双偏心椭圆高斯光束在一阶ABCD光学系统中的传输特性

通过求解时谐条件下的亥姆霍兹方程,得到一个特解双偏心椭圆高斯光束,该光束由两个偏心椭圆高斯光束叠加而形成的,可用于描述大功率激光二极管远场分布双峰特性.分析了该光束的光场模型,运用惠更斯-菲涅尔广义积分公式,得到了该光束在一阶ABCD光学系统中的传输场分布和解析表达式,在此理论基础上,数值计算得到光场分布和远场发散角,并运用该光束模型模拟了新型激光二极管光场分布,理论结果与实际结果吻合.     

Propagation properties of apertured laser beams with amplitude modulations and phase fluctuations through atmospheric turbulence

The propagation properties of apertured laser beams with amplitude modulations (AMs) and phase fluctuations (PFs) through atmospheric turbulence are studied in detail both analytically and numerically. The analytical expressions for the average intensity, power in the bucket (PIB) and Strehl ratio (S _R ) of apertured laser beams with AMs and PFs propagating through atmospheric turbulence are derived. It is found that the worse the phase fluctuation and the higher the amplitude modulation are, the less laser beams are affected by turbulence. Furthermore, apertured Gaussian beams are more sensitive to turbulence than apertured laser beams with AMs and PFs. The average intensity of apertured laser beams with AMs and PFs may be even larger than that of apertured Gaussian beams due to turbulence. In particular, the influence of turbulence on the average maximum intensity of apertured laser beams with PFs and AMs may become serious if an unsuitable truncated parameter is chosen, which should be avoided in practice.     

Beam quality of truncated laser beams with amplitude modulations and phase fluctuations in turbulence

The closed-form expressions for the Rayleigh range z_R and the M²-factor of truncated laser beams with amplitude modulations (AMs) and phase fluctuations (PFs) in turbulence are derived, and the beam quality is studied by taking the z_R and the M²-factor as the characteristic parameters of beam quality. The M²-factor of truncated laser beams with AMs and PFs is always larger than that of truncated Gaussian beams both in free space and in turbulence. However, in turbulence the beam quality of truncated laser beams with AMs and PFs may be better than that of truncated Gaussian beams if the z_R is taken as the characteristic parameter of beam quality. For laser beams with AMs and PFs in turbulence, the beam quality expressed in terms of z_R is consistent with that in terms of the M²-factor versus the phase fluctuation parameter α, but not versus the intensity modulation parameter σ_A. The beam quality of truncated laser beams with AMs and PFs is less sensitive to turbulence than that of truncated Gaussian beams. The beam quality of laser beams with smaller α and larger σ_A is less affected by turbulence than those with larger α and smaller σ_A.     

截断的有振幅调制和位相畸变光束的等效曲率半径

高功率激光通常具有振幅调制和相位畸变. 采用统计光学方法推导了截断的有振幅调制和位相畸变光束在大气湍流中传输 的等效曲率半径R的解析公式.研究表明:随着位相畸变参量、振幅调制参量和光 束截断参量的增大,光束在自由空间中的 R增大,但R受湍流的影响也会增大; 并且高斯光束在自由空间中的R最大, 但其受湍流影响也最大. 因此,在大气湍流中传输到足够远时, 截断的有振幅调制和位相畸变光束的R就要比高斯光束的大.特别地, 相对等效曲率半径R_r随传输距离为非单调变化, 存在一个最小值, 即在该位置处R受湍流的影响最大. 此外, 达到 R_r最小值所需传输距离随光束位相畸变和振幅调制的加剧而增大.     

高功率激光多程放大系统光束传输的计算分析

 报道了高功率激光多程放大系统光束传输的模拟程序, 该程序考虑了放大介质的增益分布、增益饱和、增益恢复系数、介质吸收损耗、B积分以及光阑和空间滤波器等光学元件对激光传输和放大的影响, 并给出了典型的计算实例。     

高功率激光在非均匀大气中传输的自聚焦效应研究进展

地基激光空间碎片清除和利用激光辐射把转换的太阳能从空间轨道输运到地面等应用中,不可避免地遇到高功率激光在非均匀大气中的传输问题。由于激光功率已远远超过大气非线性自聚焦临界功率,大气自聚焦效应是影响光束质量的一个重要物理因素。概述了近年来国内外高功率激光在非均匀大气中上行或下行传输的自聚焦效应研究进展,主要介绍了高功率激光在非均匀大气中的传输模型、理论基础、数值和解析研究方法,着重介绍了自聚焦效应对激光传输特性和光束质量的影响,并总结了优化靶面光束质量的方案。此外,还介绍了大气群速度色散效应和大气湍流效应等物理因素对激光光束质量的影响。最后,还提出了该领域值得进一步深入研究的一些问题。     

Propagation of a flattened Gaussian beam through multi-apertured optical ABCD systems

By expanding the hard-aperture function into a finite sum of complex Gaussian functions, the recurrence propagation formula of a flattened Gaussian beam through multi-apertured optical ABCD systems is derived, and the propagation of a Gaussian beam is regarded as a special case in our theoretical model. The extension to the three-dimensional case is described. Numerical examples of the beam propagation through a multiple aperture-lens system and an aperture-spatial filter are given and compared with those by the straightforward numerical integration of the Collins formula. It is shown that our analytical results give a good trade-off between the computational time and accuracy, and provide a useful tool for simulating the beam propagation through complicated optical systems including multiple apertures and spatial filters. Finally, a comparison with the previous work is made and the main results obtained in this paper are summarized.     

Propagation of a Laguerre–Gaussian beam through a slightly misaligned paraxial optical system

Based on the generalized diffraction integral formula for treating the propagation of a laser beam through a slightly misaligned optical system in a cylindrical coordinate system, an analytical formula for a Laguerre–Gaussian beam passing through such an optical system is derived. Furthermore, an approximate analytical formula is derived for a Laguerre–Gaussian beam passing through an apertured slightly misaligned optical system by expanding the hard aperture function as a finite sum of complex Gaussian functions. Some analytical formulas are also given for a flattened Gaussian beam by expanding its field as a superposition of a finite series of Laguerre–Gaussian beams. PACS 42.25.Bs; 41.85.Ew; 41.85.Ct     

Propagation of flat-topped beams

The propagation of flat-topped beams passing through paraxial ABCD optical system is investigated based on the propagation formulas of Gaussian beam. The focal shift of focused coherent flat-topped beam is also studied in detail. Analytical expressions of the M² factor and the far-field intensity distribution for flat-topped beams are derived on the basis of second-order moments.     

无衍射光束的产生及其应用

近年来,随着激光技术的快速发展,相继产生了多种在远距离传输后中心光斑保持不变的无衍射光束,包括贝塞尔光束、高阶贝塞尔光束、马丢光束、高阶马丢光束、余弦光束、抛物线光束以及艾里光束.无衍射光束在激光打孔、激光精密准直、光学精密控制、光学微操控、光通信、等离子体导向、光子弹产生、光通信、自聚焦光束的合成以及非线性光学等领域中有着广泛的应用.本文介绍了各类无衍射光束的数学表达式、产生方法及对应的实验结果;就无衍射光束的特性和应用进行了归纳和讨论;并对其在未来的研究与应用前景中发挥的重要作用进行了简要总结与展望.     

高能固态激光阵列光束合成技术浅析

建立了高能固态激光阵列合成的模型,对相干合成型和非相干合成型的高能固态激光系统进行了分析和比较.引入光束传输因子(BPF)作为评价合成光束的光束质量,对湍流大气对板条激光器和光纤激光器相干合成与非相干合成远场光束质量的影响进行了定量分析.计算模型和结果为工程实际中合成方案的选择和评估提供了参考.     

大功率激光二极管双峰结构远场分布模型

为了合理地设计光学系统以整形激光二极管出射光束,必须准确了解激光二极管的远场分布,然而对于大功率激光二极管仍没有形式简单并且较好反映实际器件特性的光束模型。基于亥姆霍兹方程的严格远场解,提出使用两个离心高斯光束描述场源处平行结平面方向的模式场分布,将其代入严格远场解中得到一种描述大功率激光二极管远场光分布模型．用于描述其双峰远场结构。理论模型与三种实际器件的测量数据进行了比较,曲线主要部分都能很好吻合,并且偏差部分的能量仅占总能量的1％～2％。该模型数学表达形式简单,可以方便地用于研究光束经光学系统后的变换,以及计算光学系统的耦合效率,而且对于定量设计光学整形系统十分有用。     

高斯涡旋光束的光束传输因子和峭度参数

基于强度二阶矩定义, 导出了高斯涡旋光束光束传输因子即M² 因子的解析表达式, 高斯涡旋光束的M² 因子唯一取决于拓扑电荷数n. 数值计算表明, 高斯涡旋光束的M² 因子随着拓扑电荷数n的增大而增大. 基于强度高阶矩, 还导出了高斯涡旋光束经傍轴ABCD光学系统传输时峭度参数的解析表达式, 高斯涡旋光束的峭度参数取决于拓扑电荷数n、参数δ、矩阵元A和矩阵元D. 在自由空间传输时, 高斯涡旋光束的峭度参数仅取决于拓扑电荷数n和参数δ. 自由空间传输时, 高斯涡旋光束峭度参数的变化规律为: 峭度参数随参数δ的增大先减小而后趋向于一最小值, 随拓扑电荷数n的增大而减小. 这一研究有助于高斯涡旋光束的实际应用.     

复宗量双曲余弦高斯光束的束腰及其位置

 由复宗量双曲余弦高斯光束通过近轴-ABCD-光学系统传输公式，推导出了基于二阶矩定义的光斑尺寸的解析表达式，给出了复宗量双曲余弦高斯光束在自由空间传输和通过薄透镜时的光斑尺寸、束腰宽度及其位置的解析表达式，并进行了数值计算，对计算结果进行了分析和讨论，该方法可用于其它光束通过近轴ABCD光学系统的类似计算。     

Incoherent combination of fiber lasers using a collimating and focusing optical system in fiber-based laser fusion

The incoherent combination of fiber laser beams using a collimating and focusing optical system in fiber-based laser fusion is theoretically and numerically studied. The propagation of the fiber lasers passing through the optical system is analyzed by the ABCD law. The super-Gaussian fitting is performed to study the synthetic intensity profile near the focal spot quantitatively. The intensity profile of the combination beam is dependant on the defocusing distance, the number of the fibers, the separation of the fibers, and the beam expansion ratio of the collimating system.     

Definition and measurement of the beam propagation factor M2 for chromatic laser beams

The concept of the beam propagation factor M2 is extended for chromatic laser beams. The definition of the beam propagation factor can be generalized with the weighted effective wavelength. Using the new definition of factor M2, the propagation of chromatic beams can be analyzed by the beam propagation factor M2 as same as that of monochromatic beams. A simple method to measure the chromatic beam factor M2 is demonstrated. The chromatic factor M2 is found invariable while the laser beam propagates through the dispersion-free ABCD system.     

Propagation properties of partially polarized Gaussian Schell-model beams through an axis-unsymmetric paraxial ABCD system

By using the beam coherence-polarization (BCP) matrix approach, analytical propagation equations of partially polarized Gaussian Schell-model (PGSM) beams through an axis-unsymmetric paraxial optical ABCD system are derived, which enable us to study the propagation-induced polarization changes and irradiance distributions at any propagation distance of PGSM beams through axis-unsymmetric systems within the framework of the paraxial approximation. Detailed numerical results for a PGSM beam passing through a bifocal lens are presented to illustrate the propagation properties of PGSM beams. A comparison with the previous work is also made.     

Propagation of elegant Hermite cosine Gaussian laser beams

In this paper, a more generalized beam containing an elegant Hermite Gaussian beam and a cosine Gaussian beam, which is called elegant Hermite cosine Gaussian (EHcoG) beam, is introduced and studied. The propagation properties of the EHcoG laser beams through a first-order paraxial optical system are demonstrated analytically and numerically. The recurrence propagation equations of the EHcoG beams through a first-order paraxial optical system with and without aperture are derived, from which the analytical propagation expression for EHcoG beams of any order can be obtained by means of the recursive procedures. The validity of the analytical results is confirmed by the numerical results.     

非高斯光束的传输

提出一种能处理非高斯非轴对称光束传输的张量方法,引入三个表征任意分布光束的特征张量,运用非对称光学系统的惠更斯衍射积分公式导出了它们的变换规律.讨论了任意光束的质量因子.作为一个实例,分析了高阶厄米-高斯光束通过柱面透镜的变换.     

Propagation of a hollow Gaussian beam through a paraxial misaligned optical system

Based on the generalized diffraction integral formula for treating the propagation of a laser beam through a paraxial misaligned optical system in the cylindrical coordinate system, we obtain an analytical formula for a hollow Gaussian beam passing through a paraxial misaligned optical system. Furthermore, we also obtain the approximate analytical formula for a hollow Gaussian beam passing through a paraxial circularly apertured misaligned optical system by expanding the hard aperture function into a finite sum of complex Gaussian functions. As a numerical example, the propagation properties a hollow Gaussian beam through a misaligned thin lens are studied numerically.