Characterization of focusing performance of spiral zone plates with fractal structure

We propose an efficient method of generating a vortex beam with multi-foci by using a fractal spiral zone plate(FSZP), which is designed by combining fractal structure with a spiral zone plate(SZP) in the squared radial coordinate.The theoretical analysis reveals that the number of foci that embed vortices is significantly increased as compared with that obtained by using a conventional SZP. Furthermore, the influence of topological charge on the intensity distribution in focal plane is also discussed in detail. For experimental investigation, an FSZP with topological charge p = 1 and 6.4 mm diameter is fabricated by using a photo-etching technique. The calibration indicates that the focusing performances of such a kind of zone plane(ZP) accord well with simulations, thereby providing its potential applications in multi-dimensional optical manipulation and optical imaging technology.     

Optical vortices generated by multi-level achromatic spiral phase plates for broadband beams

We analyze the characterizations of the optical vortices generated by a multi-level achromatic spiral phase plate. The effective topological charge of the multi-level fractional spiral phase plate is expanded into Fourier series and the analytical formula of the relative intensity of each component is obtained. It is shown that the fractional part of the topological charge sharply reduces the purity of vortices. Using the 36 levels achromatic spiral phase plate, we can obtain a vortex beam with purity larger than 95% across a bandwidth exceeding 140 nm in the visible region of the spectrum.     

Observation of the rotational doppler effect for optical beams with helical wave front using spiral zone plate

A rotating spiral zone plate was used to implement and measure the rotational Doppler effect for plane-polarized optical beams with helical wave front (optical vortices). The frequency shift was analyzed in terms of energy exchange between the beams and moving optical elements.     

Generation of optical vortices with tunable intensity modulation

We analyze vortex properties of the optical beams generated by a spiral phase plate (SPP) which cannot modulate the phase of the incident beam range from 0 to 2π nicely, and find that the vortices have intensity modulation (IM) with central bright speckle. We construct an improved SPP to produce high quality optical vortices with definite IM. Theoretical analysis and real experiments show that this improved SPP can be used to produce optical vortices with configurable intensity modulation degree and without central bright spot.     

螺旋型波带片聚焦特性研究

提出了一种计算螺旋型波带片聚焦特性的方法。从衍射积分理论出发对螺旋型波带片的聚集特性进行了理论计算,推导出了级数形式的解析解,获得了螺旋型波带片"空心"焦点的场强分布。利用螺旋型波带片的聚焦特性,对其成像进行了数值模拟和理论分析。理论分析表明螺旋型波带片的空间分辨率与其"空心"焦点的环宽有关。通过验证实验证明理论分析与实验测试一致,为螺旋型波带片成像理论和模拟计算提供了一种有效手段。     

受限空间内旋流回流区特性

为了研究受限空间内旋流回流区的三维结构特性,采用realizable k-ε模型模拟了旋流数等于0.884时,不同受限空间内的旋流流场.受限率是影响回流区形态的重要因素,受限率大于6时,中心回流区与下游回流区是两个独立的区域,有两对涡结构;受限率在3～6之间时,中心回流区与下游回流区合并到一起,存在两对独立的涡结构;受...     

Optical vortex beam shaping by use of highly efficient irregular spiral phase plates for optical micromanipulation

Optical dark traps such as Laguerre-Gaussian beams, modulated optical vortices, and high-order Bessel beams have been used in the micromanipulation of microparticles. Such optical traps are highly versatile, as they are able to trap both high- and low-index microparticles as well as to set them into rotation by use of the orbital angular momentum of light. Holography has been widely used to modulate the shape of an optical vortex for new optical traps. We show that, by designing the shape of a spiral phase plate and using electron-beam lithography for fabrication, one can modulate the amplitude and the phase of an optical vortex with respect to the specific shape of the spiral phase plate as required. Furthermore, to the best of our knowledge this is the first report of transferring orbital angular momentum from a spiral phase plate to an absorptive microparticle in an experiment. Hence, with this technique, optical dark traps can easily be designed and fabricated.     

Improving the resolution of a solid immersion lens optical system using a multiphase Fresnel zone plate

We propose a method to improve the resolution of near-field optical system with a solid immersion lens by using a multiphase level Fresnel zone plate. The analyses are based on scalar angular spectrum theory. The results show that the multiphase Fresnel zone plate can not only decrease the spot size but also decrease the sidelobe intensity and enhance greatly the diffractive efficiency compared with annular amplitude filter or binary 2-, 3-, 4-zone phase filter.     

准随机点阵二值化Gabor波带片聚焦特性的数值计算

 Fresnel波带片有多个焦点,作为单色器波长选择元件使用时会受到高级衍射的影响。而Gabor波带片只有一个焦点,有更好的聚焦特性,但制作难度较大,准随机点阵二值化Gabor波带片概念的提出则解决了这个问题。介绍了准随机点阵二值化Gabor波带片的设计,并利用优化的程序分别对Fresnel波带片和准随机点阵二值化Gabor波带片的聚焦特性进行了模拟计算,通过对计算结果进行分析比较,发现准随机点阵二值化Gabor波带片具有抑制高阶衍射的特性。     

应用反射型球面菲涅耳波带片的成像物镜设计

设计了一种应用球面菲涅耳波带反射面与非球面反射面结合的成像物镜。对球面结构的菲涅耳波带反射面进行分析,推导了球面菲涅耳波带反射面近似替代非球面的方法,采用单片球面菲涅耳波带反射面和三片非球面反射面设计成像物镜,在放大倍数100×、视场角120°、菲涅耳数2.5情况下,调制传递函数在放大成像侧可实现0.6 lp/mm的40%以上,畸变小于2.2%。该设计方法为菲涅耳波带片应用于可见光成像提供了参考,并随着菲涅耳器件加工技术的不断发展具有良好的应用前景。     

Phase zone photon sieve

A novel diffractive optical element, named phase zone photon sieve (PZPS), is presented. There are three kinds of phase plates in PZPSs: PZPS1, PZPS2, and PZPS3. Each of the PZPSs has its own structure and is made on quartz substrate by etching. The three PZPSs have stronger diffraction peak intensity than a photon sieve (PS) when the margin pinhole and zone line width are kept the same. The PZPS3 can produce a smaller central diffractive spot than the ordinary PS with the same number of zones on the Fresnel zone plate. We have given the design method for and the simulation of PZPS and PS. PZPS has potential applications in optical maskless lithography.     

使用二元相位菲涅尔波带片产生轴向线聚焦

介绍了一种全新的轴向线聚焦方案.采用菲涅尔波带片，在实验中产生了沿轴向长为5mm，宽 100μm的线聚焦.光学测量表明，线聚焦轴向强度分布比较均匀.这些参数基本上可以满足激 光等离子体实验的要求. 关键词： 菲涅尔波带片 轴向线聚焦     

Manipulation of polarization-dependent multivortices with quasi-periodic subwavelength structures

Multiple vortices with different topological charges are formed by the use of two sequential geometric phase elements. These elements are realized by quasi-periodic subwavelength gratings. The first element is a spiral phase element and the second element is a spherical phase element. We provide a theoretical analysis and an experimental demonstration of the formation of the multiple vortices that comprise scalar vortices and a vectorial vortex.     

Diffractive Beam-Shaping Element for Generating Multiple Structured Beams with Distinct Spatial Structures

This paper presents a novel approach for generating structured light using a diffractive beam-shaping element that can generate multiple beams with distinct spatial structures in the focal plane. The element is constructed by restructuring a spiral zone plate with fork gratings, providing a tunable and controllable means for generating structured light. The element can create linear and 2D arrays of various structured beams, including vortices with adjustable charge and vorticity, petallike beams, and ring-lattice structures. To control the generation of these beams, it introduces several parameters of the fork gratings, enabling tailoring of the beam properties to specific applications. The proposed approach involves significant mathematical analysis, including the derivation of complex equations and expressions to understand the behavior of the proposed element and its impact on the generated beams. It conducts simulations and experiments to validate the mathematical analysis and demonstrate the feasibility of the proposed approach.     

Fresnel波带板编码成像技术

 介绍了Fresnel波带板编码成像原理,并设计出高空间分辨率的Fresnel波带板编码相机,用双孔可见光源对编码相机的成像进行了实验研究,表明该编码相机可以真实地还原源区的空间大小和形状。     

相因子判断法分析菲涅耳波带片的衍射场

基于波前相因子判断法,并考虑到波带片孔径的影响,揭示了波带片的衍射场所含基元成分及各成分在衍射场的积分表达式,并导出了沿轴的衍射场振幅分布公式及沿轴的振幅分布曲线,得到多个实焦斑的横向半值线宽和轴向半值线宽公式.本研究为波带片作为一种光学元件提供了一理论基础.     

Compound Fresnel Zone Lens Conformal to Truncated Cone: Antenna Application

A millimeter wave antenna consisting of two Fresnel zone plate lenses, plane and conical, is examined numerically by use of the vector diffraction theory. The lenses are of Wood-Wiltse (double-dielectric) or Soret (half-open) type, and are designed for the frequency of 117 GHz. The lenses are made conformal to a truncated circular cone with a base diameter of 500 mm and a plateau diameter of 250 mm. Designs for two opening semi-angles, 45° and 75° each of them with a particular lens thickness are presented. For the angle of 90° the cone lens becomes a plane ring lens, which in combination with the plateau zone lens forms a plane lens of size equal to the cone base diameter. Illuminated by directive feeds set at a focal distance of 525 mm from the cone apex, the double-dielectric and half-open compound and plane lenses, form three pairs of Fresnel zone lens antennas, the co-polar and cross-polar radiation characteristics of which have been compared numerically. The double-dielectric lens antennas examined are about 5 dB superior in gain to the half-open lens antennas, which has a gain of approximately 45 dBi. Because all lenses are of equal transverse aperture, the corresponding lens antennas exhibit the same −3 dB beamwidth of about 0.33 degrees. The plane zone lens antenna is very thin and simple. Instead, the antenna comprising a 3-D compound Fresnel zone lens is thicker but can be made conformal to a specific surface shape and possesses more levels of design and optimization freedom.     

激光直写制作高阶螺旋相位板及其性能

将拓扑荷为4的螺旋相位光束与平面光干涉的计算全息图输入到空间光调制器中,得到含有多个衍射级次的高阶涡旋光束。为提高衍射效率,利用激光直写技术制作拓扑荷为4的高阶螺旋相位板,经测定,相位板深度理论数值为1.073 m,测量数值为1.082 m,相位板制作误差在0.83%以内。平行光束通过此相位板时,在夫琅和费衍射场获得一个高质量的高阶光学涡旋,光强分布与理论数值基本吻合,衍射效率达到86%。     

An efficient and general numerical method to compute steady uniform vortices

Steady uniform vortices are widely used to represent high Reynolds number flows, yet their efficient computation still presents some challenges. Existing Newton iteration methods become inefficient as the vortices develop fine-scale features; in addition, these methods cannot, in general, find solutions with specified Casimir invariants. On the other hand, available relaxation approaches are computationally inexpensive, but can fail to converge to a solution. In this paper, we overcome these limitations by introducing a new discretization, based on an inverse-velocity map, which radically increases the efficiency of Newton iteration methods. In addition, we introduce a procedure to prescribe Casimirs and remove the degeneracies in the steady vorticity equation, thus ensuring convergence for general vortex configurations. We illustrate our methodology by considering several unbounded flows involving one or two vortices. Our method enables the computation, for the first time, of steady vortices that do not exhibit any geometric symmetry. In addition, we discover that, as the limiting vortex state for each flow is approached, each family of solutions traces a clockwise spiral in a bifurcation plot consisting of a velocity-impulse diagram. By the recently introduced “IVI diagram” stability approach [Phys. Rev. Lett. 104 (2010) 044504], each turn of this spiral is associated with a loss of stability for the steady flows. Such spiral structure is suggested to be a universal feature of steady, uniform-vorticity flows.     

Absolute interferometric test of Fresnel zone plates

An absolute interferometric test of two-level binary Fresnel zone plates (FZPs) is presented. Five measurements with a wavefront testing interferometer are required to fully separate interferometer errors from those of the FZP. The method provides both errors, pattern errors and surface figure errors of the zone plate absolutely. The test method is suitable for zone mirrors and zone lenses. Test setups are explained, equations are derived and experimental results are presented. Further, applications of the absolute diffractive test method are described. For the estimation of the accuracy of the diffractive calibration method a comparison with the classical three-position test was carried out.