.     

Partially coherent nonparaxial Hermite-Gaussian beams and their propagation properties

The concept of partially coherent nonparaxial Hermite-Gaussian (HG) beams is proposed. By using the generalized Rayleigh-Sommerfeld diffraction integral, the closed-form propagation equations of partially coherent nonparaxial HG beams in free space are derived. The on-axis intensity, far-field and paraxial expressions, and specifically, the free-space propagation equations of partially coherent nonparaxial Gaussian Schell-model beams are given, and treated as special cases of our results. It is found that the f and f_σ parameters play a crucial role in determining the nonparaxiality of partially coherent TEM_mn-mode HG beams. Only if the f and f_σ parameters are small enough, the paraxial approximation is applicable.     

厄米-高斯光束在热非局域介质中传输的数值模拟研究

基于非线性薛定谔方程和热扩散的泊松方程,采用分步傅里叶算法以及多重网格法对厄米-高斯光束在不同形状的热非局域介质铅玻璃中的传输进行了数值模拟研究. 结果表明,低阶厄米-高斯光束可以较为稳定地在铅玻璃中传输. 高阶厄米-高斯光束在铅玻璃中传输变得不稳定,并且阶数越高,稳定性越差. 样品的形状对于厄米-高斯光束的影响很大. 在正方形样品中,厄米-高斯光束的传输与Snyder-Mitchell模型符合得相对较好. 在矩形样品中厄米-高斯光束在传输过程中的强度分布将发生较大的变化. 关键词： 非局域非线性介质 厄米-高斯光束 光束传输     

非傍轴部分相干厄米-高斯光束的相干和非相干合成

推导出二维非傍轴部分相干厄米-高斯（H-G）光束相干合成和非相干合成的交叉谱密度和光强的解析公式,并分析了一些特例. 合成光束的光强不仅决定于f参数,f_σ参数,离轴参数,合成光束的束数和阶数以及传输距离z,而且还决定于合成方式. 对部分相干光的相干合成和非相干合成概念做了物理诠释,其正确性为数值计算例证实. 关键词： 部分相干光的相干和非相干合成 非傍轴部分相干厄米-高斯（H-G）光束 自由空间中的传输方程     

Intensity-based modal analysis of partially coherent beams with Hermite-Gaussian modes

Many partially coherent beams are made up of a superposition of mutually uncorrelated Hermite-Gaussian modes. We prove that knowledge of the transverse intensity profile of such a beam is sufficient for evaluating the weights of the modes in an exact way. Simulations indicate that the proposed method resists noise well.     

Harmonic generation with non collinear laser beams. Application to pulse stacking

Harmonic generation in KDP crystals is of great interest in application to high power Nd laser chains. A non collinear beams technique has been investigated numerically and experimentally. It has been pointed out that an optimum separation angle can be found where tolerance on divergence of one beam is increased. The process provides angular separation of the fundamental and harmonic beams and allows a pulse stacking compression technique, which is described, and which could improve the performances of a laser chain.     

部分相干厄米-高斯光束杨氏实验中的光强分布

将杨氏干涉实验作为双缝衍射现象处理,以部分相干厄米-高斯(H-G)光束为例,研究分析了多模部分相干光的杨氏双缝干涉光强和干涉条纹可见度的空间分布。数值计算说明,多模部分相干光束的空间相干参数、模阶数和缝遮拦比对衍射场中光强的空间分布(干涉花样)都有影响。当多模部分相干光的阶数为奇数时,轴上光强与光束的相干性会出现相消干涉;当多模部分相干光的阶数为偶数时,轴上光强与光束的相干性会出现相长干涉等。     

Spatiotemporal behaviors and singularity of ultrashort pulsed Elegant Hermite-Gaussian beams

Analytical propagation expressions of ultrashort pulsed Elegant Hermite-Gaussian beams are derived and spatiotemporal properties of the pulses with different transverse modes are studied. Singularity of the complex amplitude envelope solution of the pulses obtained under slowly varying envelope approximation is analyzed in detail. The rigorous analytical solution of the pulse is deduced and no singularity emerges in the solution. The obtained results indicate that the transverse mode affects not only the spatiotemporal properties but also the singularity of the pulses. Time delay of the off-axis maximum intensity is more obvious and the singularity is located nearer to the z-axis for the pulse with higher transverse modes.     

部分相干厄米高斯光束在斜程大气湍流中的扩展

基于广义惠更斯-菲涅耳原理,推导出部分相干厄米高斯（H-G）光束通过斜程大气湍流传输的均方根束宽和角扩展的解析表达式,并用以研究了传输路径和光束阶数对部分相干H-G光束传输的影响。引入相对束宽和相对角扩展来定量描述光束抗拒大气湍流的能力。结果表明：在相同条件下,部分相干H-G光束斜程传输受大气湍流的影响要小于水平传输,与水平传输相比斜程传输更有利于部分相干光束在大气湍流中的传输,光束阶数越大部分相干H-G光束受大气湍流的影响越小。     

Phase-flipped Hermite-Gaussian beams and their propagation beyond the paraxial approximation

An extension of phase-flipped Gaussian (PFG) beams to the multi-mode nonparaxial case is made. The recurrence propagation expressions for phase-flipped Hermite-Gaussian (PFHG) beams beyond the paraxial approximation are derived and used to study nonparaxial propagation properties of PFHG beams in free space and through a knife edge and an aperture, and to compare nonparaxial results with paraxial ones. The propagation of paraxial PFHG beams and PFG beams and nonparaxial PFG beams is treated as special cases of nonparaxial PFHG beams. Numerical examples are given to illustrate the theoretical results.     

湍流大气中厄米-高斯光束M2因子的变化

基于广义惠更斯-菲涅耳原理和Wigner分布函数二阶矩的定义,推导出直角坐标系下大气湍流中部分相干光的M2因子传输公式。以厄米-高斯（H-G）光束为例,给出了H-G光束通过大气湍流传输后M2因子的解析表达式,并采用Tatarskii谱,详细讨论了M2因子的主要影响因素。结果表明,M2因子主要由光束的束腰宽度、波长、光束阶数、大气湍流的折射率起伏结构常数和在湍流中传输距离决定。随着光束阶数、折射率起伏结构常数及传输距离的增大,M2因子明显增大,光束阶数越高,湍流对M2因子变化的影响越小。对于给定的传输距离,存在最佳初始束宽,使M2因子最小。     

Partially coherent non-paraxial vectorial Hermite-Gaussian beams and their far-field properities

The far-field theory of partially coherent vectorial non-paraxial beams is expanded and their analytical propagation expressions of the Wigner distribution function matrices and the cross-spectral-density matrices in free space are derived using the far-field approximation. Some interesting cases, in particular the vectorial non-paraxial partially coherent Hermite-Gaussian (HG) beams, are discussed and treated as special cases of our general expressions. It is shown that the f_σ and f parameters play an important role in determining vector and non-paraxiality of partially coherent HG beams. When two parameters are small enough, scalar and paraxial vectorial approximation is allowed; otherwise, non-paraxial vectorial approximation is applied. But the decided parameters additionally affect their far-field divergence angles.