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。     

Focal properties of cylindrically polarized axisymmetric Bessel-modulated Gaussian beams by a high NA parabolic mirror

Focusing properties of the cylindrical vector axisymmetric Bessel-modulated Gaussian beam with quadratic radial phase dependence (QBG beam) in high numerical aperture parabolic mirror system is investigated theoretically by vector diffraction theory. Results show that intensity distribution in focal region can be altered considerably by beam parameter μ and polarization angle. The tightly focused cylindrically polarized axial symmetric Bessel-modulated Gaussian beams by a high numerical aperture parabolic mirror have possible applications in particle acceleration, optical trapping and manipulating, single molecule imaging and high resolution imaging microscopy.     

Focusing properties of spirally polarized hollow Gaussian beam

Focusing properties of spirally polarized hollow Gaussian beam (HGB) are investigated theoretically by vector diffraction theory in this article. Results show that the optical intensity in focal region of spirally polarized HGB can be altered considerably by the beam order, numerical aperture of the focusing system, and spiral parameter that indicates the polarization spiral degree of the spirally polarized HGB. Spiral parameter can induce focal pattern change in axial direction remarkably, while beam order and numerical aperture affect radial foal pattern more obviously. The tunable principle of the focal pattern by spiral parameter differs very considerably under condition of different numerical aperture and beam order. Many novel focal patterns may occur in focal pattern evolution. It was also found that focal shift and focal depth can be altered significantly by spiral parameter and beam order.     

Properties of circularly polarized vortex beams

The properties of circularly polarized vortex beams in cylindrical polarization bases are studied. A circularly polarized vortex beam is decomposed into radial and azimuthal polarization. With the proper combination of vortex charge and the handedness of the circular polarization, a focal field with an extremely strong longitudinal component as well as a flat-topped profile can be obtained. The cylindrical decomposition also sheds light on the connections between orbital angular momentum and the spin of the light beams.     

Nondiffracting transversally polarized beam

Generation of a nondiffracting transversally polarized beam by means of transmitting an azimuthally polarized beam through a multibelt spiral phase hologram and then highly focusing by a high-NA lens is presented. A relatively long depth of focus (～4.84λ) of the electric field with only radial and azimuthal components is achieved. The polarization of the wavefront near the focal plane is analyzed in detail by calculating the Stokes polarization parameters. It is found that the polarization is spatially varying and entirely transversally polarized, and the polarization singularity disappears at the beam center, which makes the central bright channel possible.     

Manipulation of the overall polarization orientation in the focal volume of high numerical objectives

We propose an approach for tuning the three-dimensional polarization of a focusing subwavelength spot by a high numerical aperture objective. The incident beams are composed of a radially polarized beam, an azimuthally polarized beam, and a linearly polarized beam with three different weighting factors, respectively. A specially designed adjustable amplitude angular selector is also inserted at the back aperture of the objective for tuning the polarization azimuthally. It is shown that any desired overall polarization orientation can be obtained. We calculated the overall polarization orientation in the focal volume. It is found that the polar angle of the overall polarization orientation can be arbitrarily tuned by the combination of a radially polarized beam and a linearly polarized beam with different weighting factors, and the azimuthal angle can be tuned by rotating the orientation of the linearly polarized beam azimuthally.     

Tightly focusing of spirally polarized Quadratic Bessel Gaussian beam through a dielectric interface

Based on vector diffraction theory, the tight focusing properties of spirally polarized axisymmetric Bessel-modulated Gaussian beam through a dielectric interface on high numerical aperture (NA) are investigated theoretically. The optical intensity distribution in the focal region of high NA objective lens is investigated in detail by numerical calculations. The results show that the focal shift induced in the focal region is by mismatch of refractive indices across the dielectric interface. It is also found that the optical intensity in focal region of spirally polarized Quadratic Bessel Gaussian (QBG) beam can be altered considerably by changing spiral parameter C that indicates the polarization spiral degree of the incident beam.     

Focus shaping of cylindrically polarized vortex beams by a high numerical-aperture lens

The focus-shaping technique of a cylindrically polarized vortex beam by a high numerical-aperture lens is reported. Such a polarized vortex beam is decomposed into radial and azimuthal polarization. It is shown that the total intensity distribution in the focal region is dependent not only on the numerical-aperture maximal angle and the polarization rotation angle but also on the topological charge. By choosing the proper combination of parameters, the adjustably confined flat-topped focus and focal hole can be obtained. The focus-shaping technique may find wide applications, such as optical tweezers, laser printing and material processing.     

基于紧聚焦方式的阵列光束相干合成特性分析

为获得高功率、波长量级尺寸的聚焦光斑,提出利用紧聚焦方式实现阵列光束相干合成的新方案.通过建立阵列光束经紧聚焦方式相干合成的物理模型,分析了阵列光束的排布方式、偏振态、束宽、间距和紧聚焦系统数值孔径等参数对合成光束特性的影响及规律.结果表明,阵列光束经紧聚焦方式合束时,线偏振及圆偏振阵列光束均能获得较好的合成效果,径向偏振阵列光束次之,而角向偏振阵列光束则不能有效地合成.通过优化阵列光束的排布方式、束宽和间距,以及合理选择紧聚焦系统的数值孔径,能在保持较好光束质量和较高合成效率的前提下获得能量集中度高的焦斑.     

基于可调谐复振幅滤波器的超长焦深矢量光场

根据矢量光场衍射积分理论和离散复振幅光瞳滤波原理, 通过一种由双λ/2波片和离散复振幅滤波器组成的可调谐复振幅滤波器, 研究了大数值孔径下超长焦深聚焦矢量光场的构建与调控. 给出了一个六环带区的离散复振幅滤波器, 对入射光场的偏振态、振幅滤波和相位滤波三者进行同步优化, 获得了焦深接近10λ的三维平顶光场; 通过调控双λ/2波片夹角来改变聚焦光场的矢量化结构, 使之在光针场、平顶光场、光管场及中间结构光场之间交替变化. 研究结果揭示了入射光场矢量化结构演化与聚焦光场矢量化结构变换之间的关系, 解决了获取动态的、可调控的超长焦深聚焦光场的问题. 两种基本的聚焦光场光针场、光管场的独自使用或三维平顶光场的调和使用, 将会在光学显微、光学微纳操控以及光学精细加工领域获得重要应用.     

Focal shift of cylindrical vector axisymmetric Bessel-modulated Gaussian beam with radial variance phase wavefront

Axisymmetric Bessel-modulated Gaussian beam with quadratic radial dependence (QBG beam) has attracted much attention recently. In this paper, the focal shift of the cylindrical vector QBG beam with radial variance phase wavefront is investigated theoretically by vector diffraction theory. Results show that focus shifts considerably by changing the phase parameter C that indicates the radial phase variance speed. Under condition of small beam parameter μ of cylindrical vector QBG beam, there is one focal peak that shifts far away from optical aperture on increasing C. When μ increases, there may occur two focal peaks that also shift remarkably on increasing C. And it was found that the dependence of focal shift distance on increasing phase parameter is linear. Phase parameter adjusts the focal shift distance, while, polarization angle does not affect focal shift obviously.     

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.     

双环角向偏振光束深聚焦特性

基于Richards-Wolf矢量衍射积分公式,研究了双环角向偏振光束经环状高数值孔径透镜的聚焦特性,推导了双环角向偏振光束经环状透镜深聚焦的光强表达式。根据数值模拟结果,比较了相关参量的变化对深聚焦特性的影响。研究表明:入射光束经环状高数值孔径透镜聚焦后,在焦平面得到了具有广泛应用的亚波长空心光斑,并且入射光束的相关参数和聚焦透镜的数值孔径大小都会影响光束的聚焦特性,使聚焦空心光斑达到亚波长量级;双环角向偏振光束经环状高数值孔径透镜的聚焦以后,在焦平面附近产生了一个更长的焦深（约28倍入射光波长）。     

Focusing of linearly-, and circularly polarized Gaussian background vortex beams by a high numerical aperture system afflicted with third-order astigmatism

Effects of third-order astigmatism on the focused structure of linearly and circularly polarized Laguerre-Gaussian beams have been investigated by using vectorial Debye-Wolf integral. The results have been presented for total intensity distribution and squares of the polarization components at the focal plane of a high numerical aperture system, for two values of the topological charge. Astigmatism results in the stretching of the intensity pattern as well as of the squares of the polarization components. A split is observed in the intensity pattern of a focused beam having double topological charge, and also in the pattern of the longitudinal polarization component of circularly polarized beam even with unit topological charge.     

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。     

Tight focusing of J0-correlated Gaussian Schell-model beam through high numerical aperture

Based on the vectorial Debye diffraction theory, the tight focusing of a linearly polarized J₀-correlated Gaussian Schell-model (JGSM) beam through high numerical aperture (NA) is investigated. The components of intensity distributions as well as the 3D degree of polarization of light at the focal plane are depicted by numerical integrations, respectively. It is shown that intensity distributions as well as the degree of polarization of focused field not only strongly depend on the global correlation length of the JGSM beam but also relate to the focusing parameter of NA. It is also indicated that the weight of the longitudinal intensity component would enhance in the focal plane, as long as either the correlation length of the JGSM beam or the focusing parameter of NA increases.     

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.     

Focusing of radially polarized beam with radial cosine phase wavefront

Radially polarized beam has gained much interest recently due to its properties and applications. In this article, the focusing properties of radially polarized beam with radial cosine phase wavefront are investigated theoretically. Results show that when the radially polarized beam with radial cosine wavefront phase is focused, the focal pattern differs considerably with frequency parameter in the cosine function term. In the high numerical aperture focusing system, focal shift occurs, and novel focal patterns evolve considerably, for instance, from only one peak to two or multiple overlapping peaks. In addition, peak intensity ratio of radially polarized component to longitudinal polarized component in the focal region fluctuates smoothly for low-frequency parameter, then drops sharply, and comes back remarkably with increasing frequency parameter. Simultaneously focal shift increases slowly, and then decreases, suddenly, focal shift sign changes that results from focal switch phenomenon, and then fluctuates.     

慧差对线偏振贝塞耳-高斯光束聚焦场的影响

利用Richards-Wolf矢量衍射积分公式,获得线偏振贝塞耳-高斯光束经具有初级慧差的高数值孔径系统聚焦后的三维光场复振幅函数,根据复振幅函数模拟了不同慧差系数下线偏振贝塞耳-高斯光束各分量及总光场在焦平面上的光强分布模式。研究结果表明,初级慧差使线偏振贝塞耳-高斯光束聚焦光场在焦平面的分布由双轴对称变成单轴对称,光强模式发生改变;各分量及总光场的光强模式中的光斑位置随初级慧差系数的增大偏离光轴;大的初级慧差使焦平面出现干涉条纹。     

Focusing properties of concentric piecewise cylindrical vector beam

The focusing properties of a concentric piecewise cylindrical vector beam is investigated theoretically in this paper. The beam consists of three portions with different and changeable phase retardation and polarization. Numerical simulations show that the evolution of the focal shape is very considerable by changing the radius and polarization rotation angle of each portion of the vector beam. And some interesting focal spots may occur, such as two- or three-peak focus, dark hollow focus, ring focus, and two-ring-peak focus. Corresponding gradient force patterns are also computed, and novel trap patterns, including cup shell shape trap with one trap at its each side along axis, rectangle shell shape trap with one trap at its each side, dumbbell optical trap, spherical shell optical trap, may occur, which shows that the concentric piecewise cylindrical vector beam can be used to construct controllable optical tweezers.