Propagation properties of vector Mathieu-Gauss beams

The vector Helmholtz-Gauss (vHzG) beam is known as a general family of localized vector beam solutions of the Maxwell equations in the paraxial limit and the vector Mathieu-Gauss beam constitutes its version in elliptic cylindrical coordinates system. In this work, starting from the expansion of the scalar Mathieu-Gauss beam in term of Bessel-Gauss beams, we give a general expression of vector Mathieu-Gauss beams in cylindrical coordinates. Within the frame work of the Collins diffraction integral formula we derive the analytical expressions of transverse vector Mathieu-Gauss beams through an axisymmetric ABCD optical system. Some numerical calculations are performed to illustrate the propagation of the vector Mathieu-Gauss beam in free space and through a simple lens system. The results are analyzed and discussed.     

Ein ionenoptisches System zur Dämpfung transversaler Schwingungen in Strahlen schwerer Ionen

An ion-optical system of new type capable to reduce the divergency of heavy ion beams is proposed. The action of this system is based on the difference of mean charge of heavy ions in gas and in condensed matter. The beam is split into two parts of different mean charge and merged by unification of the mean charge alternately by local application of the different charge exchange media. Considering the beam to be bound to an axis by a series of identical coaxial lenses the ions will oscillate around the axis. Since one part of the beam remains unaffected by charge exchange processes on the average the particles of the other part are forced to increase their charges at positions near to the center line and to reduce their charges at positions of maximum elongation. This process will absorb oscillation energy from the beam. Also, the coordinates of the particles of the second part of the beam move differently in phase space while the particles are in higher charge states: the coordinates are shifted into the phase space domain occupied by the coordinates of the particles of the first part of the beam thus yielding an overall reduction of beam divergency.     

Induced focusing and conversion of a Gaussian beam into an elliptic Gaussian beam

We have presented an investigation of the induced focusing in Kerr media of two laser beams, the pump beam and the probe beam, which could be either Gaussian or elliptic Gaussian or a combination of the two. We have used variational formalism to derive relevant beam-width equations. Among several important findings, the finding that a very week probe beam can be guided and focused when power of both beams are well below their individual threshold for self-focusing, is a noteworthy one. It has been found that induced focusing is not possible for laser beams of any wavelength and beam radius. In case both beams are elliptic Gaussian, we have shown that when power of both beams is above a certain threshold value then the effective radius of both beams collapses and collapse distance depends on power. Moreover, it has been found that induced focusing can be employed to convert a circular Gaussian beam into an elliptic Gaussian beam.     

光束分数傅里叶变换几何特性的相空间束矩阵分析方法

提出一种分析傍轴光束分数傅里叶变换几何特性的相空间束矩阵变换的简单方法. 以分析椭圆高斯光束分数傅里叶变换几何特性为例，研究表明，利用本方法讨论傍轴束分数傅里叶变换的几何特性简单可靠、从几何图像理解傍轴束分数傅里叶变换清晰直观. 为研究光束传输变换的特性提供了一种简单方便的新途径. 关键词： 相空间束矩阵 分数傅里叶变换 椭圆高斯光束     

Z-scan technique for elliptic Gaussian beams

A novel z-scan technique suitable for elliptic Gaussian beams is proposed. It is based on the direct measurement of the beams semiaxes in the far field instead of the irradiance transmitted through an aperture, as in the case of circular beams. This technique overcomes, for the first time, the insurmountable obstacles encountered when a z-scan technique based on transmittance measurements is used in the case of elliptic beams. The experimental procedure of this technique is realized using a CCD camera connected to a laser beam profiler, and has the advantage of being insensitive to beam pointing instability and energy fluctuations. It also reveals the different influence of the optical non-linearities on the two principal semiaxes of the elliptic beam. PACS 42.65.-k; 42.65.An; 42.65.Jx     

Off-axis collimation of diode laser beams by means of single-element holographic diffractive optics

Principles of single-element holographic diffractive optics for collimation of diode laser beams with a large divergence, an elliptic cross-section, and astigmatism are presented. Holographic off-axis transformation enables collimation of the beam in two variants: one with a perpendicular input beam and an oblique output beam, and the other with the beams arranged vice-versa. Diffraction due to an elliptic aperture is analyzed. Inspection of experimental samples demonstrates an agreement with theory in the case of diffraction limited focal pattern and shows increase of astigmatism with the departure from diffraction only limitation.     

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.     

Propagation of paraxial circular symmetric beams in a general optical system

Starting from flattened Gaussian beams, we deduce analytical expressions for the propagation of paraxial circular symmetric beams through a general first-order optical system. It is shown that the propagation of any scalar beam in a paraxial domain takes the same form as that in free space. Three parameters were introduced to characterize the evolution of the propagating beam. Numerical examples are also presented to illustrate the effectiveness of this method.     

Structural stability of a nonparaxial singular mode beam

The exact explicit solution of the Maxwell equations for nonparaxial singular beams propagating in free space or in a homogeneous isotropic medium is considered. It is shown that, in the paraxial approximation, such solutions for mode beams of both lower and higher orders may turn into the solutions for guided modes or vortices of optical fibers. It is found that a variation of the Rayleigh length for a mode beam does not change the structure of phase and polarization singularities; it merely transforms their coordinates. In the paraxial limit, the singularities are shifted off the axis to regions with negligible light fluxes.     

Propagation properties of anomalous hollow beams in a turbulent atmosphere

Propagation of circular and elliptical anomalous hollow beams in a turbulent atmosphere is investigated in detail. Based on the extended Huygens–Fresnel integral, analytical formulae for the average irradiance of circular and elliptical anomalous hollow beams propagating in a turbulent atmosphere are derived. The irradiance and spreading properties of circular and elliptical anomalous hollow beams in a turbulent atmosphere and in free space are studied numerically. It is found that circular and elliptical anomalous hollow beams at short propagation distance in turbulent atmosphere have similar propagation properties to those of free space, while at long propagation distance, circular and elliptical anomalous hollow beams eventually become circular Gaussian beams in a turbulent atmosphere, which is much different from their propagation properties in free space. The conversion from an anomalous hollow beam to a circular Gaussian beam becomes quicker and the beam spot spreads more rapidly for a larger structure constant, a shorter wavelength and a smaller waist size of the initial beam.     

基于格林函数法的奇型Mathieu-Gaussian光束

根据光束传播的独立性和叠加性原理,引入了一组能够产生第一类(2n+2阶)奇型Mathieu-Gaussian光束的虚光源点.利用虚源点技术和格林函数法,计算得到第一类奇型Mathieu-Gaussian光束的严格解析积分表达式.利用该表达式得到了轴上光场分布的积分解析解.以三阶非旁轴修正为例,得到了第一类奇型Mathieu-Gaussian光束保留到三阶非旁轴修正项的轴上光场分布精确解.     

强非局域非线性介质中光束传输的Ince-Gauss解

利用强非局域非线性介质中傍轴光束传输的线性模型（Snyder-Mitchell模型）讨论了椭圆坐标系下光束传输过程,通过设立Ince多项式对Gauss函数的调制解得到了强非局域非线性介质中光束稳定传输的Ince-Gauss解.当Ince-Gauss光束的入射功率为临界功率时,光束保持孤子形式传输,否则传输光束的束宽呈现周期性波动,即为呼吸子形式.同时还数值模拟了呼吸子的传输过程.Ince-Gauss光在一定条件下可以连续转换为Hermite-Gauss光或Laguerre-Gauss光,图示展现了几个低阶Ince型光孤子及其转换情况. 关键词： 强非局域非线性介质 Ince-Gauss光 Laguerre-Gauss光 Hermite-Gauss光     

Circular beams

A very general beam solution of the paraxial wave equation in circular cylindrical coordinates is presented. We call such a field a circular beam (CiB). The complex amplitude of the CiB is described by either the Whittaker functions or the confluent hypergeometric functions and is characterized by three parameters that are complex in the most general situation. The propagation through complex ABCD optical systems and the conditions for square integrability are studied in detail. Special cases of the CiB are the standard, elegant, and generalized Laguerre-Gauss beams; Bessel-Gauss beams; hypergeometric beams; hypergeometric-Gaussian beams; fractional-order elegant Laguerre-Gauss beams; quadratic Bessel-Gauss beams; and optical vortex beams.     

Generation of diffraction-free vectorial elliptic hollow beams with space-varying inhomogeneous polarizations

Diffraction-free vectorial elliptic hollow beams (vEHBs) are generated by an optical system composed of a short elliptic hollow fiber (EHF) and an axicon. Each beam has a closed elliptic annular intensity profile and space-varying polarization states in its diffraction-free distance of more than 1 m. The generated beams have a counter-clockwise or clockwise periodically-rotated inhomogeneous polarization. And the spin angular momentum (SAM) of the vEHBs is 1ħ or -1ħ which is consistent with the type of dual-mode in the EHF and the periodic polarization rotations of the vEHBs. The vEHBs have potential applications in optically trapping and micromanipulating the micro- or nano-particles, quantum information transmission, and Bose-Einstein condensates, etc.     

Cartesian beams

A new and very general beam solution of the paraxial wave equation in Cartesian coordinates is presented. We call such a field a Cartesian beam. The complex amplitude of the Cartesian beams is described by either the parabolic cylinder functions or the confluent hypergeometric functions, and the beams are characterized by three parameters that are complex in the most general situation. The propagation through complex ABCD optical systems and the conditions for square integration are studied in detail. Applying the general expression of the Cartesian beams, we also derive two new and meaningful beam structures that, to our knowledge, have not yet been reported in the literature. Special cases of the Cartesian beams are the standard, elegant, and generalized Hermite-Gauss beams, the cosine-Gauss beams, the Lorentz beams, and the fractional order beams.     

Instrumentation with polarized neutrons

Neutron scattering with polarization analysis is an indispensable tool for the investigation of novel materials exhibiting electronic, magnetic, and orbital degrees of freedom. In addition, polarized neutrons are necessary for neutron spin precession techniques that path the way to obtain extremely high resolution in space and time. Last but not least, polarized neutrons are being used for fundamental studies as well as very recently for neutron imaging. Many years ago, neutron beam lines were simply adapted for polarized beam applications by adding polarizing elements leading usually to unacceptable losses in neutron intensity. Recently, an increasing number of beam lines are designed such that an optimum use of polarized neutrons is facilitated. In addition, marked progress has been obtained in the technology of ³He polarizers and the reflectivity of large-m supermirrors. Therefore, if properly designed, only factors of approximately 2–3 in neutron intensity are lost. It is shown that S-benders provide neutron beams with an almost wavelength independent polarization. Using twin cavities, polarized beams with a homogeneous phase space and P>0.99 can be produced without significantly sacrificing intensity. It is argued that elliptic guides, which are coated with large m polarizing supermirrors, provide the highest flux.     

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.     

On Transporting an Elliptic Charged-Particle Beam

Physics of Particles and Nuclei Letters - The configuration of a drift tube with high beam/tube area ratios is calculated for intense elliptic beams based on a model differing from the classical one.