Topological charge inversion in polynomial astigmatic Gaussian beams

The evolution of the global topological charge in a general polynomial astigmatic Gaussian beam is investigated. The leading order terms of the polynomial prefactor determines the global topological charge and can be expressed as a product of first order polynomials, each representing an optical vortex function. We show that the global topological charge is bounded by the order of the polynomial and change during propagation in steps of 2 every time one of the optical vortices undergo topological charge inversion. We investigate the locations of the flip planes where charge inversions occur and provide expressions for a number of special cases. Numerical results are provided for an example of such a polynomial astigmatic Gaussian beam.     

Propagation properties of partially polarized Gaussian Schell-model beams through an astigmatic lens

Based on the beam coherent-polarization (BCP) matrix approach and propagation law of partially coherent beams, analytical propagation equations of partially polarized Gaussian Schell-model (PGSM) beams through an astigmatic lens are derived, which enables us to study the propagation-induced polarization changes and irradiance distributions at any propagation distance of PGSM beams through an astigmatic lens within the framework of the paraxial approximation. Detailed numerical results for a PGSM beam passing through an astigmatic lens are presented. A comparison with the aberration-free case is made, and shows that the astigmatism affects the propagation properties of PGSM beams.     

Kerr非线性介质中聚焦像散高斯光束的传输特性

当高功率激光通过Kerr非线性介质传输时,Kerr效应会严重影响激光的传输特性.实际应用中常遇到像散光束.迄今为止,像散光束传输特性的研究大都局限于在线性介质中的传输,而在非线性介质中传输的研究较少,且还未涉及像散激光束通过含光学系统的Kerr非线性介质传输变换的研究.本文主要研究Kerr效应对聚焦光束像散特性和焦移特性的影响,以及聚焦像散高斯光束的自聚焦焦距和光束焦点调控.在光束扩展情况下,推导出了聚焦像散高斯光束在Kerr非线性介质中传输的束宽、束腰位置和焦移的解析公式,研究表明:在自聚焦介质中,随着自聚焦作用增强(如光束功率增强),光束像散越强,但焦移越小;在自散焦介质中,随着自散焦作用增强(如光束功率增强),光束像散越弱,但焦移越大.另一方面,在光束自聚焦情况下,推导出了自聚焦焦距的解析公式,研究表明利用光束像散可以调控光束焦点个数.     

The connection of geometrical optics with the propagation of gaussian beams and the theory of optical resonators

The propagation of light near the axis of astigmatic optical systems may be described by the geometrical-optics approximation with the aid of ray-matrices. The application of the theory of diffraction to the propagation of light in such systems leads to integrals containing essentially the elements of the ray-matrices as parameters. The ABCD-law is derived by evaluating these integrals for gaussian beams. Integral equations applicable to astigmatic optical resonators, having nearly vanishing diffraction losses, are set up. They are only valid under certain conditions, which are comprehensively discussed. The eigensolutions and the eigenvalues of these integral equations are given. The spot-sizes at the resonator mirrors are derived from the eigensolutions, and the eigenvalues lead to the resonance condition. Spot-sizes and resonance condition appear as functions of the elements of the characteristic resonator matrices. The methods described here are applied to the propagation of gaussian beams through gas-lenses and to a resonator containing an internal gas-lens.     

完美涡旋光中微米级粒子的受力与力矩特性分析

基于紧聚焦方法在几何焦平面处获得了完美涡旋光场,理论分析了该光场中微米级尺寸微粒受到的光学力与轨道矩。结果表明,该完美涡旋光可以在横平面上捕获微粒并驱动其绕光轴做轨道旋转运动,微粒受到的轨道矩随着拓扑荷的增大先增大后趋近于稳定。此外,分析了圆偏振、径向偏振和方位角偏振完美涡旋光对微粒施加的光学力和轨道矩。结果表明完美涡旋光的偏振态在一定程度上会影响微粒的轨道运动,圆偏振完美涡旋光更适合用于诱导微粒轨道旋转。     

Scintillation index of astigmatic annular beams in a turbulent atmosphere

The scintillation properties of astigmatic annular beams in a weak turbulent atmosphere are investigated. Expression for the on-axis scintillation index of an astigmatic annular beam is derived. It is found that the scintillation index of an astigmatic annular beam can be smaller than that of a Gaussian beam, an elliptical Gaussian beam and a stigmatic annular beam in a weak turbulent atmosphere under certain conditions. The scintillation properties of astigmatic annular beams are closely controlled by its beam parameters.     

Vortices in ultrashort laser pulses

The propagation of optical vortices nested in broadband femtosecond laser beams was studied both numerically and experimentally. Based on the nonlinear Schrödinger equation, the dynamics of different multiple-vortex configurations with varying topological charge were modelled in self-focussing and self-defocussing Kerr media. We find a similar behavior in both cases regarding the vortex–vortex interaction. However, the collapsing background beam alters the propagation for a positive nonlinearity. Regimes of regular and possibly stable multiple filamentation were identified this way. Experiments include measurements on pairs of filaments generated in a vortex beam on an astigmatic Gaussian background with argon gas as the nonlinear medium. Spectral broadening of these filaments leads to a supercontinuum which spans from the visible range into the infrared. Recompression yields <19 fs pulses. Further optimization may lead to much better recompression.     

Analytical propagation equation of astigmatic Hermite–Gaussian beams through a 4×4 paraxial optical system and their symmetrizing transformation

Starting from the Collins formula, a closed-form propagation equation of astigmatic Hermite–Gaussian (H–G) beams through a 4×4 paraxial optical system is derived, which permits us to calculate the irradiance distribution at any propagation plane and to study the symmetrization of astigmatic standard and elegant H–G beams. A detailed symmetrizing transformation of astigmatic H–G beams through a three-cylindrical-lens mode converter is illustrated both analytically and numerically. It is found that in accordance with the second-order moments characterization, there are two types of beam symmetrization. The transformation of standard H–G beams through the three-cylindrical-lens mode converter belongs to the perfect symmetrization, whereas the transformation of elegant H–G beams is the imperfect one.     

Transformation and spatial shaping of partially coherent cosh-Gaussian beams through an astigmatic lens

Based on the propagation law of partially coherent beams, the closed-form propagation expression for partially coherent cosh-Gaussian (ChG) beams through an astigmatic lens is derived. The transformation and spatial shaping of partially coherent ChG beams through the astigmatic lens are studied and illustrated by numerical examples. It is shown that a suitable choice of the spatial coherence parameter and/or astigmatic coefficient, different beam profiles, such as Gaussian-like, flat-topped and bottle beam profiles, and beam profile with a central dip, at the geometric focal plane and at a certain plane are realizable.     

Effects of misalignments in the optical vortex transformation performed by holograms with embedded phase singularity

Spatial characteristics of diffracted beams produced by a “fork” hologram from an incident circular Laguerre-Gaussian beam whose axis differs from the hologram optical axis are studied theoretically. General analytical representations for the complex amplitude distribution of a diffracted beam are derived in terms of superposition of Kummer beams or hypergeometric-Gaussian beams. The diffracted beam structure is determined by combination of the “proper” topological charge m of the incident vortex beam and the topological charge l of the singularity “imparted” by the hologram. Evolution of the diffracted beam structure is studied in detail for several combinations of m and l and for various incident beam displacements with respect to the optical axis of the hologram. Variations of the intensity and phase distribution due to the incident beam misalignment are investigated and possible applications for the purposeful optical vortex beam generation and optical measurements are discussed.     

Propagation of Airy Gaussian vortex beams in uniaxial crystals

The propagation dynamics of the Airy Gaussian vortex beams in uniaxial crystals orthogonal to the optical axis has been investigated analytically and numerically. The propagation expression of the beams has been obtained. The propagation features of the Airy Gaussian vortex beams are shown with changes of the distribution factor and the ratio of the extraordinary refractive index to the ordinary refractive index. The correlations between the ratio and the maximum intensity value during the propagation, and its appearing distance have been investigated.     

像散Bessel光束自重建特性的理论和实验研究

基于菲涅耳衍射积分理论和巴比涅原理,推导出像散Bessel光束经圆形障碍物后的光强分布一般表达式.数值模拟了像散Bessel光束经圆形障碍物遮挡后光场的自重建过程,并设计相关实验进行验证,实验结果与理论模拟基本符合.结果表明：零阶像散Bessel光束经过轴上和离轴障碍物后均会发生光束重建现象.随着传输距离的增加,像散Bessel光束的外轮廓尺寸变大、中心光点阵列数增多,逐渐重建出不同于障碍物前的完整光束.并且观察到光束在重建过程中横向和纵向的重建速度并不一致,存在一定的速度差.利用螺旋相位板产生高阶像散Bessel光束,验证了高阶像散Bessel光束经障碍物遮挡后同样具有自重建特性.研究结果对像散Bessel光束在多层面粒子操纵方面的应用具有参考价值.     

部分相干余弦-高斯光束

引入部分相干余弦-高斯光束,推导出部分相干余弦-高斯光束通过近轴ABCD光学系统的传输公式和M2因子,研究了部分相干余弦-高斯光束通过像散透镜的传输特性.结果表明,部分相干余弦-高斯光束的M2因子与部分相干余弦-高斯光束的空间相干参量和离心参量有关,但与透镜的像散系数无关.适当选取空间相干参量,离心参量或像散系数,在几何焦面处可得到类高斯、平顶和空心等不同的光强剖面,实现部分相干余弦-高斯光束的空间整形.     

Switchable vector vortex beam generation using an optical fiber

We present our experimental results on directly transforming a circular-polarized Gaussian beam into linear-polarized vector vortex beams using a two-mode fiber and demonstrate switching between the different 0th-order vector vortex modes excited and guided in the fiber. Depending on the handiness of circular-polarization of the input Gaussian light beam, its launch angle with respect to the fiber axis and by changing them appropriately it is possible to excite and switch between the different vector vortex modes and its coherent linear superposition supported by the two-mode fiber. The output optical beams due to the selectively excited vector modes in the fiber are characterized by using a rotating analyzer and a two-beam interferometer setup to study the polarization and the phase behavior of the vector vortex beam.     

Self-focusing of femtosecond diffraction-resistant vortex beams in water

We report experiments on self-focusing of femtosecond diffraction-resistant vortex beams in water. These beams are higher-order Bessel beams with weak azimuthal modulation of the transverse intensity patterns. The modulation overrides the self-focusing dynamics and results in the formation of regular bottlelike filament distributions. The peak-power thresholds for filamentation, at a particular distance, are relatively accurately estimated by the adaptation of the Marburger formula derived earlier for Gaussian beams. The nonlinear conversion of the incident conical waves into the localized spatial wave packets propagating near the beam axis is observed.     

Vortex-edge dislocation interaction in the presence of an astigmatic lens

The vortex-edge dislocation interaction in the presence of an astigmatic lens is studied both analytically and numerically, where the effect of astigmatism is stressed. It is shown that for the aberration-free case the edge dislocation bending and break up into a pair of oppositely charged vortices and the shift of the initial vortex appear. The astigmatism leads to some richer vortex evolution behavior. By suitably varying the astigmatic coefficient of the lens, the motion, creation, annihilation and shift to infinity of vortices take place. The off-axis distance additionally affects the vortex evolution behavior for the case of the on-axis vortex and off-axis edge dislocation interaction. In the vortex evolution process the total topological charge is not conserved in general.     

像散透镜对高斯光束的变换特性

 基于广义惠更斯-菲涅尔衍射积分,并考虑了像散的影响,对高斯光束通过像散透镜后的传输特性作了解析研究,以光束传输因子和桶中功率为参数分析了像散高斯光束的光束质量,并以数值计算例加以说明。     

On-axis spectral shifts and spectral switches of Gaussian Schell-model beams focused by an astigmatic aperture lens

Starting from the propagation law of partially coherent light, the on-axis spectral shifts and spectral switches of Gaussian Schell-model (GSM) beams focused by an astigmatic aperture lens are studied. It is shown that, as compared with an aberration-free case whose spectral shifts and spectral switches are induced by spatial correlation and aperture diffraction, the spectral shifts and spectral switches of GSM beams also depend upon the astigmatism of the lens for an astigmatism case. Detailed numerical calculations are made to illustrate the behavior of spectral shifts and spectral switches of GSM beams focused by an astigmatic aperture lens.     

多环涡旋光束的实验研究

涡旋光束的产生、传输与应用是当前光学领域热门的研究课题之一.本文提出的新型多环涡旋光束,包括双环涡旋及三环涡旋光束,它是由多束携带不同拓扑电荷数且束腰半径不同的拉盖尔-高斯涡旋光束共轴叠加而成,其光强分布为多环结构.从理论上研究了多环涡旋光束的形成与分布特征,基于共轭对称延拓Fourier计算全息方法生成了多环涡旋光束的计算全息图,并利用一个空间光调制器实验产生了与理论一致的高质量的多环涡旋光束.研究表明多环涡旋光束的各环携带不同的轨道角动量,空间分布保持相互独立.这种新型的多环涡旋光束相对于携带单一拓扑电荷数的涡旋光束,提供了更多的控制参数和更加多样化的结构分布,因此在光学镊子、光学捕获等微操控以及光通信领域具有潜在的应用潜力.     

汉克-贝塞尔光束在海洋湍流信道中的螺旋相位谱分析

携带轨道角动量的汉克-贝塞尔(Hankel-Bessel,HB)光束具有无衍射和自聚焦特性,用来作为信息传输的载体有望增大信息传输容量.基于Rytov近似理论,推导得到了HB涡旋光束经过海洋水平弱湍流信道后的螺旋相位谱的解析表达式,并利用数值仿真方法研究了海洋湍流参数对轨道角动量模式探测概率的影响.结果表明,海洋湍流导致发射轨道角动量模式的探测概率下降,出现模式串扰和螺旋相位谱扩展.海洋湍流对HB涡旋光束的负面影响随着轨道角动量模式数、传输距离、温度方差耗散率的增加而增强,随湍流动能耗散率的增加而减弱.HB涡旋光束受以盐度波动驱动的海洋湍流的负面影响更大.另外,在弱湍流及几十米传输距离条件下,HB涡旋光束的传输性能要差于最佳束腰大小设置的拉盖尔-高斯涡旋光束.这些结果有望为海洋环境水下光通信链路的实现提供一定的参考价值.