Propagation properties of hollow conical double half-Gaussian beams

In this paper, we present a new hollow beams - hollow conical double half-Gaussian beams - and deduce the analytical equation of propagation and transformation of these through the paraxial optical system by using the Collins formula. By using the formula deduced, we calculate and analyze the propagation properties of these in free space. In an experiment, we have obtained hollow conical double half-Gaussian beams, which are cone-angle controllable by using the combinational optical system of the spherical reflector, reflecting positive-axis cone and zoom lens, and we obtain the beam loop of far field in different distances. The results show good coherence between theory and experiment. This paper will play a guiding role in the practical application of hollow conical double half-Gaussian beams.     

The research of propagation characteristic and formation of double half-Gaussian hollow beams

A new kind of hollow beams, double half-Gaussian hollow beams, was put forward. With the help of the Collins formula, the analytical equation of propagation and transformation of the hollow laser beams in free space was deduced. The simulation shows that the intensity exhibits the three-dimensional trap distribution in the near-field, while the double half-Gaussian hollow beams turn into solid laser beams when propagating a certain distance, which shows the characteristics of self-focus. The double half-Gaussian hollow beams were obtained by means of the dual-reflecting splitting optical system. The intensity of the vertical loop in different distances was tested, which shows that the analytical equation of propagation and transformation is in agreement with the result. Supported by the National Natural Science Foundation of China (Grant No. KB92009)     

Theory of third-harmonic generation using double half-Gaussian hollow beams and self-phase-matching

We first (to best of out knowledge) use the slowly varying envelope approximation (SVEA) to obtain the equation of third harmonic (TH) generated by focusing the double half-Gaussian hollow beams into an atomic medium. The two-dimension intensity distribution is achieved by simulating, and it is similar to that generated by the 0th order Bessel beams. In addition to the similarities between the experimental setups, we demonstrate the accuracy of the equation. Compared with that generated by the Bessel beams, the pattern of the TH intensity generated by the double half-Gaussian hollow beams has salient features.     

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。     

湍流介质折射率结构常数C_n~2对双半高斯空心光束传输特性影响的研究

基于瑞利-索末菲衍射积分理论,利用交叉谱密度函数推导出双半高斯空心光束在湍流大气中传输时的解析表达式,并主要研究了湍流介质折射率结构常数C2n对空心光束传输特性的影响,得到了双半高斯空心光束在不同条件下传输时的光强分布.研究表明,C2n的增大加剧了近场中传输的空心光束的衍射效应,这不仅缩短了空心光束完全演变成为高斯光束时所需的传输距离,而且还增加了此后高斯光束向外扩展的程度.     

空心锥状双高斯光束传输特性研究

建立了空心锥状双高斯光束的模型.在空心高斯光束模型的基础上,由初始光场的光强分布,利用柱坐标下的柯林斯公式,导出了空心锥状双高斯光束经过傍轴光学系统的解析传输变换式由传输变换式计算分析了空心锥状双高斯光束在自由空问的可控传输特性,及在1,10和60 m的截面光环的光强分布.用KNbO3双轴晶体进行实验,获得了空心锥状双高斯光束,外锥折射的锥角等于入射光会聚角.实验表明,当空心光束处于锥状发射状态时,空心光束的光环内黑斑面积随传输距离的增加而增加,实验结果与模型吻合较好.该研究为进一步设计制备基于空心锥状舣高斯光束的新型激光元件提供了理论依据和设计参量.     

非傍轴矢量高斯光束的圆屏衍射

利用矢量瑞利衍射积分公式，推导出非傍轴矢量高斯光束圆屏衍射的解析表示式.非傍轴矢量高斯光束圆屏衍射的轴上场分布、远场表示式、自由空间中的传输公式，以及傍轴近似下高斯光束圆屏衍射的菲涅耳和夫琅禾费衍射公式可以作为一般公式的特例统一处理.数 值计算和比较实例说明了非傍轴矢量高斯光束的光强分布和远场特性.分析表明，在圆屏衍 射中，f参数和截断参数决定光束的非傍轴行为. 关键词： 传输光学 非傍轴矢量高斯光束 圆屏衍射 矢量瑞利衍射积分公式     

被光阑衍射部分偏振高斯-谢尔模型光束的远场特性

从部分相干光的传输理论出发,采用光束相干-偏振矩阵方法研究了被光阑衍射部分偏振高斯-谢尔模型光束的远场特性,对远场偏振和光强特性作了详细的数值计算和物理分析。研究结果表明,光阑衍射部分偏振高斯-谢尔模型光束的远场特性与光阑截断参量、光的空间相干性和衍射角有关。并与自由空间的传输特性和以前的工作作了比较分析。     

Propagation properties of vectorial elliptical Gaussian beams beyond the paraxial approximation

Starting from the vectorial Rayleigh diffraction integral formula and without using the far-field approximation, a solution of the wave equation beyond the paraxial approximation is found, which represents vectorial non-paraxial elliptical Gaussian beams in free space. The far-field expressions for non-paraxial Gaussian beams and elliptical Gaussian beams can be regarded as special cases treated in this paper. Some basic propagation properties of vectorial non-paraxial elliptical Gaussian beams, including the irradiance distribution, phase term, beam widths and divergence angles are studied. Numerical results are given and illustrated.     

一种新空心光束的理论及实验研究

提出了一种用来描述空心光束的新理论模型——空心高斯光束模型，通过控制光束参数可以方便地调制空心光束黑斑的大小.导出了空心高斯光束经傍轴光学系统的解析传输变换公式.利用导出的公式计算分析了空心高斯光束在自由空间的传输特性.在实验上利用矩阵本征值方法设计了能输出空心高斯光束的光学谐振腔，对实验上得到的空心高斯光束进行了传输特性的研究.结果表明，理论和实验相吻合.该空心高斯光束产生的光势阱为控制冷原子提供了一条新途径. 关键词： 空心高斯光束 光学谐振腔 传输特性     

Propagation properties of ultrashort pulsed beams with constant waist width in free space

Based on the Rayleigh diffraction integral and complex analytical signal representation, the strict propagation expression and its Fourier spectrum for ultrashort pulsed Gaussian beams with constant waist width are derived, which have the general applicable advantage, because the paraxial approximation, pulsed envelope representation and far-field approximation are not invoked. The far-field and paraxial expressions are obtained as the special cases of our general results. Numerical calculation results are given to illustrate the spatiotemporal propagation properties of few- and single-cycle pulsed Gaussian beams with constant waist width. A comparison with the paraxial results and previous work is also made.     

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。     

基于零级贝塞尔光束干涉产生的局域空心光束

通过对由两个零级贝塞尔光束相干叠加形成的三维衍射光场的理论分析和计算机模拟,发现当双零级贝塞尔光束的有关参量满足一定条件时,会在光轴上形成一系列高质量的局域空心光束。在此基础上,进一步分析了这种阵列局域空心光束的大小、阵列周期及局域空心光束的质量与双零级贝塞尔光束和光路参量的定量关系。推导出双零级贝塞尔光束叠加时在中心暗斑位置达到完全干涉相消的条件是通过两个环缝的能量要相同,以及产生最佳局域空心光束的内外环缝光源半径的比值为0.465。该研究为进一步设计制备基于双零级贝塞尔光束干涉实现阵列局域空心光束的新型衍射光学元件提供了理论依据和设计参量。     

径向阵列非傍轴椭圆高斯光束的相干和非相干合成

 从瑞利-索末菲衍射积分公式出发,推导出径向阵列非傍轴离轴椭圆高斯光束相干合成和非相干合成在自由空间中的解析传输公式,给出其远场分布和傍轴表示式。研究表明:合成光束的光强分布与f参数、径向阵列半径、光束数、传输距离和合成方式有关;N束光相干合成和非相干合成在远场的光强最大值分别为单光束在远场最大值的N₂和N倍。     

Evolution of Anomalous Hollow Gaussian Beams in Strongly Nonlocal Nonlinear Media Under the Off-Waist Incident Conditions

We investigate the evolution of anomalous hollow Gaussian beams in strongly nonlocal nonlinear media under the off-waist incident condition. We obtain analytic expressions of the beam propagation, the on-axis intensity, and the beam width and curvature. We perform some numerical simulations to illustrate the propagation properties of anomalous hollow Gaussian beams. The results show that, under the off-waist incident condition, the beam evolution is always periodic, whatever the input power is, being different from that under the on-waist incident condition. We discuss the influences of the input power and the departure distance on the propagation properties and present the physical reasons.     

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.     

Nonparaxial propagation of vectorial Gaussian beams diffracted at a circular aperture

Based on the vectorial Rayleigh diffraction integral, the nonparaxial propagation of vectorial Gaussian beams diffracted at a circular aperture is studied. The far-field and paraxial cases are treated as special cases of our general result. It is shown that for the apertured case the f parameter still plays an important role in determining the nonparaxiality of vectorial diffracted Gaussian beams, but both the f parameter and truncation affect the beam evolution behavior.     

双光束入射下掺杂KNSBN晶体的各向异性锥形衍射

利用掺杂ＫＮＳＢＮ晶体，报道了两束异常偏振光所引起的各向异性锥形衍射现象。首次观察到一种由三个衍射光锥所组成的各向异性衍射图样，并且提出了由入射光和满足相位匹配条件的前向散射光所参与的光折变四波混频机制。对双光束对称入射这种特殊实验配置情形，给出了衍射光锥的锥角随入射角的变化关系式，理论分析和实验结果符合得很好。     

Hollow Gaussian beams in strongly nonlocal nonlinear media

The propagation of hollow Gaussian beams in strongly nonlocal nonlinear media is studied in detail.Two analytical expressions are derived.For hollow Gaussian beams,the intensity distribution always evolves periodically.However the second-order moment beam width can keep invariant during propagation if the input power is equal to the critical power.The interaction of two hollow Gaussian beams and the vortical hollow Gaussian beams are also discussed.The vortical hollow Gaussian beams with an appropriate topological charge can keep their shapes invariant during propagation.     

等束宽超短脉冲光束的远场特性

利用角谱法和复解析信号法推导出了等束宽超短高斯脉冲光束在远场的解析传输公式及其傅里叶谱.研究了若干个甚至一个光周期数的等束宽超短高斯脉冲光束的远场特性，并与等衍射长度超短高斯脉冲光束作了比较.研究表明，等束宽超短高斯脉冲光束在远场存在脉冲展宽、光谱变窄、离轴光谱红移、轴上光谱蓝移等特性. 关键词： 角谱法 复解析信号法 等束宽超短高斯脉冲光束