Spatial distribution of the intensity of laser beam diffracted on the conical surface of an axicon

The field of diffraction from an axicon irradiated by a He-Ne laser has been studied. For this purpose the diffracting surface of the axicon is conceptually divided into tangential Fresnel regions. It is shown that evaluation of the Fresnel integral from only the first region provides a correct pattern of spatial distribution of the diffraction field of the axicon. The calculated distribution coincides sufficiently well with the experimental pattern. It is also shown that with a change in the laser beam radius and in the rounding of axicon vertex the location of maxima and minima of the diffraction field does not practically change.     

A practical ultrasound axicon for non-destructive testing

A practical water-coupled ultrasound axicon has been developed, which is realized by a combination of an annular PZT and a conical plexiglass wedge bonded to it. The acoustic beam from the PZT is refracted by the wedge and focused over a certain range in the axial direction. Two kinds of axicon are prepared for flaw examination of metals or ceramics. Suppression of the surface echo and sidelobes is discussed. Some examples which show the abilities of the axicons are also presented.     

Multiple filamentation generated by focusing femtosecond laser with axicon

Multiple filamentation has been observed when focusing a femtosecond laser pulse into a methanol solution with an axicon. It is found that multiple long filaments are located on the central spot and ring structures of the quasi-Bessel beam created by the axicon. Since the quasi-Bessel profile is determined by the axicon properties, the axicon has been suggested as a simple optics to control multiple filaments.     

Azimuthal variations in the brightness of Fabry-Perot axicon fringes

According to Fresnel relations, the transmission through an inclined dielectric plate depends on the orientation of the light vector relative to the plane of incidence. Since an axicon has a conical surface, linearly polarized incident light has different transmissivity through different portions of the axicon. It is shown that the difference in transmissivity, as a function of azimuthal angle, increases with increasing values of the vertex angle of the axicon. This effect causes inhomogeneity in the brightness of Fabry-Perot fringes, and for a slightly misaligned system can distort the shape of the scanning spectral line.     

用三光束干涉模型解释锥镜产生类贝塞尔光束

对高斯光束通过锥镜产生类似贝塞尔光束的环形光束进行了理论分析及实验研究.数值模拟过程中，基于相干光干涉理论，考虑到实际情况中锥尖不尖带来的影响，建立了三光束干涉的数学模型.模拟得到的光场分布与实验结果及基于菲涅尔衍射积分理论或空间光谱理论得到的零阶贝塞尔光束很接近.这种光场具有非衍射特性，可应用于新型光镊研究.     

Pattern generation using axicon lens beam shaping in two-photon polymerisation

The fabrication of three-dimensional microstructures by two-photon polymerisation has been widely reported as a viable route to the development of photonic crystals, rotors, bridges and other complex artefacts requiring nanoscale resolution. Conventionally, single point serial writing is used to write the structures but recently multipoint beam delivery using beam division optics has been reported as a method of introducing parallel processing. In this paper we present an alternative and novel approach using an axicon lens to give profiled beam delivery. This enables complete three-dimensional annular structure fabrication without the use of scanning stages. In addition, the concept of axicon delivery is developed further to investigate three-dimensional structure as a function of axicon geometry.A Ti:sapphire laser, with wavelength 795 nm, 80 MHz repetition rate, 100 fs pulse duration and an average power of 700 mW, was used to initiate two-photon polymerisation. The axicon was used, in combination with a 100× microscope objective, to form representative three-dimensional structures based on the annular cell with varying diameter. The structures were written in a Zr-loaded resin prepared on a glass substrate using dip coating deposition of a Zr/PMMA hybrid prepared by the sol-gel method. Annuli with diameters up to 50 μm were characterised in terms of topography and surface roughness using SEM and Zygo interferometer. The writing technique was also extended to fabrication of stacked structures.     

An absolute test for axicon surfaces

We present a method for absolute testing of axicon surfaces in a null test setup. The absolute test exploits the symmetry of axicons, which allows us to introduce a shift of the surface under test in both the axial and rotational directions while still maintaining the null test condition. With two shifts of the surface under test and four measurements, the interferometer and null optics error can be removed. The absolute surface local deviation can be obtained by wavefront reconstruction with a double-side spiral-path direct integration method. A simulation of the method, including typical systematic as well as statistical errors as input, is presented to estimate the error propagation. Experimental absolute test results of a 90° axicon surface are given.     

采用非线性相位拟合法设计长焦深透镜

针对惯性约束聚变(ICF)激光等离子体诊断系统应用的需求,提出一种采用非线性相位拟合法设计单透镜代替理想对数轴锥镜的方法。对所要得到的球面透镜与理想对数轴锥镜的相位进行拟合,求解得出所需要的球面透镜参量。设计了用于激光等离子体诊断系统的长焦深透镜,并对透镜的焦深、轴向光场均匀性、横向均匀性、焦斑旁瓣等指标进行分析。数值分析结果表明,长焦深透镜具有与理想对数轴锥镜相同的相位分布,焦深、轴向光场均匀性、横向均匀性、焦斑旁瓣均符合设计要求,验证了非线性相位拟合法的正确性。     

轴棱锥对无衍射光束的线聚焦特性

基于汉克尔波理论和衍射积分理论详细分析了轴棱锥对无衍射光束的线聚焦特性, 提出了一种产生周期性局域空心光束的新方法, 即无衍射贝塞尔光束经过轴棱锥聚焦后产生具有塔尔博特效应的局域空心光束. 数值模拟了无衍射贝塞尔光束照射轴棱锥后, 沿传输距离变化的光强分布及一个周期内光强的演变和局域空心光束的形成过程. 设计实验系统, 由He-Ne激光经过一套光学系统后透过轴棱锥, 产生近似无衍射贝塞尔光束, 再由第二个轴棱锥对产生的无衍射贝塞尔光束进行线聚焦, 在第二个轴棱锥后面由显微镜观测到周期性局域空心光束, 并用CCD照相机拍摄了两个周期内的光斑图, 实验结果和理论分析相符合. 研究结果可用于多层面微粒的操控, 对周期性局域空心光束在光学微操控领域的应用具有重要的指导意义. 关键词： 贝塞尔光束 轴棱锥 线聚焦 局域空心光束     

Formation of expanded smooth quasi-Bessel beam range due to the transformation of the Gaussian beam in absorbing axicon

The quasi-Bessel beam range produced by an absorbing axicon is investigated. It is shown that when an incident Gaussian beam is used, the absorbing axicon stretches (with respect to transparent axicon case) the uniform on-axis light intensity distribution length, as well as expanding the quasi-Bessel beam range. In addition, the peak of axial light distribution is shifted from the axicon tip. As a result any spatial modulation formed due to the bluntness of the tip is reduced close to the on-axis intensity peak, which becomes more smooth and uniform.     

液晶实时掩膜技术制作连续微光学元件

提出制作连续微光学元件的一种新技术———液晶实时掩膜技术 ,阐述了其基本原理和制作方法。基于部分相干光成像理论 ,采用计算机模拟了用实时掩膜制作微透镜和微轴锥镜阵列的过程。同时建立了实验装置进行实验 ,用全色银盐干板 (Kodak 131)通过酶刻蚀得到口径为 118.7μm ,深为 1.32 2 μm的 5 6× 48的轴锥镜的列阵。     

On-axis irradiance distribution of axicons illuminated by spherical wave

The focusing properties of an axicon illuminated by spherical wave are investigated. We define the Fresnel number of the focusing axicon impinged on by spherical wave. The on-axis irradiance distribution versus Fresnel number is studied. It is shown that, similar with the plane wave, focal squeeze, which is defined as deviations for the position of the maximum irradiance, also appears in low Fresnel number. Besides, the on-axis irradiance will be smoothed for appropriate curvature radius of the divergent spherical wave; meanwhile, when the convergent spherical wave is incident on the axicon, the on-axis irradiance varies more seriously.     

Converging-axicon-based radially polarized ytterbium fiber laser and evidence on the mode profile inside the gain fiber

The radially polarized mode is achieved from an active Yb fiber by utilizing of an intracavity converging axicon, where the axicon acts as a TM(01) mode selector based on not only its Brewster convex surface but also the distance between its vertex and plane output coupler. The polarization state of the annular laser beam is checked by using a home-made eight-hole aperture. Furthermore, an uncoated plane glass plate is inserted into the cavity, and the reflected beam points to the existence of an annular lasing mode inside the gain fiber. The issues for developing high-power radially polarized fiber lasers also are considered.     

产生不同类型局域空心光束的可拆式组合轴棱锥

提出一种产生尺寸可调局域空心光束的新型光学元件——可拆式组合轴棱锥,这种新型光学元件是在传统轴棱锥的中部沿其轴线方向贯通开设一圆孔,在圆孔内嵌设一第二轴棱锥组成。通过更换不同底角的第二轴棱锥(或第一轴棱锥),可形成不同尺寸的单个局域空心光束或周期性局域空心光束。从几何光学出发分析了产生局域空心光束的原理,计算了局域空心光束的相关参量。由衍射积分理论分析和模拟了新型光学元件的光强分布特性。几何光学和衍射理论所得分析结果基本吻合。     

像散对轴棱锥衍射特性的影响与修正

光束斜入射到轴棱锥上引起的像散将导致其衍射光场发生畸变,由衍射理论出发推导了受像散影响的轴棱锥衍射光场表达式. 通过模拟不同像散的衍射光斑图和同一像散影响下随轴向距离变化的光强分布图,分析了轴外像散对轴棱锥衍射特性的影响. 提出修正像散的方法并通过实验验证利用可调精密旋转轴棱锥修正轴外像散导致的光束畸变,理论分析和实验结果相符合,研究结果使轴棱锥的应用更加广泛. 关键词： 像散 贝塞尔光 轴棱锥 光束畸变     

基于无衍射光莫尔条纹的轴锥透镜锥角测量方法

为了准确地测量轴锥透镜锥角值，根据无衍射光同心圆环间距不随距离改变的特点和莫尔条纹放大的特性，提出了一种基于无衍射光莫尔条纹的轴锥透镜锥角的测量方法。当无衍射光束经分束器分光合束后形成莫尔条纹，平移其中一束光在图像传感器上的位置，实现莫尔条纹数量的变化，通过记录不同莫尔条纹下的中心距离计算出轴锥透镜锥角。实验以锥角为0.5°的轴锥透镜作为被测对象，与CMM测量结果进行比较，该文提出的方法相对测量误差近似为0.54%，重复性为0.86″，验证了该文方法测量轴锥透镜锥角的可行性。     

新型锥透镜产生局域空心光束

首次提出产生局域空心光束(Bottle beam)的另一类新型锥透镜模型.讨论了凹凸两种模型,分别是在传统轴棱锥的底部磨削和胶合圆台结构形成.研究结果表明平面波正入射新型凹锥透镜可产生单个Bottle beam,正入射新型凸锥透镜可形成具有周期性的Bottle beam.通过几何光学分析了产生Bottle beam的原理,计算了Bottle beam的相关参数.由衍射积分理论分析和模拟了新型锥透镜后的光强分布特性,所得分析结果与几何光学分析基本符合. 关键词： 新型锥透镜 Bottle beam 轴棱锥 Bessel光     

Design and fabrication of a double-axicon for generation of tailorable self-imaged three-dimensional intensity voids

We propose a new design for fabrication of a highly power-efficient double axicon to generate self-imaged three-dimensional intensity voids along the propagation of a beam. The conventional conical structure of an axicon is modified and shaped like an axiconlike structure with a double-gradient surface profile. The gradient conical surfaces generate Bessel beams with varying radial wave vectors that are superimposed and interfere to generate a sequence of three-dimensional intensity voids. The proposed element was fabricated using electron-beam lithography, and experimental verification of the design is reported.     

基于圆锥透镜生成双级无衍射光束的理论分析

为进一步完善多级无衍射光束的传输与转换理论,基于轴锥镜法和菲涅耳衍射理论对双级无衍射光束的光场分布做了详细理论分析,采用数值模拟软件对双级无衍射光束的空间光强分布与轴上光强分布进行仿真;基于锥镜加工工艺对锥镜顶点和一、二级锥镜临界点呈双曲线分布的双级轴棱锥透镜的光场分布进行研究,分析了双级无衍射光场的场强大小和影响光场振荡周期的因素。结果表明:理想双级轴棱锥透镜生成的无衍射光场由4个区域组成,在干涉重合区其光强为一、二级轴棱锥衍射场的耦合叠加,其余区域仍保持单级无衍射光场分布特性;锥镜顶点和一、二级锥镜临界点呈双曲线分布的双级轴棱锥透镜的光场分布受双曲线特征参数影响较大。其特殊的光场分布为多级无衍射光束拓展至大尺寸空间测量以及粒子微操作等提供了新的可能。     

DESIGN OF DIFFRACTIVE-PHASE AXICON ILLUMINATED BY A GAUSSIAN-PROFILE BEAM

The diffractive-phase axicon can convert the Gaussian-profile beam into axial uniform intensity distribution with long focal depth and high lateral resolution. Two types of phase-retardation functions for the nonuniform-illuminating axicon are derived in terms of the ray tracing and the geometrical law of energy conservation. Based on the general theory of the amplitude-phase retrieval in optical system and the iteration algorithm, the optimization design of the phase distribution of the diffractive-phase axicon can be achieved. The simulation celculations show that the new approach may successfully offer the design of the desired diffractive-phase axicon with long focal depth and high lateral resolution. A comparison of the performances of the holographic axicon with the phase-retardation functions from the geometrical optics prediction and the diffractive-phase axicon designed by the new approach is also presented.