部分相干光经柱面球差透镜聚焦所产生的焦移

利用Collins公式得出光强均匀部分相干光经柱面球差透镜聚焦后的轴上光强分布,并通过数值模拟的方法研究了入射光的菲涅耳数、相干度和透镜的球差对轴上点光强分布的影响.结果显示,当菲涅耳数较小、空间相干度较小的部分相干光经无球差透镜聚焦时,轴上点光强分布会产生焦移现象,而当部分相干光被球差透镜聚焦时,也会有焦移现象产生.     

椭圆高斯光束产生近似无衍射Bessel-Gauss光

研究了轴棱锥聚焦像散椭圆高斯光束的光场分布特性,根据菲涅耳衍射积分理论导出了椭圆高斯光束经轴棱锥衍射后的光场分布,通过数值积分给出椭圆高斯光束经轴棱锥聚焦后的近轴光场强度分布情况,将其与圆高斯光束产生的近似Bessel-Gauss场进行比较,发现椭圆高斯光束经轴棱锥聚焦后的光束在一定的传播距离内也具有无衍射特性,且轴上光强分布与圆高斯光束产生的Bessel-Gauss光束的轴上光强分布具有相似的形式,而这种无衍射光场的强度在垂直于光轴的平面上不再是柱对称分布。根据近轴球面波产生近似Bessel光束的最大无衍射距离公式计算了椭圆Bessel-Gauss光束在子午面和弧矢面上的最大无衍射距离,整个光束的无衍射距离由入射到轴棱锥上的椭圆光斑短轴方向的尺寸决定。     

轴锥镜光强分布的角谱衍射数值分析法

针对理论上推导轴锥镜的衍射光场分布解析式较为困难,且用菲涅耳衍射理论分析时存在近轴近似及不能适用于近场衍射光场分析的问题,采用了严格遵从标量衍射亥姆霍兹方程的角谱衍射波前重建方法,对轴锥镜在单色和准单色高斯光波照射下的横向和轴向衍射光强分布特性,以及在单色均匀平面光波照射下的轴向衍射光强分布进行了数值计算和分析。结果表明,轴锥镜后单色光衍射光强分布在几何光束重叠的菱形区域内为近似无衍射贝塞尔光强分布,轴上光强沿光轴方向呈振荡变化,轴上光强分布规律与入射光波的垂轴横向光强分布有关;入射光的准单色性使得贝塞尔衍射条纹对比度略下降、轴上光强沿光轴方向振荡程度减小,但分布规律与单色光一致。     

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.     

Generation of long plasma channels in air by focusing ultrashort laser pulses with an axicon

We show that by focusing ultrashort-pulsed laser beams in air with an axicon, relatively long plasma channels can be generated. The axicon generates Bessel-like beams, where the on-axis intensity stays high over distances much longer compared to focusing with conventional lenses. We developed a scheme to detect the presence of the plasma, based on its screening property. Using this scheme, we detected plasma channels longer than 1 m and 3.5 m generated by 8 mJ and 90 mJ input pulse energies, respectively. Our simulations show that axicon focusing can yield self-guided propagation with or without contribution of plasma, depending on the input pulse power.     

部分相干光被环形透镜聚焦而产生的焦移

 从理论上研究部分相干光被一环形透镜聚焦,在焦点附近的轴上点的光强分布。研究结果表明,当部分相干光被一环形透镜聚焦时,最大聚焦光强不在几何焦点,而是位于透镜与几何焦点之间,出现焦移现象。并且,焦移量不仅依赖于透镜外半径的菲涅耳数,还依赖于部分相干光的空间相干度和中心拦截比。透镜的菲涅耳数越小,焦移越大;部分相干光的空间相干度越低,焦移越大。当菲涅耳数一定时,环形透镜的中心拦截比越大,焦移越大;当空间相干度很小时,情况就变得比较复杂。     

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.     

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。     

The anomalous propagation of phase in the focus: A re-examination

The classical theory for focusing predicts that when a converging spherical wave is diffracted at an aperture on an opaque screen, the light ray undergoes a rapid π radian phase change in passing through its focus. In the present note, an objection to this prediction is put forward which embodies evidence that when the Fresnel number of the focusing system is of the order of unity or smaller, the phase change near the focus is neither rapid enough nor large enough to reach π radian and that, as a result, the anomalous propagation of the phase near focus is a specific phenomenon which is apparent only in systems of conventional optics, i.e., in systems with considerably large Fresnel numbers.     

Fresnel approximations for acoustic fields of rectangularly symmetric sources

A general approach is presented for determining the acoustic fields of rectangularly symmetric, baffled, time-harmonic sources under the Fresnel approximation. This approach is applicable to a variety of separable source configurations, including uniform, exponential, Gaussian, sinusoidal, and error function surface velocity distributions, with and without focusing in either surface dimension. In each case, the radiated field is given by a formula similar to that for a uniform rectangular source, except for additional scaling of wave number and azimuthal distance parameters. The expressions presented are generalized to three different Fresnel approximations that correspond, respectively, to diffracted plane waves, diffracted spherical waves, or diffracted cylindrical waves. Numerical results, for several source geometries relevant to ultrasonic applications, show that these expressions accurately depict the radiated pressure fields, except for points very near the radiating aperture. Highest accuracy near the source is obtained by choice of the Fresnel approximation most suited to the source geometry, while the highest accuracy far from the source is obtained by the approximation corresponding to diffracted spherical waves. The methods are suitable for volumetric computations of acoustic fields including focusing, apodization, and attenuation effects.     

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.     

Focusing properties of Gaussian Schell-model beams by an astigmatic aperture lens

This paper studies the focusing properties of Gaussian Schell-model (GSM) beams by an astigmatic aperture lens. It is shown that the axial irradiance distribution, the maximum axial irradiance and its position of focused GSM beams by an astigmatic aperture lens depend upon the astigmatism of the lens, the coherence of partially coherent light, the truncation parameter of the aperture and Fresnel number. The numerical calculation results are given to illustrate how these parameters affect the focusing property.     

Intensity distribution around the focal regions of real axicons

We present a theoretical and experimental study of the intensity distribution of a laser beam, after its propagation through a real axicon. We show that, while an ideal axicon generates Bessel-like radial intensity profile and smooth on-axis intensity around the focal region, in practice, the bluntness of the tip of the axicon causes significant deviations from these profiles. In particular, strong oscillations occur on the on-axis intensity. The input beam size also plays a strong role; for small beams the axicon acts more like a conventional lens, while for the large ones, it exhibits two focal regions. We also propose scheme for apodization. In all cases, the experiments match closely with the calculations. Our results show that axicons cannot be assumed to always generate smooth on-axis intensities and the structures coming from the real profiles should be taken into account for most applications.     

Extending the depth of focus with high NA lens axicon

Based on vectorial Debye theory, tight focusing of x-polarized beam with high NA lens axicon is studied. The high NA lens axicon utilizes spherical aberration to duplicate the performance of an axicon and to create an extended focal line. The intensity distribution in the focal region is illustrated by numerical calculations. We show that the high NA lens axicon system can generates a sub wavelength beam (0.826λ) with depth of focus around 10λ.     

高斯光束经过负球差透镜的聚焦

本文讨论高斯光束经过负球差透镜的聚焦，得到了聚焦光场轴上点的光强分布的表示式，并对其进行数值计算。数值计算结果表明，在负球差的情况下，得到光强的最大点位置（最佳聚焦点）相对于无球差情况，往透镜方向移动，并且，最佳聚焦点的光强较无球差时大，当Ｎｗ＝１，Ｎａ＝５，ｋＳ１＝－０．２时，得到的最佳聚焦点的光强是无球差时的１．３４倍。本文还讨论了透镜的菲涅尔数对聚焦光场分布的影响。结果表明，当透镜的菲涅尔数小于１时，球差对高斯光束的聚焦的影响可以忽略。     

应用于ICF等离子体诊断系统的长焦深光学元件设计

 针对惯性约束聚变激光等离子体诊断系统的特殊需求，提出采用对数型轴锥镜来实现长焦深功能，并采用超高斯边缘匀滑、中心切趾及选择合适的器件参数等方法优化了长焦深器件的性能。模拟实验证明，为了得到满足要求的长焦深、小焦斑、小旁瓣和均匀的轴上及横向光场分布的聚焦光束，对数型轴锥镜的焦深应为3~5 mm；元件中心须采用切趾，而且切趾半径应为15~60 mm；元件边缘宜采用5阶超高斯匀滑。设计出焦深长达3 mm、轴上光强均匀、旁瓣峰值小于中心强度的2%且横向光斑较均匀的长焦深器件，可以满足激光等离子体诊断的要求，并用菲涅耳衍射积分对该元件光场的模拟实验验证了该方法的可行性。     

High Efficient Tunable Fractal Axicon Based on LCoS

Based on the Cantor function and phase modulation, a tunable fractal axicon is formed on a liquid crystal on silicon （LCoS） with an improved generating method. It has higher focusing efficiency in higher fractal stage and approaches to 100% theoretically. The on-axis intensity keeps its fractal structure unchanged in operation of fractal stages. The tunability of the axicon is demonstrated by tune fractal stage from 1 to 3 and focal length from 0.8 m to 1 m. We also provide details of theoretical analyses and experimental results.     

Diffractive Multifocal Focusing of Gaussian Beams

The problem of diffraction of a spherical wave with Gaussian amplitude distribution on two infinitesimally thin and ideally reflecting screens with apertures on an optical axis is solved within the quasi-optical approximation. It is shown that when a Gaussian beam illuminates a bicomponent diffraction system with small Fresnel numbers in a near zone of the second screen, the effect of diffractive multifocal focusing of radiation is observed. In this case, the diffraction picture from the second screen in the focal planes represents the circular nonlocal bands of the Fresnel zones with a bright narrow peak at the center, whose intensity can exceed by six times the value of the incident wave intensity. The energy efficiency of diffractive focusing of Gaussian beams by the bicomponent diffraction system can be as high as 70%. The proposed diffractive method allows the focusing of the wide-aperture beams without using classical refraction elements such as lenses and prisms, and it is applicable to both low-intensive and high-power radiation.     

Diffractive Focusing of a Gaussian Beam

The problem of diffraction of a spherical wave with Gaussian amplitude distribution on two infinitesimally thin and ideally reflecting screens with apertures on an optical axis is solved within the framework of the quasi-optical approximation. It is shown theoretically and experimentally that when a Gaussian beam illuminates such a type of bicomponent diffraction system with small Fresnel numbers in a near zone of the second screen, the effect of diffractive multifocal focusing of radiation is observed. In this case, the diffraction picture from the second screen in the focal planes represents the circular nonlocal bands of the Fresnel zones with a bright narrow peak at the center, whose intensity can exceed by six times the value of the incident wave intensity. The energy efficiency of diffractive focusing of Gaussian beams by the bicomponent diffraction system can be as high as 70%. The diffractive method proposed allows the focusing of wide-aperture beams without using classical refraction elements such as lenses and prisms, and it is applicable to both low-intensity and high-power radiation.     

Diffractive Multifocal Focusing of Gaussian Beams

The problem of diffraction of a spherical wave with Gaussian amplitude distribution on two infinitesimally thin and ideally reflecting screens with apertures on an optical axis is solved within the quasi-optical approximation. It is shown that when a Gaussian beam illuminates a bicomponent diffraction system with small Fresnel numbers in a near zone of the second screen, the effect of diffractive multifocal focusing of radiation is observed. In this case, the diffraction picture from the second screen in the focal planes represents the circular nonlocal bands of the Fresnel zones with a bright narrow peak at the center, whose intensity can exceed by six times the value of the incident wave intensity. The energy efficiency of diffractive focusing of Gaussian beams by the bicomponent diffraction system can be as high as 70%. The proposed diffractive method allows the focusing of the wide-aperture beams without using classical refraction elements such as lenses and prisms, and it is applicable to both low-intensive and high-power radiation.