Tight focusing of radially polarized Gaussian and Bessel-Gauss beams

We examine the effects of tightly focusing a radially polarized beam with uniform, Gaussian, or Bessel-Gauss pupil functions. The resulting FWHM is smallest for the case of a uniform amplitude profile, while the Bessel-Gauss beam results in the largest FWHM. The uniform amplitude profile also results in an axial field component that increases fastest with increasing NA. The ratio of the axial component to the transverse component is also the greatest for the uniform pupil function. On the other hand, the Bessel-Gauss beam benefits the most from the use of an annulus.     

The focusing property of vector Bessel-Gauss beams by a high numerical aperture objective

The rich available transverse intensity structure of vector Bessel-Gauss beams make it important to probe into the focusing property by high numerical aperture objective. In this paper, we obtain the analytical expressions of azimuthally, radially and longitudinally polarized components in the focal area of the objective after tight focusing. Theoretical analysis and the numerical simulation show that, the transverse intensity distributions of the focused beams still have doughnut-like structure, two separate peak structure and circularly aligned array structure. The focused beam spots obtained by an objective with annular aperture usually have smaller spots than with circular aperture. The focused beam of the vector Bessel-Gauss beam with lowest mode number m = 0 is a radially and azimuthally polarized doughnut-like beam with no longitudinal component. These properties and results are useful in optical trapping and particle alignment.     

Bessel-Gauss beams: Investigations of thermal effects on their generation

The effects of heat load on longitudinally diode-pumped solid-state laser for generation of Bessel-Gauss (BG) beams are considered and the beam profile under Gaussian and super-Gaussian pump profiles are fully investigated. The results are not only in good agreement with the experimental results of a 2W Nd:YAG laser generating the BG beams but also explain the discrepancy between the theory and experiment reported by Hakola et al. [A. Hakola, S.C. Buchter, T. Kajava, H. Elfstrom, J. Simonen, P. Paakkonen, J. Turuen, Opt. Commun. 238 (2004) 335.]     

超短脉冲贝塞尔-高斯光束在自由空间的传输特性

 使用复解析信号法研究了束宽与频率无关的超短脉冲贝塞尔-高斯光束在自由空间的传输特性。研究表明：在无衍射长度内,超短脉冲贝塞尔-高斯光束的横向光强分布几乎不变并集中在传输轴附近,轴上脉冲随传输距离增加而展宽。在无衍射长度外,横向光强分布显著扩展。随传输距离增加,轴上光谱蓝移先增加,达到极大值后逐渐减小,最后在远场趋于一渐近值。对单周期的超短脉冲贝塞尔-高斯光束的轴上光谱蓝移先增加,达到极大值0.50 fs^-1。然后逐渐减小,在远场蓝移趋于渐近值0.16 fs^-1。     

贝塞尔-高斯脉冲光束在色散介质中的时间和光谱特性

对等衍射长度贝塞尔-高斯脉冲光束在色散介质中的时间和光谱特性作了研究,结果表明,通过选择适当的空间参数,贝塞尔-高斯脉冲光束沿轴上传输时,脉冲宽度不变。传输距离小于无衍射长度时,随衍射角增加,功率谱形状未变,脉冲波形保持不变;传输距离大于无衍射长度时,随衍射角增加,光谱由蓝移变为红移,脉冲展宽。     

贝塞尔-高斯脉冲光束在色散介质中的时间和光谱特性

 对等衍射长度贝塞尔-高斯脉冲光束在色散介质中的时间和光谱特性作了研究,结果表明,通过选择适当的空间参数,贝塞尔-高斯脉冲光束沿轴上传输时,脉冲宽度不变。传输距离小于无衍射长度时,随衍射角增加,功率谱形状未变,脉冲波形保持不变;传输距离大于无衍射长度时,随衍射角增加,光谱由蓝移变为红移,脉冲展宽。     

Intensity and spatial correlation properties of tightly focused partially coherent radially polarized vortex beams

By expanding the Debye theory into the tight focusing of partially coherent field, the intensity and spatial correlation properties of partially coherent radially polarized vortex beams are studied. Expressions are derived for the intensity distribution and the spectral degree of coherence in the focal region. It is found that the intensity and the transverse and longitudinal coherence degrees in the focal region change with the variation of the topological charge and coherence length of the vortex beam. In addition, the degree of coherence is shown to exhibit phase singularities.     

Hollow Gaussian beams and their propagation properties

A new mathematical model, described as hollow Gaussian beams (HGBs), is proposed to describe a dark hollow laser beam (DHB). The area of the dark region across the HGBs can easily be controlled by proper choice of the beam parameters. Based on the Collins integral, an analytical propagation formula for the HGBs through a paraxial optical system is derived. The HGBs also can be expressed as a superposition of a series of Lagurerre-Gaussian modes by use of a polynomial expansion. As a numerical example, the propagation properties of a DHB in free space are illustrated graphically. The HGBs provide a convenient and powerful way to describe and treat the propagation of DHBs and can be used conveniently to analyze atoms manipulated with a DHB.     

轴对称矢量光束聚焦特性研究现状及其应用

轴对称矢量光束是一种空间非均匀偏振光束, 中心光强为零, 经物镜聚焦后能在焦点附近产生空间场分量. 在高变迹系数光学系统成像情况下, 与线偏光、圆偏光相比, 径向偏振光与光瞳滤波技术及图像复原技术结合, 能获得较小焦斑, 提高横向分辨力. 介绍了轴对称矢量光束的特性, 基于电偶极子辐射模型和矢量衍射理论研究了轴对称矢量光束经高数值孔径物镜聚焦后的特性, 系统介绍了基于轴对称矢量光束实现光斑紧聚焦的几种方法, 并简述了轴对称矢量光束在差动共焦超分辨成像领域的研究设想. 关键词： 差动共焦显微技术 紧聚焦 光瞳滤波 轴对称矢量光束     

Axial intensity distribution of truncated Bessel-Gauss beams in a turbulent atmosphere

By means of the extended Huygens-Fresnel integral formula in the paraxial approximation and based on the fact that a hard aperture function can be expanded into a finite sum of complex Gaussian functions, an approximate analytical expression for Bessel-Gauss beams propagating in a turbulent atmosphere truncated by an aperture has been derived. The result is more convenient for studying the axial intensity distribution properties of Bessel-Gauss beams with different topological charges in a turbulent atmosphere than the usual way by using diffraction integral directly. Utilizing the analytical expression, the axial intensity distribution of such kind of beam in a turbulent atmosphere is investigated numerically in detail. Results show that the intensity distribution on the axis changes with the variation of the beam topological charge m, the wavelength and beam waist width of the initial beam and the turbulent strength.     

Design of projective zone plates and their focusing properties

Transmittances are designed by generation of a family of curves whose local geometry is similar to that of zone plates. The family is obtained by means of projective mapping in the normal direction of an initial curve, so that all the curves of the family have a common evolute. This property allows the prediction of the geometry of the focusing region of the transmittance. Experimental results with an ellipse as the initial curve are shown. We show that the proposed zone plates can be considered a generalization of conventional zone plates.     

Off-axial elliptical cosine-Gaussian beams and their propagation properties

In this paper, a new kind of light beam called off-axial elliptical cosine-Gaussian beam (ECosGBs) is defined by using the tensor method. An analytical propagation expression for the ECosGBs passing through axially nonsymmetrical optical systems is derived by using vector integration. The intensity distributions of ECosGBs on the input plane, on the output plane with the equivalent Fresnel number being equal to 0.1 and on the focal plane are respectively illustrated for the propagation properties. The results indicate that an ECosGB is eventually transformed into an elliptical cosh-Gaussian beam. In other words, ECosGBs and cosh-Gaussian beams act in a reciprocal manner after propagation.     

Partially coherent nonparaxial Hermite-Gaussian beams and their propagation properties

The concept of partially coherent nonparaxial Hermite-Gaussian (HG) beams is proposed. By using the generalized Rayleigh-Sommerfeld diffraction integral, the closed-form propagation equations of partially coherent nonparaxial HG beams in free space are derived. The on-axis intensity, far-field and paraxial expressions, and specifically, the free-space propagation equations of partially coherent nonparaxial Gaussian Schell-model beams are given, and treated as special cases of our results. It is found that the f and f_σ parameters play a crucial role in determining the nonparaxiality of partially coherent TEM_mn-mode HG beams. Only if the f and f_σ parameters are small enough, the paraxial approximation is applicable.     

Surface plasmon interference excited by tightly focused laser beams

We show that interfering surface plasmon polaritons can be excited with a focused laser beam at normal incidence to a plane metal film. No protrusions or holes are needed in this excitation scheme. Depending on the axial position of the focus, the intensity distribution on the metal surface is either dominated by interferences between counterpropagating plasmons or by a two-lobe pattern characteristic of localized surface plasmon excitation. Our experiments can be accurately explained by use of the angular spectrum representation and provide a simple means for locally exciting standing surface plasmon polaritons.     

On focusing of terahertz radiation beams and pulses

We show that, for terahertz (THz) radiation, the effective focal length of a lens differs significantly from its geometrical-optics (nominal) focal length. As a pulse of THz radiation with a bell-shaped (Gaussian) transverse profile is incident on a lens, the field-amplitude distribution in the nominally focal plane of the lens may radically change, up to the formation of dips in the paraxial region. These changes in the spatiotemporal shape of the beam (pulse) may considerably distort the results of pulsed THz spectroscopy. These distortions can be minimized by using media with anomalous dispersion, including metamaterials.     

Experimental verification on tightly focused radially polarized vortex beams

The theoretical and experimental results of tightly focused radially polarized vortex beams are demonstrated. An auto-focus technology is introduced into the measurement system in order to enhance the measurement precision, and the radially polarized vortex beams are generated by a liquid-crystal polarization converter and a vortex phase plate. The focused fields of radially polarized vortex beams with different topological charges at numerical apertures （NAs） of 0.65 and 0.85 are measured respectively, and the results indicate that the total intensity distribution at focus is dependent not only on the NA of the focusing objective lens and polarization pattern of the beam but also on the topological charge l of the beam. Some unique focusing properties of radially polarized vortex beams with fractional topological charges are presented based on numerical calculations. The experimental verification paves the way for some practical applications of radially polarized vortex beams, such as in optical trapping, near-field microscopy, and material processing.     

紧聚焦轴对称矢量光场波前调控及应用

作为光波最重要的本征物理属性之一,光场偏振态在研究光与物质相互作用中占有重要地位。矢量光场的波前调控为其聚焦场提供了更加复杂、更加灵活可控的振幅、相位以及偏振态分布,丰富了光与物质相互作用的手段,为材料表征提供了传统线偏振、圆偏振光场所不可替代的研究方法,具有重要的物理意义和实际应用价值。本文将综述矢量光场最新的研究进展,详细介绍矢量光场的偏振态特性、产生方法,以及紧聚焦轴对称矢量光场波前调控在远场小尺度光斑的产生、磁光记录、单分子/颗粒取向探测、任意三维偏振态的产生、高密度数据存储、信息加密以及矢量光场波前重构等方面的重要应用。     

Tight focusing of spirally polarized vortex beams

The tight focusing of spirally polarized focused vortex beams is analyzed numerically based on the vectorial Debye theory. The expressions for the electric field and the orbital angular momentum of focused beams are derived. It is shown that the intensity distribution in the focal plane is dependent on the specific spirally polarized state and the coefficient of the spiral polarization function. By presenting the phase contours of the component polarized in the radial direction, it is found that the radii of dislocation lines will increase with the increase of the power of the spirally polarization function. It is reveled that the same orbital angular momentum can be obtained for different spirally polarized state at certain distance along the propagation direction in the focal region. Besides, the orbital angular momentum distributions for different polarized states have fewer crossover points with each other for higher topological charge. The influence of the spirally polarized state on the orbital angular momentum in the focal plane is also studied.