Efficient extracavity generation of radially and azimuthally polarized beams

We demonstrate an efficient transformation of a linearly polarized Gaussian beam to a radially or an azimuthally polarized doughnut (0,1)* Laguerre-Gaussian beam of high purity. We use a spatially variable retardation plate, composed of eight sectors of a lambda/2 retardation plate, to transform a linear polarization distribution to radial/azimuthal distribution. We transformed an Nd:YAG Gaussian beam with M(2)=1.3 to a radially and azimuthally polarized (0,1)* Laguerre-Gaussian beams with M(2)=2.5 and degree of radial/azimuthal polarization of 96-98%.     

Vortex solitons with inhomogeneous polarization in nonlocal self-focusing nonlinear media

Both azimuthally and radially polarized vortex solitons are investigated to be able to exist in highly nonlocal nonlinear media. We get exactly analytical solutions of azimuthally polarized vortex solitons with only polarization singularities and radially polarized vortex solitons with both phase singularities and polarization singularities. Both azimuthally and radially polarized vortex solitons can exist in nonlocal self-focusing nonlinear media with proper modulation of the beam power and the degree of nonlocality. Contrary to those of radially polarized counterparts in local Kerr media, the topological charge can be any integer. When the topological charge m ≠ 0, both phase singularities and polarization singularities work. When m = 0, the polarization singularities work. Azimuthally polarized vortex solitons with polarization singularities corresponds to the linearly polarized vortex solitons with single charge. Our results show that polarization singularities work the same way as phase singularities in some sense.     

三环非均匀混合偏振同轴矢量光束的聚焦特性

基于Richards-Wolf矢量衍射积分公式,数值分析了同轴三环非均匀混合偏振矢量光束经过高数值孔径透镜的聚焦特性。该矢量光束由同轴三环局域线偏振矢量光束通过一个相位延迟角为δ的液晶相位延迟器产生,光束偏振变为包含线偏振、圆偏振和椭圆偏振的混合态。同轴三环局域线偏振矢量光束的偏振分布是由径向向内偏振的外环光束、径向向外偏振的内环光束和线偏振方向与径向方向夹角为φ2的中环光束构成。数值模拟结果显示该混合偏振矢量光束的聚焦强度分布与参数φ2和相位延迟角δ密切相关,当选取适当的φ2和δ时,在焦平面附近产生沿光轴方向的三维多点光俘获结构——暗光链,这在光学微操纵领域具有潜在的应用价值。     

Effect of polarization on focal depth in high numerical apertures optical systems

The generalized cylindrical vector beam is just a linear combination of radial and azimuthal polarization. For radially polarized light in the focal plane, there are two electric field components, the radial component and z-component whose magnitude increase with the increase of numerical aperture. By contrast, for azimuthally polarized light in the focal plane, there is only one electrical field component in the azimuthal polarization, it is easy to understand the difference between the two polarization effects. In this paper, we demonstrate how this phenomenon can be harnessed to make a properly selected polarization component to achieve high focal depth in high numerical aperture systems. Numerical simulations show that the evolution of the focal shape is very considerable by changing polarization rotation angle of the generalized cylindrical vector beam. And some interesting focal spots and focal split may occur. And if the ratio of radial and azimuthal polarization is set properly by changing the polarization rotation angle, a largest focal depth is achieved. The tunable range of the focal depth is very considerable. The ratio of radial and azimuthal polarization is different in different NA optical system for obtaining the largest focal depth. We will denote a technique of polarization-assisted high focal depth in high numerical aperture systems.     

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 beams: Effects of polarization

An approximation to a Bessel beam produced by tightly focusing linearly polarized light is known to produce a smaller central lobe than focusing plane polarized light. This is because the plane polarized wave gives a broad central lobe caused mainly by a parasitic longitudinal field component. It is known that this problem can be overcome by focusing radially polarized light. Here we demonstrate that other polarization distributions based on a linear combination of transverse electric (TE1) and transverse magnetic (TM1) fields can give a beam even narrower than for the radially polarized case. Special cases of this combination are identified, corresponding to the smallest width (TE1), and the maximum peak intensity compared with the side lobes (electric dipole polarization). Axially-symmetric forms can be generated by illumination with elliptically polarized light. A particular case is azimuthal polarization with a phase singularity, which is equivalent to TE1. For a semi-angular aperture of 60°, the TE1 case gives a central lobe width 9% narrower than for radially polarized illumination, while for plane polarized illumination it is 12% wider than the radially polarized case.     

Two-dimensional polarization distribution controller based on variable retarder array

Two-dimensional polarization distribution controller which can transform linearly polarized beam into two-dimensional polarization distributed beam has been presented and investigated. The two-dimensional polarization distribution controller consists of two quarter-wave plates and a variable retarder array. The principles of the two-dimensional polarization distribution controller are analyzed and calculated results show when the directions of fast axes of these three components meet a particular constraint equation set, these three optical components could be regarded as a two-dimensional polarization distribution controller. Experiments have been carried out, and the light intensity distribution of radially and azimuthally polarized beams after an analyzer are obtained.     

Generation of azimuthally and radially polarized beams by coherent polarization beam combination

A new architecture for generating pure azimuthally and radially polarized beams is presented. It involves coherent polarization beam combination of two orthogonally polarized LP(11) fiber modes. Experimental results reveal that high purely polarized (polarization purity of 95% or better) azimuthal and radial beams can be generated.     

Natural shaping of the cylindrically polarized beams

We have experimentally and theoretically shown that the circularly polarized beam bearing a singly charged optical vortex propagating through a uniaxial crystal can be split after focusing into the radially and azimuthally polarized beams in the vicinity of the focal area provided that the polarization handedness and the vortex topological charge have opposite signs.     

Sharper focus for a radially polarized light beam

We experimentally demonstrate for the first time that a radially polarized field can be focused to a spot size significantly smaller [0.16(1)lambda(2)] than for linear polarization (0.26lambda(2)). The effect of the vector properties of light is shown by a comparison of the focal intensity distribution for radially and azimuthally polarized input fields. For strong focusing, a radially polarized field leads to a longitudinal electric field component at the focus which is sharp and centered at the optical axis. The relative contribution of this component is enhanced by using an annular aperture.     

Propagation and parametric characterization of the polarization structure of paraxial radially and azimuthally polarized beams

Analytical expressions are provided for describing the free-space evolution of the polarization structure of paraxial beams whose electric-field vector at some transverse plane exhibits either a radially or an azimuthally polarized behavior. At each transverse plane, the polarization distribution across the beam profile is characterized by means of two sets of parameters, namely, the so-called (local) radial Stokes representation, and the (overall) percentage of the irradiance associated with the radial and azimuthal field components. The propagation laws for these sets of parameters are also shown. As an illustrative example, a radially polarized beam is analized whose wavefront contains a spiral phase factor.     

Three-dimensional multiple optical cages formed by focusing double-ring shaped radially and azimuthally polarized beams

We propose and simulate a method for generating a three-dimensional(3D) optical cage in the vicinity of focus by focusing a double-ring shaped radially and azimuthally polarized beam. Our study shows that the combination of an inner ring with an azimuthally polarized field and an outer ring with a radially polarized field and a phase factor can produce an optical cage with a dark region enclosed by higher intensity. The shape of the cage can be tailored by appropriately adjusting the parameters of double-mode beams. Furthermore, multiple 3D optical cages can be realized by applying the shift theorem of the Fourier transform and macro-pixel sampling algorithm to a double-ring shaped radially and azimuthally polarized beam.     

大数值孔径光子筛偏振特性研究

根据角谱理论建立不同偏振照明条件下的光子筛矢量衍射模型。在此基础上,对入射光分别为线偏振光、径向偏振光、切向偏振光三种特殊偏振状态下的光子筛聚焦光强分布进行了模拟分析。研究结果表明,对于大数值孔径光子筛,入射光的偏振特性将对光子筛聚焦光强分布产生巨大影响。线偏振光将使聚焦光斑沿偏振方向拉伸,切向偏振光产生的聚焦光斑具有"中空"结构,而径向偏振光所产生的聚焦光斑呈较为规则的圆形,且其焦深优于线偏照明情况。在激光直写及高分辨成像等光子筛典型应用中采用径向偏振照明将进一步提高系统分辨力。     

Vectorial structure of far field of cylindrically polarized beams diffracted at a circular aperture

Based on the vector angular spectrum representation and the method of stationary phase, the analytical vectorial structure of the cylindrically polarized Laguerre-Gaussian beam diffracted at a circular aperture is derived in the far field, which provides an approach to further comprehend the vectorial properties of the apertured cylindrically polarized beams. The radially polarized, azimuthally polarized, and unapertured cases can be viewed as the special cases of our general result. The analyses show that the far-field energy flux distributions of the entire beam, the TE term, and the TM term depend on the beam order, the ratio of the waist width to the wavelength, the truncation parameter, and the angle between the electric field vector and the radial direction.     

Production of radially or azimuthally polarized beams in solid-state lasers and the elimination of thermally induced birefringence effects

Production and amplification of radially and azimuthally (tangentially) polarized laser beams are demonstrated. Based on the different focusing between radially and tangentially polarized light in thermally stressed isotropic laser rods, Nd:YAG laser oscillators were developed to produce low-loss stable oscillation in a single polarization. Pure radially polarized light at 70 W with M2 = 2 and on-axis impure radially polarized light at 150 W with M2 = 2.5 were achieved. The radially polarized beams were then amplified while good beam quality and polarization purity were retained. Complete elimination of thermal-birefringence-induced aberrations was demonstrated. This should allow much better beam quality from rod-based high-power lasers.     

Material processing with pulsed radially and azimuthally polarized laser radiation

We report on the generation of radially and azimuthally polarized Q-switched laser radiation and its application in material processing. The power levels were sufficiently high to study micro-hole drilling in different metals. Depending on the optical properties of the metal, either radial or azimuthal polarization shows the best efficiency and the effect is attributed to waveguiding. For steel, a comparison to linearly or circularly polarized laser radiation indicates that the doughnut-shaped beam with azimuthal polarization is the most energy-efficient in producing holes of the same diameter and depth. PACS 79.20.Ds; 29.27.Hj; 81.05.Bx     

Forces in optical tweezers with radially and azimuthally polarized trapping beams

It has been suggested that radially polarized beams can be used to improve the performance of optical tweezers, with reduced scattering force resulting from both the polarization and the dark center of the beam [Opt. Lett. 32, 1839 (2007)]. We calculate the forces on particles in such traps, using rigorous electromagnetic theory, comparing the results with azimuthally polarized beam, circularly polarized LG 01 beams, and Gaussian beams. Our results agree qualitatively with Opt. Lett. 32, 1839 (2007), but differ quantitatively.     

Geometrical phase and surface plasmon focusing with azimuthal polarization

Owing to a geometric phase effect, an isosceles triangular aperture etched into thin metal film leads to constructive or destructive interference of surface plasmons excited at the two equal sides under linearly polarized illumination. Through appropriate spatial arrangement of an array of triangles, a highly confined focal spot beyond the diffraction limit can be achieved at the geometric center under azimuthally polarized excitation with field enhancement comparable to a bull's eye plasmonic lens under radially polarized illumination. Through simply rotating the orientation of each triangle aperture by 90°, the plasmonic structure defocuses the same azimuthal polarization illumination due to destructive interference caused by a geometric π-phase difference between the two sides of the triangle and between the adjacent triangles.     

显微物镜聚焦光场任意三维偏振方向的控制

线性偏振光在显微物镜焦斑处入射,与径向偏振光相干叠加产生三维偏振光场,通过调节两束光光强比率和入射线偏振光偏振方向实现聚焦光场任意三维偏振方向的控制.基于矢量光场衍射理论建立了仿真计算模型,对所提三维偏振方向控制方法的可行性进行理论验证和实验评估.构建实际控制光路并进行初步测试,实验结果表明了该方法的可行性,且相比于其他三维偏振控制方法,本文所提方法和其控制光路更为简单易实现.     

Complex cylindrical vector beam excludes the orientation dependence of the intensity of scanning fluorescence images of single molecules

A polarization inhomogeneous vector beam, which is the complex superposition of radially and azimuthally polarized beams, has been studied computationally and theoretically in application to scanning fluorescence microscopy of single molecules. It has been shown that its application makes it possible to almost exclude the dependence of the intensity maximum of the scanning fluorescence image of a single molecule on its orientation. It has been demonstrated that the scanning of one horizontal plane of a solid matrix containing impurity luminescent molecules provides images of all molecules located in a 1-μm-thick layer, replacing three-dimensional scanning. Recommendations on the technical implementation of the proposed beam have been given.