Super-resolution light needle achieved by tightly focusing azimuthally polarized airy beam
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摘要: 为了研究角向偏振艾里光束的紧聚焦特性，采用理查德-沃夫矢量衍射理论分析优化了艾里光束的指数衰减因子、主环半径与比例因子对其入射光场分布的影响；分别研究了角向偏振艾里光束聚焦场分布与涡旋滤波器调制的角向偏振艾里光束的聚焦场分布，得到亚波长的角向中空场分布与亮场分布，实验结果与理论模拟基本一致。进一步利用粒子群算法设计多环涡旋相位滤波器调制角向偏振艾里光束，紧聚焦后得到了超长无衍射超分辨的横向偏振光针。结果表明，光针的半峰全宽为0.395λ，聚焦深度为37.432λ，纵横比达到94.788；通过计算斯托克斯参量分析聚焦光场的偏振分布，发现聚焦光场在径向偏振与角向偏振之间交替变化，且光束中心奇异点消失，实现了横向偏振的亮场分布。该研究在高密度的磁光存储、超分辨的光学成像、纳米光刻与粒子操作等领域具有广泛的应用。Abstract: To study the tight focusing characteristics of azimuthally polarized Airy beams, the Richards-Wolf vector diffraction theory was adopt. The influences of the exponential attenuation factor, the radius of the main ring, and the proportional factor of the airy beams on the incident field patterns were respectively studied. The focal field distributions of the azimuthally polarized airy beams and the azimuthally polarized airy beams modulated by a vortex phase filter were studied, from which a sub-wavelength azimuthally polarized doughnut field and a transversally polarized bright field were garnered. The experimental results are basically consistent with the theoretical simulations. Furthermore, the multi-ring vortex phase filter was designed to modulate the azimuthally polarized airy beams according to the particle swarm algorithm, and an ultra-long and non-diffracting super-resolution transversally polarized light needle was produced on tight focusing. It turns out that the full width at half maximum and the depth of focus of the light needle are 0.395λ and 37.432λ respectively, which corresponds to an aspect ratio of 94.788. The polarization patterns of the focal fields are analyzed by calculating the Stokes polarization parameters. It is found that the focal field alternates between the radial polarization and azimuthal polarization and the singularity at the center of the beam disappears, which testify that the transversally polarized bright field distribution is realized. The research holds broad applications in high-density magneto-optical storage, super-resolution optical imaging, nanolithography and particle manipulation.
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Figure 1. Schematic setup to generate the super-resolution and transversally polarized light needle
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Figure 3. a~c—the normalized intensity patterns of input Airy beams for given input parameters r0=2.8mm, w=0.03mm and a0=0.01, 0.1 and 1, respectively in the x-y plane d~f—the normalized intensity patterns of input airy beams for given input parameters a0=0.25, w=0.03mm and r0=2mm, 2.5mm and 3mm, respectively in the x-y plane g~i—the normalized intensity patterns of input Airy beams for given input parameters a0=0.25, r0=2.8mm and w=0.05mm, 0.1mm and 0.5mm, respectively in the x-y plane
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Figure 4. a~c—the normalized intensity profiles, normalized intensity patterns in the x-y planes and experimental results of unmodulated azimuthally polarized beam by tightly focusing, respectively d~f—the normalized intensity profiles, normalized intensity patterns in the x-y planes and experimental results of modulated azimuthally polarized beam by tightly focusing, respectively
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Figure 5. a~c—the normalized intensity patterns of the light needle in the y-z planes for N=1, 4 and 5, respectively d~e—the depth of focus and full width at half maximum of transversally polarized Airy light needle for N=1, 4 and 5, respectively
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Figure 6. a—cross section of the ellipticity of local polarization ellipses in the x-z planes b—the azimuthal angle distribution in the focal plane
Table 1 The essential parameters of the multi-loop vortex phase filter and properties of airy light needle
N=1 N=4 N=5 rt 1 0.9667, 0.9754,
0.9936, 10.9555, 0.9711,
0.9867, 0.9990, 1f(θ) 1 1, 0, 1, 1 1, 1, 1, 0, 1 φ(θ) π/2 π/2, -π/2,
π/2, -π/2π/2, -π/2,
π/2, -π/2, π/2DOF/λ 10.238 37.743 37.432 FWHM/λ 0.395 0.398 0.395 DOF/FWHM 25.918 94.760 94.788 
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