双曲余弦高斯涡旋光束的远场特性研究

运用电磁光束的角谱法和稳相法, 推导出双曲余弦高斯(ChG) 涡旋光束的TE波和TM波在自由空间远场传输和能流密度的解析表达式, 用以研究了ChG涡旋光束在远场中的位相奇点和能流密度分布特性. 结果表明, 改变ChG 涡旋光束中的离心参数或束腰宽度, 位相奇点的密度、位置会发生变化. 涡旋离轴量的变化会导致能流密度分布的不对称性. 当离心参数增大时, 原点周围黑核会向原点中心移动. 关键词： 双曲余弦高斯涡旋光束 位相奇点 能流密度     

Rows of optical vortices from elliptically perturbing a high-order beam

An optical vortex (phase singularity) with a high topological strength resides on the axis of a high-order light beam. The breakup of this vortex under elliptic perturbation into a straight row of unit-strength vortices is described. This behavior is studied in helical Ince-Gauss beams and astigmatic, generalized Hermite-Laguerre-Gauss beams, which are perturbations of Laguerre-Gauss beams. Approximations of these beams are derived for small perturbations, in which a neighborhood of the axis can be approximated by a polynomial in the complex plane: a Chebyshev polynomial for Ince-Gauss beams, and a Hermite polynomial for astigmatic beams.     

Free-space propagation of autofocusing Airy vortex beams with controllable intensity gradients

Vortex splitting is one of the main causes of instability in orbital angular momentum(OAM) modes transmission. Recent advances in OAM modes free-space propagation have demonstrated that abruptly autofocusing Airy vortex beams(AAVBs) can potentially mitigate the vortex splitting effect. However, different modes of vortex embedding will affect the intensity gradients of the background beams, leading to changes in the propagation characteristics of vortex beams. This study presents the unification of two common methods of coupling autofocusing Airy beams with vortices by introducing a parameter(m), which also controls the intensity gradients and focusing properties of the AAVBs. We demonstrate that vortex splitting can be effectively reduced by selecting an appropriate value of the parameter(m) according to different turbulence conditions. In this manner,the performance of OAM-based free-space optical systems can be improved.     

Propagation dynamics of deformed 2D vortex Airy beams

We numerically and experimentally investigate the propagation of deformed 2D vortex Airy beams. Our results show that, for different topological charges, two parabolic trajectories that can be controlled by changing the initial wing angle always dominate the beam propagations. In this case, the main lobes take different propagation distances to restore to the peak intensity. The profiles tend to evolve into 1D or 2D Airy-like patterns to various degrees in the same propagation distance. Furthermore, the whole profiles yield a small change in their acceleration direction, depending on the topological charge and the initial wing angle.     

Three-Airy autofocusing beams

We numerically and experimentally demonstrate that a three-Airy autofocusing beam can be generated by superposing three deformed two-dimensional(2 D) Airy beams with a triangle symmetry. When the initial angle between two wings of the deformed 2 D Airy beams increases, such a three-Airy autofocusing beam exhibits that the focusing length decreases and the intensity contrast at the focal point changes. Moreover, after introducing an optical vortex phase, this three-Airy autofocusing beam displays a transverse rotation in propagation. The rotation angle is determined by the topological charge of the vortex and the initial wing angle. Our results may have some potential applications in optical manipulation.     

The optical Airy transform and its application in generating and controlling the Airy beam

We propose an optical Airy transform in this paper, and obtain the analytical expressions for the Airy transform of fundamental Gaussian beams and finite energy Airy beams. The setup for performing the optical Airy transform is presented. The Airy transform for Gaussian beams and finite energy Airy beams are theoretically calculated and analyzed. Our results show that the Airy beam can be conveniently generated and controlled through the optical Airy transform of the Gaussian beam. The optical Airy transform also can be used to directly modulate the beam parameters of the incident Airy beam, and it can transform the incident Airy beam into the Gaussian beam.     

数字全息术测定涡旋光束拓扑电荷数

提出了一种基于数字全息技术测定涡旋光束拓扑电荷数的方法.该方法通过数字全息技术获取涡旋光束和参考光的全息图并重构出涡旋光束的波前相位,判定相位围绕相位奇点的周期性分布来测定涡旋光束的拓扑电荷数.在拓扑电荷数取值分别为整数和分数的情况下,通过对数值模拟和实验结果的比较,表明该方法能够较准确地测定出拓扑电荷数.     

Nonparaxial propagation properties of the chirped Airy Gaussian vortex beams in uniaxial crystals orthogonal to the optical axis

In this article, we investigate the nonparaxial propagation properties of the chirped Airy Gaussian vortex(CAiGV)beams in uniaxial crystals orthogonal to the optical axis analytically and numerically. We discuss how the linear chirp parameters, the quadratic chirp parameters, and the Gaussian factors influence the nonparaxial propagation dynamics of the CAiGV beams. The intensity, the energy flow, the beam center, and the angular momentum of the CAiGV beams are deeply investigated. It is shown that the Gaussian factors have a great effect on the intensity and the centroid positions of the CAiGV beams. With the Gaussian factors increasing, the intensity of CAiGV beams decreases rapidly. The main lobes of the transverse intensity distribution of the CAiGV beams are similar to triangles.     

High-aperture binary axicons for the formation of the longitudinal electric field component on the optical axis for linear and circular polarizations of the illuminating beam

Diffraction of uniformly polarized laser beams with vortex phase singularity is theoretically analyzed using the plane wave expansion. It is shown that for a high numerical aperture, an intense longitudinal electric field component is formed on the optical axis in this case. It is numerically demonstrated that an analogous effect is ensured for diffraction of a conventional Gaussian beam from asymmetric binary axicons. The field intensity on the optical axis can be varied either by rotating the optical element or by changing the direction of polarization of radiation.     

Propagation dynamics of ring Airy Gaussian beams with cosine modulated optical vortices

We numerically investigate the propagation properties of ring Airy Gaussian beams(RAGBs) with cosine modulated optical vortices(CMOV). In comparison to the common RAGBs without any modulation, the dynamic propagation of RAGBs with CMOV exhibits a unique feature: the rings of RAGBs with CMOV will gradually shrink into several main lobes with the increase of the propagation distance. The number of lobes and the peak intensity of each lobe are determined by the factors of cosine modulated function. By designing the initial phase,we can easily change the transversal location of the peak intensity. Our results may find potential applications in optical manipulations.     

Propagation properties of chirped Airy vortex beams with x-polarization through uniaxial crystals

The propagation dynamics of a chirped Airy vortex(CAiV) beam with x-polarization in uniaxial crystals orthogonal to the optical axis is studied analytically and numerically. The effect of the ratio of extraordinary and ordinary refractive indices, the chirp parameter, as well as the propagation distance is analyzed, which shows that the focused position of the CAi V beams can be controlled through changing the ratio of the extraordinary and ordinary refractive indices. In addition,with the propagation distance increasing, the asymmetry of the intensity and the angular momentum of the CAi V beam during propagation becomes much more visible. The variation of the chirp parameters can change the attenuation velocity of the vortex as well.     

Composite coherence vortices and their propagation in free space

Taking Gaussian Schell-model (GSM) background vortex beams as an example of partially coherent vortex beams, the composite coherence vortices resulting from the superposition of the cross-spectral density function of two parallel, noncollinear partially coherent vortex beams and their propagation in free space are studied, and the main attention is paid to the effect of relative off-axis distance, coherence parameter and propagation distance on the composite coherence vortices. The number and location of composite coherence vortices vary by changing the relative off-axis distance, coherence parameter or propagation distance. In the coherent limit, the composite coherence vortex becomes the composite optical vortex.     

Propagation dynamics of an optical vortex imposed on an Airy beam

In this Letter, we demonstrate the general propagation dynamics of an Airy beam (AiB) carrying unit phase singularity, i.e., optical vortices (OVs). For the OV with a unit charge, theoretical analysis indicates that the OV carried by the AiB will propagate along the parabolic trajectory with an acceleration velocity twice as fast as conventional AiBs before a critical position. Thereafter, the AiB main lobe destroyed by OV will be reconstructed and the phase singularity will reappear in the middle of the AiB profile.     

Propagation properties and radiation force of circular Airy Gaussian vortex beams in strongly nonlocal nonlinear medium

We study the abruptly autofocusing and autodefocusing properties of the circular Airy Gaussian vortex(CAi GV)beams in strongly nonlocal nonlinear medium for the first time through numerical simulations.The magnitude of topological charges and the position of the vortex could change not only the light spot pattern but also the intensity contrast.Meanwhile,we can change the position of the autofocusing and autodefocusing planes by changing the parameter of the incident beam.Furthermore,we can control the peak intensity contrast through choosing properly the truncation factor.As for the radiation force,we study the gradient and the scattering forces of CAi GV beams on Rayleigh dielectric sphere.Our analyses demonstrate that the radiation force can be enhanced by choosing proper parameters of CAi GV beams.     

Enhancement of Autofocusing Performance for Circular Arrayed‐Airy Vortex Beams

Numerically and experimentally circular arrayed‐Airy vortex beams (CAAVBs) are demonstrated, of which propagation dynamics and autofocusing performance are investigated. In contrast to the classical circular Airy beams, the focal intensity of CAAVBs can be abruptly enhanced several orders of magnitude by introducing vortex arrays (VAs) and increasing Airy arrays number, and the autofocusing performance markedly increases in the focal plane due to introducing VAs. The position of the focal point can be readily controlled by varying the circular arrayed Airy radius is also demonstrated. Experimental results agree with the numerical calculations. These advantages could be beneficial for potential applications in optical trapping, the generation of high intensity laser, medical treatment, and nonlinear effect.     

Dynamic evolution of transverse energy flow in focused asymmetric optical vector-vortex beams

We present here controlled generation of asymmetric optical vector-vortex beams using a two-mode optical fiber and study the dynamic evolution of the transverse energy flow (TEF) when focused through a spherical lens. The dependence of the TEF on various factors such as the vortex charge, vortex anisotropy and polarization structure around the vortex core is explored. It is found that the TEF is directly proportional to the phase gradient and its direction is governed by the vortex charge. The presence of C-point polarization singularity in the beam and the polarization structure around it results in vibrational phase gradient which is the major factor deciding the TEF in vector-vortex beams.     

Partially coherent vortex beams propagating through slant atmospheric turbulence and coherence vortex evolution

Using the extended Huygens-Fresnel principle and the quadratic approximation of the phase structure function, and taking the Gaussian Schell-model (GSM) vortex beam as a typical example of partially coherent vortex beams, the explicit expressions for the cross-spectral density function and average intensity of GSM vortex beams with topological charge m=+1 propagating through slant atmospheric turbulence are derived, and used to study the propagation properties of GSM vortex beams in atmospheric turbulence along a slant path and evolution behavior of coherence vortices. It is shown that the spreading of GSM vortex beams along a horizontal path is larger than that along a slant path in the long atmospheric propagation. The propagation through horizontal atmospheric turbulence can be treated as a special case of the altitude-independent structure constant. The position of coherence vortices in slant atmospheric turbulence does not coincide with that in horizontal atmospheric turbulence, and the dependence of position of coherence vortices on the zenith angle, wavelength and reference point is illustrated by numerical examples. A comparison with the previous work is also made.     

Influence of retardation between orthogonal components of circularly polarized light in the vortex phase plate on the structure of diffracted beam

The influence of retardation between orthogonal components of circularly polarized light on diffraction pattern generated by the vortex phase plate with a birefringence medium is considered. It is shown that if the ideal retardation π is broken, the pattern diffracted from the phase plate is described by superposition of two components: the vortex beam with the deep hole and the incident beam which preserves its initial characteristics. The computation results characterizing the influence of retardation on the Gaussian and Airy beams transformation in the vortex phase plate are presented. These results point out that vortex beam characteristics are very sensitive to retardation shift from its ideal value. We analyze and present the characteristics of the vortex phase plate that are required for the true vortex pattern generation.     

两束离轴高斯光束干涉场中的横向光涡旋

研究了两束离轴高斯光束干涉场中的波前结构以及横向光涡旋.研究表明干涉场中的相位鞍点以及涡旋点的位置与光束的离轴参数、束腰宽度、相位以及相对振幅有关.相位鞍点既可位于涡旋点的内侧，也可以位于涡旋点的外侧，且控制参数取一定值时，相位鞍点将与涡旋点重合.对于离轴光束，XZ平面两侧的相位鞍点与涡旋点相遇时所对应的控制参数并不相同，且XZ平面上相位鞍点相遇时所对应x值，一般情况下与涡旋点相遇时所对应的x值不相同.     

基于焦散线方法的自加速光束设计

以艾里光束为代表的自加速光束是一类在自由空间中具有弯曲传播特性的新型特殊光束.这类光束因其具有无衍射、自加速和自修复等奇异特性引起了人们的广泛关注,有望应用于光学微粒操控、激光微加工、全光路由和超分辨成像等诸多领域.由于艾里光束只能沿着抛物线的轨迹传播,限制了其在实际应用中的灵活性,因而设计出能够沿着不同轨迹传播的自加速光束是这一研究领域的关键问题,而基于焦散线方法的自加速光束设计是解决该问题的有效途径之一.这一方法是将设计的传播轨迹与光学焦散线联系起来,通过分析形成该焦散线所需的光线簇构造出对应的初始场分布.基于该原理并经过不断发展,不同类型的自加速光束相继得以实现,并且借助维格纳函数还可以同时实现实空间和傅里叶空间的自加速光束设计,为自加速光束的应用提供了更多的可能性.本文对基于焦散线方法的自加速光束设计原理和进展进行全面介绍.