Generation of hollow Gaussian beams by spatial filtering

We demonstrate that hollow Gaussian beams can be obtained from Fourier transform of the differentials of a Gaussian beam, and thus they can be generated by spatial filtering in the Fourier domain with spatial filters that consist of binomial combinations of even-order Hermite polynomials. A typical 4f optical system and a Michelson interferometer type system are proposed to implement the proposed scheme. Numerical results have proved the validity and effectiveness of this method. Furthermore, other polynomial Gaussian beams can also be generated by using this scheme. This approach is simple and may find significant applications in generating the dark hollow beams for nanophotonic technology.     

Theoretical Analysis and Experimental Study on Generation of a Dark Hollow Beam by a Micron-sized Hollow Optical Fiber

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可控双空心光束的理论方案及实验研究

提出了一种利用双周期弧向非满额相位调制的方法产生双空心光束的方案. 当准直氦氖激光通过1.5 mm半径透光孔照射到该相位图样时, 在200 mm成像透镜像空间获得长30 mm, 间距57.6μm, 单管束宽度0.11–0.14 mm的双空心光束. 该方案结构简单, 产生的双空心光束具有较好的可控性, 双光管间距由相位调制因子p决定, 能够实现从双空心光束到单空心光束的双向演化. 对所提出的方案进行了实验研究并得到与理论相符的结果. 利用多种组合方式讨论了将该方案拓展到蓝失谐光学囚禁势阱, 可以实现可控的空心双光阱、四光阱与光学晶格等, 有望在冷原子、冷分子囚禁与操控等领域的实验研究中发挥重要作用.     

广义双曲正弦-高斯光束的Gyrator变换性质和暗空心光束产生

基于Gyrator变换,推导了广义双曲正弦-高斯光束场分布的解析表达式,研究了广义双曲正弦-高斯光束在Gyrator变换平面上的光强分布和相位特性.结果表明,在Gyrator变换过程中,具有边缘位错相位特性的双曲正弦-高斯光束能转换为具有涡旋的暗空心光束,并确定产生的暗空心光束的拓扑荷指数为一,而不具有边缘位错相位特性的双曲余弦-高斯光束则不可能出现空心结构.对影响变换场强度和相位分布的束结构参数及系统参数进行了分析讨论.     

Generation of a hollow laser beam by a multimode fiber

A simple method to generate a hollow laser beam by multimode fiber is reported. A dark hollow laser beam is generated from a multimode fiber and the dependence of the output beam profile on the incident angle of laser beam is analyzed. The results show that this hollow laser beam can be used to trap and guide cold atoms.     

Hollow Gaussian beam generated by beam shaping with phase-only liquid crystal spatial light modulator

Based on the refractive beam shaping system, the transformation of a quasi-Gaussian beam into a dark hollow Gaussian beam by a phase-only liquid crystal spatial light modulator (LC-SLM) is proposed. According to the energy conservation and constant optical path principle, the phase distribution of the aspheric lens and the phase-only LC-SLM can modulate the wave-front properly to generate the hollow beam. The numerical simulation results indicate that, the dark hollow intensity distribution of the output shaped beam can be maintained well for a certain propagation distance during which the dark region will not decrease whereas the ideal hollow Gaussian beam will do. By designing the phase modulation profile, which loaded into the LC-SLM carefully, the experimental results indicate that the dark hollow intensity distribution of the output shaped beam can be maintained well even at a distance much more than 550 mm from the LC-SLM, which agree with the numerical simulation results.     

用弧形波晶片产生矢量光束及其强聚焦的特性研究

提出了产生轴对称矢量光束的新方案, 根据晶体的双折射性质设计波晶片, 形成o光和e光相位板, 能够把线偏振光转换为具有旋转对称性的径向或角向矢量空心光束, 光路简单, 调节方便. 应用Richards-Wolf的经典矢量衍射模型, 分析计算了空心高斯光束照明、高数值孔径透镜聚焦条件下所产生的衍射光波电磁场分布, 结果表明: 用功率为0.5 W的激光照明, 所获得的矢量空心光束具有很高的光强、光强梯度和很强的纵向电磁场分布, 同时还能产生可实时调控的光子角动量分布, 方案在微观粒子的操控方面有很好的应用前景.     

一种新空心光束的理论及实验研究

提出了一种用来描述空心光束的新理论模型——空心高斯光束模型，通过控制光束参数可以方便地调制空心光束黑斑的大小.导出了空心高斯光束经傍轴光学系统的解析传输变换公式.利用导出的公式计算分析了空心高斯光束在自由空间的传输特性.在实验上利用矩阵本征值方法设计了能输出空心高斯光束的光学谐振腔，对实验上得到的空心高斯光束进行了传输特性的研究.结果表明，理论和实验相吻合.该空心高斯光束产生的光势阱为控制冷原子提供了一条新途径. 关键词： 空心高斯光束 光学谐振腔 传输特性     

利用纯相位型液晶空间光调制器实现空心光束

为了提高激光系统的整体效率,需要将出射光强整形为空心分布。采用纯相位型液晶空间光调制器整形近高斯分布光强到空心分布。基于能量守恒定律和等光程原理,分析了纯相位型液晶空间光调制器光束整形系统,得出了整形系统所需的相位分布。采用衍射光学方法,数值模拟了整形效果,讨论了入射光束束腰半径和强度分布等因素对整形效果的影响。利用纯相位型液晶空间光调制器实验实现了空心光束,实验测得的转换效率大于99%。     

Generations of dark hollow beams and their applications in laser cooling of atoms and all optical-type Bose－Einstein condensation

We report on a new experimental result to generate dark hollow beams by using a geometric optical method. We propose two new methods to produce focused and localized hollow laser beams by using π-phase plates. Using Monte-Carlo simulations, we have studied the Sisyphus cooling of alkali atoms in pyramidal hollow beam gravito-optical traps. We discuss some potential applications of the dark hollow beams in atom optics and the preparation of an all optically-cooled and optically-trapped atomic Bose－Einstein condensation (BEC). Our research shows that an ultracold atomic sample with a temperature of ～ 2μK can be obtained in the pyramidal hollow beam dipole trap and an all optical-type BEC may be realized in a far blue-detuned, hollow beam trap.     

Phase-Only Encryption and Single Path Decryption System Using Phase-Encoded Exclusive-OR Rules in Fourier Domain

A phase-only encryption scheme using phase-encoded exclusive-OR (XOR) rules in a Fourier plane and a single path decryption system are presented. To generate phase-only encrypted data, a zero-padded original image, multiplied by a random phase image, is Fourier transformed and its real-valued data is encrypted with key data by using phase-encoded XOR rules. Since the original information is encrypted on the Fourier plane, the proposed encryption is more tolerant to loss of key information by scratching or cutting than previous XOR encryption in a space domain. A decryption is simply performed based on 2-f setup with spatial filter by Fourier transform for multiplication phase-only encrypted data with phase-only key data. Due to single path architecture without a reference wave, the proposed system is resistant to mechanical vibrations and fluctuation. Numerical simulations have confirmed the validity of the proposed encryption scheme and simple decryption architecture.     

Modified hollow Gaussian beam and its paraxial propagation

A model named modified hollow Gaussian beam (HGB) is proposed to describe a dark hollow beam with adjustable beam spot size, central dark size and darkness factor. In this modified model, both the beam spot size and the central dark size will be convergent to finite constants as the beam order approaches infinity, which are much different from that of the previous unmodified model, where the beam spot size and the central dark size will not be convergent as the beam order approaches infinity. The dependences of the propagation factor of modified and unmodified HGBs on the beam order are found to be the same. Based on the Collins integral, analytical formulas for the modified HGB propagating through aligned and misaligned optical system are derived. Some numerical examples are given.     

用线偏振光产生可调矢量椭圆空心光束

提出了利用π相位板产生矢量空心光束的新方案,两个偏振方向互相垂直的线偏振光波分别通过π相位板调制后进行强度叠加,得到椭圆空心光束,用矩形光阑调节相位板的几何尺寸,可以实时调节椭圆的离心率;调节π相位板的方位,能够实现径向矢量空心光束到角向矢量空心光束的转换。分析、讨论了方案的可行性和在原子光学中的潜在应用,结果表明:本方案在原子光学中有很好的应用前景。     

Generation of a vectorial Mathieu-like hollow beam with a periodically rotated polarization property

We propose a promising and practical scheme to generate a vectorial Mathieu-like hollow beam (vMHB) by using an axicon optical system including a dual-mode elliptic hollow fiber (EHF), and calculate the intensity and polarization distributions of the beam and its fractional orbital angular momentum (OAM). We also fit its intensity profile and obtain suitable theoretical expressions to describe three-dimensional (3D) propagation characteristics of such a Mathieu-like hollow beam. Our study shows that the generated beam is a vMHB within the propagation distance 1.2-2.2 m, which has an unchanged (diffraction-free) intensity profile and periodically rotated polarization properties as well as an unchanged fractional OAM within 1.2-2.2 m.     

基于柱坐标系下的空心高斯光束的分数傅里叶变换

推导出分数傅里叶变换基于柱坐标系下的解析表达式,应用此解析表达式对空心高斯光束进行分析,得到其分数傅里叶变换的解析表达式。讨论其在分数傅里叶变换平面的光强分布与各种光束参数之间的变换关系,并进行数值计算,从而得出基于柱坐标系下的空心高斯光束的分数傅里叶变换的传输性质。所得结果为分析和计算这种光束的分数傅里叶变换提供了方便,同时对此类光束的传输控制提供了基础理论支持。     

Generation of a vectorial elliptic hollow beam by an elliptic hollow fiber

We propose a handy scheme to generate a vectorial elliptic hollow beam by using a short dual-mode elliptic hollow fiber, study its propagation characteristics in free space, and calculate its total angular momentum at different propagating distances. Our study shows that the resulting elliptic hollow beam has a self-focusing effect in near field, an arbitrary polarization, and a position-dependent fractional angular momentum and that the directions of the major and minor axes of the elliptical intensity profile will be interchanged after the self-focusing plane.     

Hollow Gaussian beams and their propagation properties

A new mathematical model, described as hollow Gaussian beams (HGBs), is proposed to describe a dark hollow laser beam (DHB). The area of the dark region across the HGBs can easily be controlled by proper choice of the beam parameters. Based on the Collins integral, an analytical propagation formula for the HGBs through a paraxial optical system is derived. The HGBs also can be expressed as a superposition of a series of Lagurerre-Gaussian modes by use of a polynomial expansion. As a numerical example, the propagation properties of a DHB in free space are illustrated graphically. The HGBs provide a convenient and powerful way to describe and treat the propagation of DHBs and can be used conveniently to analyze atoms manipulated with a DHB.     

产生纳米级暗中空光束的方法研究

用时域有限差分法，给出光纤头近场区电场强度模的空间分布.讨论了当光纤纤芯分别取不同尺寸时，对此空间光场强度的影响.要想得到较大范围的暗中空光束，必须增加光纤纤芯尺寸.并且，对光纤纤芯尺寸取一较大值和光纤中空区域尺寸取一较小值时的情况进行讨论，可得在光纤头附近可以出现与光纤中空区域尺寸大小相当的暗斑(10¹ nm量级).但是，暗中空光束中背景光较强.为此，将光纤的空心设计为金属. 发现此时中心暗斑的背景光明显减弱，在近场区域可获得较为理想的暗中空光束.如进一步缩小光纤中空区域尺寸，可以在光纤头附近获得暗斑更小甚至纳米量级的暗中空光束.为获得一种纳米量级的暗中空光束提供一种方法.     

Shaping the beam profile of a partially coherent beam by a phase aperture

By use of a tensor method, an analytical formula for a partially coherent Gaussian Schell-model (GSM) beam truncated by a circular phase aperture propagating through a paraxial ABCD optical system is derived. The propagation properties of a GSM beam truncated by a circular phase aperture in free space are studied numerically. It is found that the circular phase aperture can be used to shape the beam profile of a GSM beam and generate partially coherent dark hollow or flat-topped beam, which is useful in many applications, e.g., optical trapping, free-space optical communication, and material thermal processing. The propagation factor of a GSM beam truncated by a circular phase aperture is also analyzed.     

亚微米局域空心光束的产生及其在单原子囚禁与冷却中的应用理论研究

提出了一种采用单模光纤、环形二元相位板和微透镜组成的光束整形系统产生亚微米局域空心光束的方案. 根据瑞利-索莫菲衍射积分公式, 数值计算了微透镜焦平面附近的场分布, 详细研究了空心光束的暗斑尺寸与单模光纤模场半径和微透镜焦距的关系. 数值计算结果表明: 在微透镜焦平面附近光场分布近似对称, 在焦点处场强近似为零, 周围场强逐渐增大, 形成半径约为0.4 μm的三维封闭的球形空心光场区域, 即亚微米局域空心光束. 当局域空心光束为蓝失谐时, 光场中的原子将被囚禁在光场最弱处. 若加上抽运光, 原子将受到蓝失谐局域空心光束与抽运光共同激发的强度梯度Sisyphus冷却. 本文利用该方案产生的亚微米局域空心光束构建单原子的囚禁与冷却器件, 并以单个⁸⁷Rb原子为例, 利用Mont-Carlo方法研究亚微米局域空心光束中单原子囚禁与强度梯度冷却的动力学过程, 结果表明利用该器件可以获得温度在5.8 μK量级的超冷单原子.