Kurtosis parameters of super Lorentz-Gauss beams through a paraxial and real ABCD optical system

Based on the propagation equation of higher-order intensity moments, analytical propagation expressions for the kurtosis parameters of a super Lorentz-Gauss （SLG） SLG01 beam through a paraxial and real ABCD optical system are derived. By replacing the parameters in the expressions of the kurtosis parameters of the SLC01 beam, the kurtosis parameters of the SLG10 and SLGll beams through a paraxial and real ABCD optical system can be easily obtained. The kurtosis parameters of an SLG01 beam through a paraxial and real ABCD optical system depend on two ratios. One is the ratio of the transfer matrix element B to the product of the transfer matrix element A and the diffraction-free range of the super-Lorentzian part. The other is the ratio of the width parameter of the super-Lorentzian part to the waist of the Gaussian part. As a numerical example, the properties of the kurtosis parameters of an SLG01 beam propagating in free space are illustrated. The influences of different parameters on the kurtosis parameters of an SLG01 beam are analysed in detail.

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, ζ and f parameters, and to compare the difference between the paraxial and nonparaxial results.

Tunable optical gradient trap by radial varying polarization Bessel-Gauss beam

Optical tweezers play an important role in many domains, especially in life science. And optical gradient force is necessary for constructing optical tweezers. In this paper, the optical gradient force in the focal region of radial varying polarization Bessel- Gauss beam is investigated numerically by means of vector diffraction theory. Results show that the beam parameter and vary rate parameter that indicates the change speed of polarization rotation angle affect the optical gradient force pattern very considerably, and some novel force distributions may come into being, such as multiple force minimums, force ring, and force crust. Therefore, the focusing of radial varying polarization Bessel-Gauss beam can be used to construct optical traps.

A Note on Self-Accelerating Olver and Olver-Gauss Beams

The recent introduction by Belafhal et al. [Opt. and Photon. J. 5, 234-246 (2015)] of mth-order Olver beams as a novel class of self-accelerating nondiffracting solutions to the paraxial equation is a direct contradiction to the seminal work of Berry and Balazs who determined that the infinite-energy Airy wave packet is the only accelerating nondiffracting solution to the (1 + 1)D Schrödinger equation. It is shown in this note that the work of Belafhal et al. is valid only for m=0, which coincides with the Airy solution.

Ultracompact phase plate fabricated by femtosecond laser two-photon polymerization for generation of Mathieu–Gauss beams

The Mathieu beam is a typical nondiffracting beam characterized by its propagation invariance and self-reconstruction.These extraordinary properties have given rise to potentialities for applications such as optical communications,optical trapping,and material processing.However,the experimental generation of Mathieu–Gauss beams possessing high quality and compactness is still challenging.In this work,even and helical Mathieu phase plates with different orders m and ellipticity parameters q are fabricated by femtosecond laser two-photon polymerization.The experimentally generated nondiffracting beams are propagationinvariant in several hundred millimeters,which agree with numerical simulations.This work may promote the miniaturization of the application of nondiffracting beams in micronanooptics.

Nonparaxial propagation of a super-Lorentz-Gauss SLGmode beam

Based on the vectorial Rayleigh-Sommerfeld integral formulae, this paper derives the analytical nonparaxial propagation equation of a super-Lorentz-Gauss （SLG） SLGo1 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.

The Wigner distribution function of a super Lorentz–Gauss SLG_(11) beam through a paraxial ABCD optical system

An orthonormal beam family of super Lorentz-Gauss （SLG） beam model is proposed to describe the higher-order mode beams with high divergence, which are generated by a high power diode laser. Here we consider the simplest case of the SLG beams, where there are four mutually orthogonal SLG beams, namely SLG00, SLG01, SLG10, and SLGll beams. The SLG00 beam is just the Lorentz-Gauss beam. Based on the Collins integral formula and the Hermite-Gaussian expansion of a Lorentz function, an analytical expression for the Wigner distribution function （WDF） of an SLG11 beam through a paraxial ABCD optical system is derived. The properties of the WDF of an SLG11 beam propagating in free space are demonstrated. The normalized WDFs of an SLG11 beam at the different spatial points are depicted in several observation planes. The influence of the beam parameter on the WDF of an SLGI 1 beam in free space is analyzed at different propagation distances. The second-order moments of the WDF of an SLG11 beam in free space are also examined. This research reveals the propagation properties of an SLGll beam from another perspective. The WDFs of SLG01 and SLG10 beams can be easily obtained by using the WDFs of Lorentz-Gauss beam and the SLG11 beam.

Propagation of Gauss-Bessel beams in turbulent atmosphere

This paper studies the propagation properties of Gauss-Bessel beams in a turbulent atmosphere. Based on the extended Huygens-Fresnel principle, it derives the intensity distribution expression for such beams propagating in a turbulent atmosphere. Then the influence of turbulence and source beam parameters on the beam propagation is studied in great detail. It finds that the intensity distribution of Gauss-Bessel beams will change into Gaussian profile in a turbulent atmosphere, and that stronger turbulence and smaller topological charges will lead to a faster changing.

Orbital angular momentum density and spiral spectra of Lorentz–Gauss vortex beams passing through a single slit

Based on the Hermite–Gaussian expansion of the Lorentz distribution and the complex Gaussian expansion of the aperture function, an analytical expression of the Lorentz–Gauss vortex beam with one topological charge passing through a single slit is derived. By using the obtained analytical expressions, the properties of the Lorentz–Gauss vortex beam passing through a single slit are numerically demonstrated. According to the intensity distribution or the phase distribution of the Lorentz–Gauss vortex beam, one can judge whether the topological charge is positive or negative. The effects of the topological charge and three beam parameters on the orbital angular momentum density as well as the spiral spectra are systematically investigated respectively. The optimal choice for measuring the topological charge of the diffracted Lorentz–Gauss vortex beam is to make the single slit width wider than the waist of the Gaussian part.

均匀偏振cosh-Pearcey-Gauss光束的远场坡印廷矢量,自旋与轨道角动量

本文提出了均匀偏振cosh-Pearcey-Gauss光束,其主要由双曲余弦函数(n,Ω)和偏振相关角度(α,δ)所调制。基于矢量角谱法和稳相法,研究了该光束的远场坡印廷矢量、自旋角动量和轨道角动量。研究结果表明:较大的双曲余弦函数值能将远场坡印廷矢量、自旋角动量和轨道角动量分割成多瓣抛物线结构。虽然左旋和右旋椭圆偏振不能影响整个光束结构,但却可通过调节TE和TM项的左半边和右半边的分布权重,进而分辨出光束的远场坡印廷矢量和角动量分布。本文结果对信息存储与偏振成像技术领域有着潜在的应用价值。

Control of beam halo-chaos by Gauss function in the triangle periodic-focusing channel

This paper studies the Kapchinsky-Vladimirsky （K-V） beam through a triangle periodic-focusing magnetic field by using the particle-core model. The beam halo-chaos is found, and an idea of Gauss function controller is proposed based on the strategy of controlling the halo-chaos. It performs multiparticle simulation to control the halo by using the Gauss function control method. The numerical results show that the halo-chaos and its regeneration can be eliminated effectively, and that the radial particle density is uniform at the centre of the beam as long as the control method and appropriate parameter are chosen.

A Modified Beam Propagation Method Based on the Galerkin Method with Hermite-Gauss Basis Functions

A beam propagation method based on the Galerkin method with Hermite-Gauss basis functions for studying optical field propagation in weakly guiding dielectric structures is described. The selected basis functions naturally satisfy the required boundary conditions at infinity so that the boundary truncation is avoided. The paraxial propagation equation is converted into a set of first-order ordinary differential equations, which are solved by means of standard numerical library routines. Besides, the calculation is efficient due to its small resulted matrix. The evolution of the injected field and its normalized power along the propagation distance in an asymmetric slab waveguide and directional coupler are presented, and the solutions are good agreement with those obtained by finite difference BPM, which tests the validity of the present approach.

高阶Bessel-Gauss光束的产生方法

高阶贝塞尔-高斯(Bessel-Gauss)光束在一定条件下呈现"无衍射"特性,是一种具有广阔应用前景的空心光束。本文首先对高阶Bessel-Gauss光束的产生方法进行了分析和归类,将其产生方式分为主动式和被动式两大类。其次对获得高阶Bessel-Gauss光束的谐振腔法、几何光学法、光学全息法、计算全息法、非线性光学法等实验方法进行了阐述。最后总结了各种方法产生高阶Bessel-Gauss光束的优缺点。

椭圆高斯光束产生近似无衍射Bessel-Gauss光

研究了轴棱锥聚焦像散椭圆高斯光束的光场分布特性,根据菲涅耳衍射积分理论导出了椭圆高斯光束经轴棱锥衍射后的光场分布,通过数值积分给出椭圆高斯光束经轴棱锥聚焦后的近轴光场强度分布情况,将其与圆高斯光束产生的近似Bessel-Gauss场进行比较,发现椭圆高斯光束经轴棱锥聚焦后的光束在一定的传播距离内也具有无衍射特性,且轴上光强分布与圆高斯光束产生的Bessel-Gauss光束的轴上光强分布具有相似的形式,而这种无衍射光场的强度在垂直于光轴的平面上不再是柱对称分布。根据近轴球面波产生近似Bessel光束的最大无衍射距离公式计算了椭圆Bessel-Gauss光束在子午面和弧矢面上的最大无衍射距离,整个光束的无衍射距离由入射到轴棱锥上的椭圆光斑短轴方向的尺寸决定。

弱湍流大气中Mathieu-Gauss束的传输

采用弱湍流大气光传输的Rytov近似和运用非衍射光束的平面波展开原理,研究并给出了弱湍流大气中Mathieu-Gauss束的场方程和平均光强解析表达式。研究表明:弱湍流大气中传输Mathieu-Gauss束由传输距离z函数的复振幅、高斯束包络、湍流引入的复相位和复标定横向非衍射束型四个因子构成,其归一化轴上平均光强随归一化距离z=z/zR和参量γ=12kρw0的变化与此类光束在自由空间传输的规律相同。

无衍射Bessel及Bessel-Gauss光的理论与实验

理论分析Bessel光束和Bessel-Gauss光束的相互联系及区别,数值模拟理想Bessel光束和Bessel-Gauss光束在任意平面的径向光强分布,以及光腰半径和谐振腔腔长对输出Bessel-Gauss光束的影响.模拟结果表明,相对于Bessel光,Bessel-Gauss光衰减较快,实验结果也验证了理论分析.同时,光腰半径越大,光强的径向分布衰减越慢;而腔长越大,其主模式的振幅分布衰减越慢.

方位偏振Bessel-Gauss光束的传输特性研究

利用Collins衍射积分公式,给出了方位偏振Bessel-Gauss光束通过ABCD轴对称光学系统的解析表达式.对其通过自由空间和付里叶变换系统特殊情况的传输作了分析和讨论.

吸收媒质中非线性Gauss聚焦超声场的仿真研究

通过频域有限差分法求解KZK方程,对吸收媒质中Gauss聚焦超声换能器的基波和高次谐波声场进行计算和仿真,研究了各次谐波沿传播方向的分布规律,发现高次谐波声场同样具有Gauss聚焦特性,并且谐波阶次越高,聚焦特性越好.此后讨论了不同的吸收系数对Gauss声场聚焦特性的影响,结果显示吸收系数的改变不会影响Gauss声场的径向分布形状,但吸收系数的增加导致聚焦区域声场强度的减弱,甚至聚焦无法实现.

准无衍射Lommel-Gauss光束非傍轴传输的解析

为研究准无衍射Lommel-Gauss光束的非傍轴传输,根据光束传播的独立性和叠加性原理,先将Lommel-Gauss光束展开为无穷项Bessel光束的叠加,然后利用虚源法和格林函数法引入一组能够产生Lommel-Gauss光束的虚光源点,利用Fourier-Bessel变换理论,通过建立对应的非齐次亥姆霍兹方程,计算得到Lommel-Gauss光束传输的非傍轴严格积分表达式.利用该积分表达式推导给出了Lommel-Gauss光束轴上光场分布的非傍轴修正解析表达式,这为定量计算Lommel-Gauss光束的传输特性提供了方便.

弱湍流大气传输广义Helmholtz-Gauss光束

在Rvtov近似和采用Tatarskii湍流大气折射率起伏谱条件下,运用实数和复数矩阵元的ABCD矩阵研究了湍流大气中广义Helmholtz-Gauss束的传输规律,研究表明广义Hellmholtz-Gauss束的横向波数与高斯束传输参量q的积在弱湍流大气传输过程中保持不变。导出了湍流大气中传输广义Helmholtz-Gauss束的平均光强。