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.     

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.     

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。     

Design of diffractive axicons for partially coherent light

We propose a novel method of designing diffractive axicons for use in spatially partially coherent illumination. The design procedure is based on the results obtained by the stationary-phase method. The technique leads to a coherence-dependent differential equation with appropriate boundary conditions for the axicon phase function. We demonstrate the method with annular-aperture axicons generating extended focal line segments of uniform on-axis intensity.     

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。     

Fresnel axicon

A new optical element, a Fresnel axicon (fraxicon), is proposed. Similar to a Fresnel lens, this element consists of concentric prism-like grooves with an apex angle equal to that of a bulk axicon and whose action relies on refraction. The fraxicon is less chromatic and simpler to manufacture than holographic optical element-based diffractive axicons and, in comparison with regular refractive axicons, is more compact with less absorption loss in the material while allowing significant economy in mass production.     

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.     

非相干光源无衍射光的自重建

基于Hankel 波理论分析了非相干光源产生Bessel光束的自重建特性, 利用光学设计软件ZEMAX模拟了Bessel光束经过轴上圆形障碍物后的截面光强分布. 由于发光二级管(LED) 具有一定的频谱宽度且不像激光具有很高的相干度, 因此我们采用一定频宽范围的连续谱来描述. 从模拟结果可以直观地看出Bessel光束被轴上圆形障碍物遮挡后逐步完成自重建, 说明用LED非相干光作为光源具有自重建特性.实验上采用LED和轴棱锥元件产生Bessel光束, 然后通过轴上圆形障碍物、轴上方形障碍物, 并拍摄了不同位置处的截面光强分布图, 证实了非相干光源产生Bessel光束的自重建特性.实验结果和模拟结果相符合. 关键词： 无衍射光束 LED光源 轴棱锥 自重建     

衍射和干涉理论对Bessel光传输的描述

 采用衍射积分理论和干涉理论分别对轴棱锥产生的Bessel光的传输特性进行描述,并讨论了其适用条件和优缺点。数值模拟了光传输的3维强度分布,同时进行相关参数的实验测定。数值模拟和实验结果表明：在最大无衍射距离内,衍射理论能很好地描述Bessel光的轴上光强分布,当接近或超出最大无衍射距离时,干涉理论也能较好地描述Bessel 光的强度分布,实验结果和理论分析基本吻合。     

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.     

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。     

Interference patterns of two non-diffracting beams

The interference field of two non-diffracting beams is derived analytically. We arrange the experiments with an axicon illuminated by two monochromatic oblique beams. Based on the diffraction properties of an axicon in the case of oblique illumination, the intensity distribution of interference pattern was calculated, and it was demonstrated to be the superposition of zero-order Bessel functions. The locus of interference fringes is also analyzed to be hyperbola according to the zero formula of zero-order Bessel function. The experimental results are verified the numerical simulation.     

Design and Analysis of Diffractive Axicons for Gaussian Beam Illumination

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

Wavelength-dependent intensity distribution of a Gaussian beam scattered by a spherical particle

The wavelength-dependent intensity of a light beam scattered by an isotropic homogeneous particle illuminated with an on-axis monochromatic polarized Gaussian beam is calculated in this paper. The vector spherical harmonics expansion and T transformation matrix are used to form the theoretical basis. Numerical results show that the angular intensity distribution is symmetric for an on-axis polarized Gaussian beam illumination upon an aqueous spherical particle at 473, 532 and 660 nm. For the specified aqueous spherical particle, the scattered intensity distribution decreases with increase in wavelengths.     

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。     

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.     

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.     

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。     

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.     

Comparison of photonic nanojets key parameters produced by nonspherical microparticles

Photonic nanojet (PNJ) phenomenon arising near transparent dielectric microparticles subject to plane wave illumination in the visible is considered. The near-field light scattering patterns produced by shaped wavelength-sized particles (hexahedron, cuboid, sphere, hemisphere, axicon, assembled particles) are numerically simulated and key PNJ parameters are analyzed. Particle shape influence on the peak intensity and spatial resolution of produced PNJ is investigated. We demonstrate that due to the reciprocal action of spherical-type and conical-type focusing of the special type of composite particles constituted of a hemisphere and an axicon can produce highly localized PNJ with peak intensity considerable higher than that for isolated regular particle (sphere, microaxicon, hemisphere).