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光学针是一种特殊的空间光场分布, 具有极小的横向光斑尺寸, 可以突破衍射极限, 同时在纵向上拥有较长的焦深. 光学针通常利用透镜对光束进行紧聚焦来产生, 本文利用圆艾里光束固有的自聚焦特性来构建光学针. 研究结果表明, 锥角调制的圆偏振圆艾里涡旋光束在选取合适的拓扑荷后, 可以产生光学针. 这是因为在锥角调制下, 光束的纵向分量被显著增强, 而纵向分量光场具有极小的横向光斑尺寸. 光学针的焦深与光束的主环半径近似呈线性关系, 因此增大主环半径可以有效增强光学针的焦深. 此外, 具有不同拓扑荷的圆艾里涡旋光束可以构建出不同结构的空间光场. 本文的研究有望在超分辨成像和光学微操控等领域具有潜在应用价值.An optical needle is a specialized spatial light field characterized by an extremely small transverse spot size, capable of breaking the diffraction limit, and an extended depth of focus in the longitudinal direction. Typically, optical needles are generated by tightly focusing a beam using a lens. This paper demonstrates the generation of optical needles using circular Airy vortex beams (CAVBs) with modulation of the cone angle. The CAVBs have a uniform distribution of circular polarization, eliminating the need for radial polarization states. Our research findings indicate that, under the cone angle modulation, CAVBs with a topological charge of -1 (left-handed circular polarization) and 1 (right-handed circular polarization) can form optical needles. These optical needles possess a minimal transverse spot size, enabling them to exceed the diffraction limit while maintaining a long depth of focus. Furthermore, the depth of focus of the optical needle is almost linearly related to the primary ring radius of the beam. Thus, increasing the primary ring radius can effectively enhance the depth of focus. For CAVBs with other topological charges, different hollow light fields can be generated, which are distinct from optical needles. This is because, under a the cone angle modulation, the longitudinal component of the light beam is significantly enhanced. Only CAVBs with an appropriate topological charge have a longitudinal light field distributed near the optical axis, leading to the formation of optical needles. For other topological charges, the longitudinal light field remains hollow, resulting in the creation of hollow light fields. The findings of this research hold potential applications in fields such as super-resolution imaging and optical micromanipulation.
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Keywords:
- Optical needle /
- Circular Airy beam /
- Optical vortex /
- Optical modulation
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图 1 左旋圆偏振CAVBs的光场强度$ | {\bf{E}}|^2 $分布, (a) 锥角$ \gamma = 0^\circ $; (b) 锥角$ \gamma = -30^\circ $. (c) 图(b)中沿z轴光场强度的横向分量$ I_\bot $与纵向分量$ I_z $的分布. 所用参数: $ E_0 = 1 $ V/m, 波长$ \lambda = 0.532 $ μm, 主环半径$ r_0 = 10\lambda $, 主环宽度$ w_0 = 1.5\lambda $, 衰减因子$ \alpha_c = 0.08 $, 以及拓扑荷$ l = -1 $
Fig. 1. Distribution of the field intensity $ | {\bf{E}}|^2 $ of circularly polarized CAVBs with conical angles (a) $ \gamma = 0^\circ $ and (b) $ \gamma = -30^\circ $. (c) Profiles of field intensity $ I_\bot $ and $ I_z $ along z-axis corresponding to (b). The parameters are given by $ E_0 = 1 $ V/m, the wavelength $ \lambda = 0.532 $ μm, the primary ring radius $ r_0 = 10\lambda $, the primary ring width $ w_0 = 1.5\lambda $, the decay parameter $ \alpha_c = 0.08 $, and the topological charge $ l = -1 $.
图 2 基于拓扑荷为$ l = -1 $的左旋圆偏振CAVBs构建光学针. (a) 光学针的光场强度$ | {\bf{E}}|^2 $在x-z平面内的分布; (b) 光学针的光场强度$ I = | {\bf{E}}|^2 $, 以及纵向光强分量$ I_z $和横向光强分量$ I_\bot $在x-y平面内的分布, 对应的传播距离为$ z = 10\lambda $; (c) 不同传播距离处, 光学针的光强度I, $ I_z $及$ I_\bot $沿x轴的分布. 这里光束的锥角$ \gamma = -65^\circ $, 主环半径$ r_0 = 50\lambda $, 其余参数与图1相同
Fig. 2. Optical needle structured via left circularly polarized CAVBs with the topological charge $ l = -1 $. (a) Optical intensity $ | {\bf{E}}|^2 $ along the x-z plane. (b) Profile of intensity $ I = | {\bf{E}}|^2 $, longitudinal intensity $ I_z $ and transverse intensity $ I_\bot $ along the x-y plane of the optical needle with the propagation distance $ z = 10\lambda $. (c) Distributions of the intensity I, transverse intensity $ I_\bot $ and longitudinal intensity $ I_z $ along x-axis with different propagation distance. The conical angle is $ \gamma = -65^\circ $ and the primary ring radius $ r_0 = 50\lambda $, and other parameters are the same as those in Fig. 1.
图 3 左旋圆偏振CAVBs构建的光学针受锥角γ的调制, 光束的主环半径$ r_0 = 30\lambda $, 拓扑荷$ l = -1 $. (a) 不同锥角调制下的CAVBs在x-z平面内的光强度分布; (b) 不同锥角下, CAVBs的光强I及其分量$ I_\bot $与$ I_z $沿x轴的分布, 对应的传播距离z在(a)图中使用白色虚线标出. (c) 光学针的焦深随主环半径$ r_0 $的变化关系. 其余参数与图1相同
Fig. 3. Influence of conical angle γ on optical needles structured via the left-handed circularly polarized CAVBs with the primary ring radius $ r_0 = 30\lambda $ and the topological charge $ l = -1 $. (a) Distributions of the field intensity along the x-z plane and (b) profiles of the intensity I, $ I_\bot $ and $ I_z $ along the x-axis corresponding to the propagation distance z denoted via the white dash lines in (a). (c) DOF of the optical needles varying as the primary ring radius $ r_0 $. Other parameters are the same as those in Fig. 1.
图 4 (a) CAVBs在x-z平面内的光强度分布, 光束的锥角$ \gamma = -65^\circ $, 主环半径$ r_0 = 30\lambda $, 拓扑荷分别为$ l = -2 $, 0, 1, 2, 其余参数与图1相同. (b) 不同光束在$ z = 0 $平面沿x轴的归一化光强度分布, 图中的灰色区域表示中空光场的中心暗区范围
Fig. 4. (a) Field intensity profiles of CAVBs with the conical angle $ \gamma = -65^\circ $ and the primary ring radius $ r_0 = 30\lambda $ along the x-z plane for different topological charge $ l = -2 $, 0, 1, and 2, and other parameters are the same as those in Fig. 1. (b) Normalized field intensity distributions of different light beams along the x-axis on the plane of $ z = 0 $, and the gray rectangles in the figure represent the central dark area of the hollow optical fields.
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