Design and Analysis of Diffractive Axicons for Gaussian Beam Illumination

1　Ｉｎｔｒｏｄｕｃｔｉｏｎ　　Ｒｅｃｅｎｔｌｙｔｈｅｒｅｈａｓｂｅｅｎｃｏｎｓｉｄｅｒａｂｌｅｉｎｔｅｒｅｓｔｉｎｄｅｓｉｇｎａｎｄａｎａｌｙｓｉｓｏｆｔｈｅｄｉｆｆｒａｃｔｉｖｅａｘｉｃｏｎｓｔｈａｔｐｒｏｄｕｃｅａｆｏｃａｌｓｅｇｍｅｎｔｗｉｔｈｎｅａｒｌｙｕｎｉｆｏｒｍｏｐｔｉｃａｌｉｎｔｅｎｓｉｔｙａｌｏｎｇｔｈｅｓｙｓｔｅｍａｘｉｓｗｉｔｈｉｎａｓｐｅｃｉｆｉｅｄｒｅｇｉｏｎｂｅｈｉｎｄｔｈｅｅｌｅｍｅｎｔ[1～1 2 ] .Ｔｈｉｓｉｓｄｕｅｔｏｔｈｅｉｒｕｎｕｓｕａｌｐｒｏｐｅｒｔｉｅｓａ…     

部分相干光束照射的透镜轴棱锥获得均匀焦线

从部分相干光的交叉谱密度函数传输公式出发,推导了高斯谢尔模型(GSM)光束被球差透镜衍射后轴上光强分布的解析公式,并进行了数值模拟和物理分析。结果表明,具有一定束腰宽度和空间相干度的GSM光束经过负球差透镜聚焦后,可以获得轴上光强的均匀分布。通过改变GSM光束的束腰宽度和空间相干度来实现轴上光强均匀分布的方法很简单,转换效率高。     

Lens axicon illuminated by polychromatic Gaussian beams for generating uniform focal segments

In this paper, we investigate a lens axicon, which actually is a lens with spherical aberration, illuminated by a polychromatic Gaussian beam for producing an extended axial line image of a desired length and nearly uniform intensity. A numerical calculation is performed to investigate the dependence of the axial intensity distribution of the focal segment on the parameters of the incident polychromatic Gaussian beam. It is shown that, compared with monochromatic Gaussian beam illumination, the illumination of the polychromatic Gaussian beam may improve the uniformity of the distribution of the axial intensity, and this improvement in the uniformity of the axis intensity is strongly dependent on the spectral width of the incident Gaussian beam. Moreover, apodization with annular super-Gaussian amplitude distribution is employed to reduce the undesired oscillation of the axial intensity.     

基于轴棱锥产生近似无衍射Mathieu光束的新方法

提出了一种基于轴棱锥产生零阶近似无衍射Mathieu光束的新方法,利用轴棱锥聚焦具有椭圆高斯振幅调制的平面波,得到近似零阶无衍射Mathieu光束.根据椭圆高斯平面波经轴棱锥衍射的衍射积分公式,对光强分布进行了数值模拟,依据几何光学模型计算了近似无衍射Mathieu光束的最大无衍射距离,并设计了实验对理论模拟的结果进行了验证.实验采用柱透镜和准直扩束系统变换圆高斯光束产生具有椭圆高斯振幅调制的平面波,用轴棱锥聚焦该平面波后得到近似无衍射Mathieu光束,实验结果与理论模拟和计算相符.     

高数值孔径下高斯光束超分辨技术

利用矢量衍射理论,研究了高数值孔径下高斯光束的超分辨特性,对可以实现超分辨的二环和三环相位结构进行了优化求解,分析了环带半径和相位变化对超分辨性能的影响规律,给出了优化方法和优化结果.研究结果表明:当和平面波照明具有相同的旁瓣比时,使用高斯光束照明仍然可以实现光学超分辨;采用二环相位结构时,内环半径的控制比较关键,相位的微小改变对超分辨性能的影响不大,二环相位结构具有加工容差大的优点;三环相位结构在相同旁瓣比的情况下能够达到较大的压缩比和较小的主瓣峰值强度,三环结构的半径和相位的改变对超分辨性能的影响较大,其加工容差要小于二环相位结构;无论二环或三环相位结构,若提高压缩比,必然会引起主瓣峰值强度降低和旁瓣比增大.该研究为高数值孔径下,高斯光束照明时,超分辨光瞳滤波器的优化设计提供了一种新方法.     

圆锥透镜对倾斜球面波光束的衍射模式

由于球面波入射圆锥透镜所产生的出射光束具有焦深长和中心光斑直径较小的特点,适合激光通信以及长距离测量.在实际使用中,入射球面波很可能与圆锥透镜的光轴发生倾斜.研究了圆锥透镜对倾斜球面波光束的衍射特性,通过基尔霍夫衍射理论以及稳相法分析,分析了其径向衍射光场分布形式,并用计算机进行了仿真.使用了半径为15 mm、底角为1°的圆锥透镜进行实验,并对仿真结果进行了验证.仿真和实验证明,减小入射球面波曲率半径、出射光束传输距离和入射光束倾斜角都可以减弱入射光束倾斜对衍射图的影响.     

Enhancement of Axial Trapping Force in a Single-beam Gradient Optical Trap by a Pair of Axicons

1　Ｉｎｔｒｏｄｕｃｔｉｏｎ　　ＴｈｅｆｉｒｓｔｗｏｒｋｗｉｔｈｏｐｔｉｃａｌｔｒａｐｐｉｎｇｏｎｓｍａｌｌｐａｒｔｉｃｌｅｓｗｅｒｅｄｏｎｅｂｙＡｓｈｋｉｎｅｔａｌ.ｉｎ1 985ａｎｄ 1 986 [1,2 ] ,Ｗｈｏｓｕｃｃｅｓｓｆｕｌｌｙｄｅｍｏｎｓｔｒａｔｅｄｔｈａｔｍｉｃｒｏｓｃｏｐｉｃｐａｒｔｉｃｌｅｓｃｏｕｌｄｂｅｔｒａｐｐｅｄｂｙａｓｉｎｇｌｅｆｏｃｕｓｓｅｄｌａｓｅｒｂｅａｍ .Ａｎｕｍｂｅｒｏｆｄｅｍｏｎｓｔｒａｔｉｏｎｓｏｆｔｒａｐｐｉｎｇａｎｄｍａｎｉｐｕｌａｔｉｏｎｏｆｂｉｏｌｏｇｉｃａｌ…     

Enhancement of Axial Trapping Force in a Single-beam Gradient Optical Trap by a Pair of Axicons

A special kind of axicon prisms for beam transformation and enhancement of axial trapping force in a single-beam gradient optical trap is put forward. By inserting a pair of axicons into the parallel illumination path of a trapping objective, a center-weighted TEM00 Gaussian beam was transformed into an edge-weighted beam. Edge-weighted illumination for the trapping objective was thus realized, which is significant for the enhancement of axial trapping force. Based on a method of external sinusoidal excitation and lock-in detection, we precisely calibrated the axial spring constants of the same optical trap under different illumination conditions. The comparison results confirmed the feasibility of enhancing the axial trapping force by a pair of axicon. Moreover, the strength of enhancement was found to be dependent on the apodization factor for the input TEM00 Gaussian beam.     

高斯光束非对称照明锥镜时的衍射场分布

采用光的干涉方法研究了高斯光束非对称照明锥镜时的衍射场分布。数值模拟结果发现，当光束中心偏离锥镜的轴线时，衍射场的分布不再呈对称状分布，尤其在相干区。照明光束的偏离量越大，衍射光斑偏离锥镜的轴线越多。衍射光斑的平均光强随照明光束偏离量的增加迅速减小。这些结果对于锥镜在光镊和光学元件的机械排列等应用中具有一定的指导意义。     

螺旋轴棱锥的光束传输特性

 分析了螺旋轴棱锥的结构和光传输特性,基于衍射积分理论研究了发散球面波和拉盖尔-高斯光束经螺旋轴棱锥后的传输过程。研究表明,发散球面波经过螺旋轴棱锥后产生贝塞尔光束,其阶数与拓扑电荷数相同,但中心光斑（空心光斑）半径随传输距离的增加而变大;拉盖尔-高斯光束入射后同样产生贝塞尔光束,但其阶数变为拉盖尔-高斯光束和螺旋轴棱锥的拓扑电荷数之和,出射光束的拓扑电荷数与阶数相等。     

平顶飞秒激光经圆锥透镜在熔融石英中成丝及超连续辐射

实验研究了平顶飞秒激光经圆锥透镜后在熔融石英中的成丝及超连续辐射.与高斯飞秒激光的成丝对比发现,平顶飞秒激光可以获得在圆锥透镜焦深区域内强度分布更为均匀的等离子体细丝,这一特征更有利于飞秒激光在固体介质中进行微纳加工等领域的应用.并且,在不损伤熔融石英的条件下,平顶飞秒激光成丝可以获得更高能量、更高转换效率的超连续辐射,这是因为若产生光强相近的细丝,平顶飞秒激光所需的初始激光能量更高,此激光能量下产生的细丝长度更长、均匀性更好.     

Homogenization of on-axis intensity distribution produced by a Fresnel refractive axicon

The on-axis intensity distribution of a beam generated by a Fresnel axicon (fraxicon) is experimentally and numerically examined and compared to a classical axicon. Monochromatic illumination produces strong oscillations in this distribution due to diffraction from the fraxicon facets combined with shadowing effects. It is shown that by proper selection of the ratio of the illuminating light wavelength to the period of the fraxicon these oscillations can be minimized by exploiting interference. In addition, polychromatic illumination of the fraxicon also permits homogenization of the on-axis intensity with some remaining oscillations at the start of the depth of field which can be reduced by decreasing the period of the fraxicon.     

Focus shaping of tightly focused TEM11 mode cylindrically polarized Laguerre Gaussian beam by diffractive optical element

We study the focus shaping of tightly focused TEM₁₁ mode cylindrically polarized Laguerre Gaussian beam with high numerical aperture lens axicon system is investigated theoretically by vector diffraction theory. The intensity pattern at the focus can be tailored by appropriately adjusting the rotation angle. We show that the high NA lens axicon system can generates a sub wavelength focal spot, focal hole, focal splitting and flat-topped focal shapes with extended depth of focus.     

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。     

Optical properties of light filter designed on absorbing axicon

The optical properties of a light filter designed based on an absorbing axicon are studied. It is shown that if axes of the filter and a radially symmetric incident beam coincide, then the light transmission through the filter is minimal. This phenomenon can be used to find the beam center, radius and divergence, as well as to form properly collimated Gaussian beams. The filter allows the apodization and continuously tuning of the laser radiation intensity.     

Bessel光束经椭圆环形孔径后的衍射光场

基于菲涅耳衍射积分理论及硬边孔径的复高斯函数展开法导出了Bessel光束经椭圆环形孔径后的光场表达式, 数值模拟了其光场的强度分布. 研究了Bessel光束经椭圆环形孔径后的光场变化及其传播过程; 在实验上利用轴棱锥输出的近似无衍射Bessel光, 通过椭圆环形孔径, 使用电荷耦合器件拍摄得到不同传播距离处的光强分布. 理论结果和实验结果均表明无衍射光束经椭圆环形孔径后会产生空心光束.     

Measuring the topological charge of optical vortices with an axicon

We analyzed the spatial spectrum of the diffraction intensity pattern of an ideal Bessel beam and found an implicit rule that the number of the bright rings in the spatial spectrum is equal to the topological charge of the Bessel beam. The radius of the bright and dark rings has some relation with the topological charge and can be determined accurately. It provides us with a new way for measuring the topological charge of an optical vortex through its diffraction intensity pattern after an axicon. The results of simulation coincide with the theory.     

自成像局域空心光束产生的新方法及粒子俘获

本文提出了产生自成像局域空心光束(self-imaged bottle beams)的一种光学元件------液体轴棱锥.从衍射理论结合几何光学对经过轴棱锥后的光场进行了分析, 得出注入液体折射率小于轴棱锥材料折射率时可产生自成像局域空心光束.并通过软件MathCAD模拟, 得到一个完整周期光束的变换过程和局域空心光束的演变过程.研究发现液体轴棱锥产生的自成像局域 空心光束具有周期及相干长度可调的特点.分析了如何利用自成像局域空心光束对粒子进行俘获, 讨论了用自成像局域空心光束进行多层面粒子俘获的优势.     

衍射理论对局域空心光束及无衍射光束重建的描述

利用衍射理论导出了局域空心光束的传输表达式及光强分布,给出了局域空心光束的精细结构,详细分析了其演变过程。讨论了聚焦透镜的焦距f对径向暗域最大尺寸及轴上暗域长度的影响。结果表明,径向暗域最大尺寸及轴上暗域长度都随着f的增大而增大。通过轴棱锥-透镜系统获得局域空心光束,用体视显微镜和CCD照相机组成的系统拍摄光束强度分布。结果表明应用衍射理论可以较精确地描述局域空心光束的演变过程。找出了其应用中的不利因素,更清晰地展现无衍射光束的重建现象。这种描述方法弥补了几何理论和干涉理论的不足。     

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.