搜索

x

留言板

尊敬的读者、作者、审稿人, 关于本刊的投稿、审稿、编辑和出版的任何问题, 您可以本页添加留言。我们将尽快给您答复。谢谢您的支持!

姓名
邮箱
手机号码
标题
留言内容
验证码

角向偏振涡旋光的紧聚焦特性研究以及超长超分辨光针的实现

蒋驰 耿滔

引用本文:
Citation:

角向偏振涡旋光的紧聚焦特性研究以及超长超分辨光针的实现

蒋驰, 耿滔

The study of tight focusing characteristics of azimuthally polarized vortex beams and the implementation of ultra-long super-resolved optical needle

Jiang Chi, Geng Tao
PDF
HTML
导出引用
  • 系统研究了角向矢量涡旋光的紧聚焦焦斑特性, 解释了焦平面自旋角动量局域化分布的形成原因. 角向矢量涡旋光可分解为左、右旋圆偏振电场叠加, 将分解所得的左、右旋分量分别经大数值孔径透镜聚焦, 总聚焦电场可视为左、右旋分量聚焦电场的干涉叠加. 经分析研究后发现, 左、右旋分量各自聚焦电场的纵向分量大小相等、相位相反, 完全干涉相消, 使得总聚焦电场的纵向分量消失; 而各自聚焦电场的横向分量则完全相反, 几乎不发生干涉, 总聚焦电场表现为非相干叠加. 角向偏振光引入涡旋相位后, 使得左、右旋电场分量的轨道角动量的拓扑荷数发生变化, 拓扑荷数的绝对值不再相等, 而是恒定差值为2. 因此左、右旋电场的横向分量由于携带不同的拓扑荷数, 分别聚在焦平面的不同位置, 而横向分量发生非相干叠加, 不相互影响, 最终形成了总电场偏振态的局域化分布, 即自旋角动量局域化分布的现象. 随后, 本文横向对比了1阶角向矢量涡旋光和径向偏振矢量光的超分辨焦斑特性, 分析了各自的优、缺点以及影响焦斑尺寸的因素. 最后, 兼顾了超分辨光针的性能和实际实现难度, 设计了6环带的二元相位板对1阶角向矢量涡旋光进行了波前调制, 实现了横向半高全宽为$0.391\lambda $, 纵向半高全宽为$25.5\lambda $的超长超分辨光针.
    The tight focusing characteristics of azimuthally polarized vortex beams are systematically investigated in this work. The azimuthally polarized vortex beam can be decomposed into left-handed circularly polarized (LHCP) wave and right-handed circularly polarized ( RHCP) wave. It is found that the longitudinal component of LHCP and RHCP at the focal plane are equal in magnitude but opposite in phase. Thus, the total longitudinal field disappears because of the completely destructive interference. In contrast, there is almost no interference between the transverse component of LHCP and RHCP. Thus, the total transverse field is the incoherent superposition of them. Since the absolute value of the topological charge of LHCP component and RHCP component are not equal, the transverse component of LHCP and RHCP will be concentrated in the different areas on the focal plane. It is the reason for the orbit-induced SAM to be localized on the focal plane. Then, we compare the focal spot characteristics of the radially polarized beam and the azimuthally polarized beam with a first-order vortex. The advantages and disadvantages of them are discussed in detail, respectively.For the radially polarized beam, the central focal spot is mainly longitudinal component, and the sidelobe is mainly transverse component. For the azimuthally polarized vortex beam with $l = 1$, the central focal spot is mainly LHCP component, and the sidelobe is mainly RHCP component. In both cases, the field distributions of the central spots are the same, and both show a distribution similar to the zero-order Bessel function. The situation of the sidelobe is different. The sidelobe of the radially polarized beam shows a distribution similar to the first-order Bessel function and the sidelobe of the azimuthally polarized vortex beam indicates a distribution similar to the second-order Bessel function. Therefore, the sidelobe of the radially polarized beam is closer to that of the optical axis, resulting in a larger central focal spot size. On the other hand, the sidelobe of the radially polarized beam accounts for a much smaller proportion of the total energy than that of the azimuthally polarized vortex beam. So the sidelobe peak intensity of the radially polarized beam is lower. Finally, an optimal binary phase element is designed to obtain an ultra-long super-resolution optical needle. The transverse full weight of half maximum (FWHM) can achieve $0.391\lambda $ and the longitudinal FWHM can reach to $25.5\lambda $ by using only 6 belts.
      通信作者: 耿滔, Tao_Geng@hotmail.com
    • 基金项目: 国家自然科学基金(批准号: 61975125)和上海市自然科学基金(批准号: 21ZR1443800)资助的课题.
      Corresponding author: Geng Tao, Tao_Geng@hotmail.com
    • Funds: Project supported by the National Natural Science Foundation of China (Grant No. 61975125) and the Natural Science Foundation of Shanghai, China (Grant No. 21ZR1443800).
    [1]

    Li Y C, Xin H B, Lei H X, Liu L L, Li Y Z, Zhang Y, Li B J 2016 Light Sci. Appl. 5 e16176Google Scholar

    [2]

    Gong Z, Pan Y L, Videen G, Wang C 2018 J. Quant. Spectrosc. Ra. 214 94Google Scholar

    [3]

    Wetzstein G, Ozcan A, Gigan S, Fan S, Englund D, Soljačić M, Denz C, Miller D A B, Psaltis D 2020 Nature 588 39Google Scholar

    [4]

    许琳茜, 朱榕琪, 朱竹青, 贡丽萍, 顾兵 2022 物理学报 71 147801Google Scholar

    Xu L X, Zhu R Q, Zhu Z Q, Gong L P, Gu B 2022 Acta Phys. Sin. 71 147801Google Scholar

    [5]

    Zhang L, Qiu X D, Zeng L W, Chen L X 2019 Chin. Phys. B 28 094202Google Scholar

    [6]

    Zhao J, Winetraub Y, Du L, Van Vleck A, Ichimura K, Huang C, Aasi S Z, Sarin K Y, de la Zerda A 2022 Optica 9 859Google Scholar

    [7]

    Cao R, Zhao J J, Li L, Du L, Zhang Y D, Luo Y L, Jiang L M, Davis S, Zhou Q F, de la Zerda A, Wang L V 2022 Nat. Photon. 17 89Google Scholar

    [8]

    Wang H, Shi L, Lukyanchuk B, Sheppard C, Chong C T 2008 Nat. Photon. 2 501Google Scholar

    [9]

    Huang K, Shi P, Kang X L, Zhang X, Li Y P 2010 Opt. Lett. 35 965Google Scholar

    [10]

    Guo H M, Weng X Y, Jiang M, Zhao Y H, Sui G R, Hu Q, Wang Y, Zhuang S L 2013 Opt. Express 21 5363Google Scholar

    [11]

    Zhang T, Li M, Ye H, Shi C 2020 Opt. Commun. 460 125178Google Scholar

    [12]

    He J, Zhuang J C, Ding L, Huang K 2021 Appl. Opt. 60 3081Google Scholar

    [13]

    Hao X, Kuang C F, Wang T T, Liu X 2010 Opt. Lett. 35 3928Google Scholar

    [14]

    Yuan G H, Wei S B, Yuan X C 2011 Opt. Lett. 36 3479Google Scholar

    [15]

    Wang S C, Li X P, Zhou J Y, Gu M 2014 Opt. Lett. 39 5022Google Scholar

    [16]

    Liu L, Shi L, Li F, Yu S, Wang S, Du J, Liu M, Qi B, Yan W 2021 IEEE Photon. J. 13 1Google Scholar

    [17]

    Gao X Z, Zhao P C, Zhao J H, Sun X F, Liu J J, Yang F, Pan Y 2022 Opt. Express 30 26275Google Scholar

    [18]

    Zhan Q 2009 Adv. Opt. Photon. 1 1Google Scholar

    [19]

    Kozawa Y, Sato S 2021 Prog. Opt. 66 35Google Scholar

    [20]

    Sato S, Kozawa Y 2009 J. Opt. Soc. Am. A Opt. Image Sci. Vis. 26 142Google Scholar

    [21]

    Li M M, Cai Y N, Yan S H, Liang Y S, Zhang P, Yao B L 2018 Phys. Rev. A 97 053842Google Scholar

    [22]

    Monteiro P B, Neto P A M, Nussenzveig H M 2009 Phys. Rev. A 79 033830Google Scholar

    [23]

    Ostrovsky A S, Rickenstorff-Parrao C, Arrizón V 2013 Opt. Lett. 38 534Google Scholar

    [24]

    Grosjean T, Courjon D 2007 Opt. Commun. 272 314Google Scholar

    [25]

    Vaity P, Rusch L 2015 Opt. Lett. 40 597Google Scholar

  • 图 1  $l = 1$时, 焦平面的(a)光强和偏振分布; (b)斯托克斯分量S3的分布. 图尺寸为$1.5\lambda \times 1.5\lambda $

    Fig. 1.  (a) Intensity and polarization distributions of the beam at the focal plane with $l = 1$; (b) calculation results of Stokes parameters S3 at the focal plane with $l = 1$.

    图 2  (a) $l = 2$和(b) $l = 0$时, 焦平面的左旋分量${I_{{\text{EL}}}}$、右旋分量${I_{{\text{ER}}}}$、总光强${I_0}$以及斯托克斯分量S3分布

    Fig. 2.  Intensity of the left-handed component, intensity of the right-handed component, total intensity and the Stokes parameters S3 at the focal plane with (a) $l = 2$ and (b) $l = 0$.

    图 3  $l = 1$时, ${E_{{\text{0 L}}}}$${E_{{\text{0 R}}}}$的横向分量在焦平面的相干叠加和非相干叠加的光强计算结果

    Fig. 3.  Calculation results of coherent superposition and incoherent superposition of the transverse components of ${E_{{\text{0 L}}}}$ and ${E_{{\text{0 R}}}}$ with $l = 1$.

    图 4  不同情况下, ${I_{\text{A}}}$${I_{\text{R}}}$的计算结果(图中同时给出了各自的第2项计算结果以便于比较) (a) $n = 1$, ${\text{NA}} = 1$; (b) $n = 1$, ${\text{NA}} = 0.95$; (c) $n = 1.52$, ${\text{NA}} = 1.4$

    Fig. 4.  Calculation results of ${I_{\text{A}}}$ and ${I_{\text{R}}}$ under different conditions: (a) $n = 1$, ${\text{NA}} = 1$; (b) $n = 1$, ${\text{NA}} = 0.95$; (c) $n = 1.52$, ${\text{NA}} = 1.4$. The second terms of ${I_{\text{A}}}$ and ${I_{\text{R}}}$ are also shown here for the convenience of comparing

    图 5  $n = 1$, ${\text{NA}} = 0.95$时, 径向偏振光和1阶角向矢量涡旋光的焦斑FWHM随$R/T$的变化曲线

    Fig. 5.  Focus FWHM of different beams as a function of $R/T$ with $n = 1$, ${\text{NA}} = 0.95$.

    图 6  (a)六环带相位板示意图; (b)聚焦过程示意图

    Fig. 6.  (a) Phase structure of a six-belt binary element; (b) the focusing setup.

    图 7  $n = 1$, ${\text{NA}} = 0.95$, $R/T = 25$时, (a)相位调制前后的焦平面光强分布; (b)相位调制前后的光轴光强分布; (c)调制前焦点区域$\rho {\text{-}}z$面的二维光强分布; (d)调制后焦点区域$\rho {\text{-}}z$面的二维光强分布

    Fig. 7.  Under the condition of $n = 1$, ${\text{NA}} = 0.95$, $R/T = 25$, (a) the intensity distributions at the focal plane with and without phase modulation, (b) the intensity distributions at the optic axis with and without phase modulation, (c) the two-dimensional (2D) intensity distribution in the $\rho {\text{-}}z$ plane without phase modulation, and (d) the 2D intensity distribution in the $\rho {\text{-}}z$ plane with phase modulation.

    表 1  不同情况下, 由(30)式和(31)式计算获得的中心焦斑的FWHM (${\lambda _n} = \lambda /n$为介质中波长)

    Table 1.  Calculation results of FWHM of the focal spot by using Eqs. (30) and (31) under different conditions. Here, ${\lambda _n} = \lambda /n$ is the wavelength in the medium.

    $n = 1$, ${\text{NA}} = 1$$n = 1$, ${\text{NA}} = 0.95$$n = 1.52$, ${\text{NA}} = 1.4$
    ${I_{\rm A}}$的FWHM$0.371{\lambda _n}$$0.389{\lambda _n}$$0.403{\lambda _n}$
    ${I_{\text{R}}}$的FWHM$0.359{\lambda _n}$$0.391{\lambda _n}$$0.412{\lambda _n}$
    下载: 导出CSV
  • [1]

    Li Y C, Xin H B, Lei H X, Liu L L, Li Y Z, Zhang Y, Li B J 2016 Light Sci. Appl. 5 e16176Google Scholar

    [2]

    Gong Z, Pan Y L, Videen G, Wang C 2018 J. Quant. Spectrosc. Ra. 214 94Google Scholar

    [3]

    Wetzstein G, Ozcan A, Gigan S, Fan S, Englund D, Soljačić M, Denz C, Miller D A B, Psaltis D 2020 Nature 588 39Google Scholar

    [4]

    许琳茜, 朱榕琪, 朱竹青, 贡丽萍, 顾兵 2022 物理学报 71 147801Google Scholar

    Xu L X, Zhu R Q, Zhu Z Q, Gong L P, Gu B 2022 Acta Phys. Sin. 71 147801Google Scholar

    [5]

    Zhang L, Qiu X D, Zeng L W, Chen L X 2019 Chin. Phys. B 28 094202Google Scholar

    [6]

    Zhao J, Winetraub Y, Du L, Van Vleck A, Ichimura K, Huang C, Aasi S Z, Sarin K Y, de la Zerda A 2022 Optica 9 859Google Scholar

    [7]

    Cao R, Zhao J J, Li L, Du L, Zhang Y D, Luo Y L, Jiang L M, Davis S, Zhou Q F, de la Zerda A, Wang L V 2022 Nat. Photon. 17 89Google Scholar

    [8]

    Wang H, Shi L, Lukyanchuk B, Sheppard C, Chong C T 2008 Nat. Photon. 2 501Google Scholar

    [9]

    Huang K, Shi P, Kang X L, Zhang X, Li Y P 2010 Opt. Lett. 35 965Google Scholar

    [10]

    Guo H M, Weng X Y, Jiang M, Zhao Y H, Sui G R, Hu Q, Wang Y, Zhuang S L 2013 Opt. Express 21 5363Google Scholar

    [11]

    Zhang T, Li M, Ye H, Shi C 2020 Opt. Commun. 460 125178Google Scholar

    [12]

    He J, Zhuang J C, Ding L, Huang K 2021 Appl. Opt. 60 3081Google Scholar

    [13]

    Hao X, Kuang C F, Wang T T, Liu X 2010 Opt. Lett. 35 3928Google Scholar

    [14]

    Yuan G H, Wei S B, Yuan X C 2011 Opt. Lett. 36 3479Google Scholar

    [15]

    Wang S C, Li X P, Zhou J Y, Gu M 2014 Opt. Lett. 39 5022Google Scholar

    [16]

    Liu L, Shi L, Li F, Yu S, Wang S, Du J, Liu M, Qi B, Yan W 2021 IEEE Photon. J. 13 1Google Scholar

    [17]

    Gao X Z, Zhao P C, Zhao J H, Sun X F, Liu J J, Yang F, Pan Y 2022 Opt. Express 30 26275Google Scholar

    [18]

    Zhan Q 2009 Adv. Opt. Photon. 1 1Google Scholar

    [19]

    Kozawa Y, Sato S 2021 Prog. Opt. 66 35Google Scholar

    [20]

    Sato S, Kozawa Y 2009 J. Opt. Soc. Am. A Opt. Image Sci. Vis. 26 142Google Scholar

    [21]

    Li M M, Cai Y N, Yan S H, Liang Y S, Zhang P, Yao B L 2018 Phys. Rev. A 97 053842Google Scholar

    [22]

    Monteiro P B, Neto P A M, Nussenzveig H M 2009 Phys. Rev. A 79 033830Google Scholar

    [23]

    Ostrovsky A S, Rickenstorff-Parrao C, Arrizón V 2013 Opt. Lett. 38 534Google Scholar

    [24]

    Grosjean T, Courjon D 2007 Opt. Commun. 272 314Google Scholar

    [25]

    Vaity P, Rusch L 2015 Opt. Lett. 40 597Google Scholar

  • [1] 海迪且木⋅阿布都吾甫尔, 谭乐韬, 于涛, 谢文科, 刘静, 邵铮铮. 基于相干合成涡旋光束的离轴入射转速测量. 物理学报, 2024, 73(16): 168701. doi: 10.7498/aps.73.20240655
    [2] 范海玲, 郭志坚, 李明强, 卓红斌. 等离子体中涡旋光束自聚焦与成丝现象的模拟研究. 物理学报, 2023, 72(1): 014206. doi: 10.7498/aps.72.20221232
    [3] 范钰婷, 朱恩旭, 赵超樱, 谭维翰. 基于电光晶体平板部分相位调制动态产生涡旋光束. 物理学报, 2022, 71(20): 207801. doi: 10.7498/aps.71.20220835
    [4] 朱雪松, 刘星雨, 张岩. 涡旋光束在双拉盖尔-高斯旋转腔中的非互易传输. 物理学报, 2022, 71(15): 150701. doi: 10.7498/aps.71.20220191
    [5] 彭一鸣, 薛煜, 肖光宗, 于涛, 谢文科, 夏辉, 刘爽, 陈欣, 陈芳琳, 孙学成. 相干合成涡旋光束的螺旋谱分析及应用研究. 物理学报, 2019, 68(21): 214206. doi: 10.7498/aps.68.20190880
    [6] 田博宇, 钟哲强, 隋展, 张彬, 袁孝. 基于涡旋光束的超快速角向集束匀滑方案. 物理学报, 2019, 68(2): 024207. doi: 10.7498/aps.68.20181361
    [7] 付时尧, 高春清. 利用衍射光栅探测涡旋光束轨道角动量态的研究进展. 物理学报, 2018, 67(3): 034201. doi: 10.7498/aps.67.20171899
    [8] 于涛, 夏辉, 樊志华, 谢文科, 张盼, 刘俊圣, 陈欣. 贝塞尔-高斯涡旋光束相干合成研究. 物理学报, 2018, 67(13): 134203. doi: 10.7498/aps.67.20180325
    [9] 施建珍, 许田, 周巧巧, 纪宪明, 印建平. 用波晶片相位板产生角动量可调的无衍射涡旋空心光束. 物理学报, 2015, 64(23): 234209. doi: 10.7498/aps.64.234209
    [10] 王亚东, 甘雪涛, 俱沛, 庞燕, 袁林光, 赵建林. 利用非传统螺旋相位调控高阶涡旋光束的拓扑结构. 物理学报, 2015, 64(3): 034204. doi: 10.7498/aps.64.034204
    [11] 施建珍, 杨深, 邹亚琪, 纪宪明, 印建平. 用四台阶相位板产生涡旋光束. 物理学报, 2015, 64(18): 184202. doi: 10.7498/aps.64.184202
    [12] 易煦农, 李瑛, 凌晓辉, 张志友, 范滇元. 光在Metasurface中的自旋-轨道相互作用. 物理学报, 2015, 64(24): 244202. doi: 10.7498/aps.64.244202
    [13] 周巧巧, 施建珍, 纪宪明, 印建平. 用弧形波晶片产生矢量光束及其强聚焦的特性研究. 物理学报, 2015, 64(5): 053702. doi: 10.7498/aps.64.053702
    [14] 王林, 袁操今, 聂守平, 李重光, 张慧力, 赵应春, 张秀英, 冯少彤. 数字全息术测定涡旋光束拓扑电荷数. 物理学报, 2014, 63(24): 244202. doi: 10.7498/aps.63.244202
    [15] 黄素娟, 谷婷婷, 缪庄, 贺超, 王廷云. 多环涡旋光束的实验研究. 物理学报, 2014, 63(24): 244103. doi: 10.7498/aps.63.244103
    [16] 张进, 周新星, 罗海陆, 文双春. 涡旋光束在反射中的正交偏振特性研究. 物理学报, 2013, 62(17): 174202. doi: 10.7498/aps.62.174202
    [17] 丁攀峰, 蒲继雄. 离轴拉盖尔-高斯涡旋光束传输中的光斑演变. 物理学报, 2012, 61(6): 064103. doi: 10.7498/aps.61.064103
    [18] 王铮, 高春清, 辛璟焘. 高阶矢量光束高数值孔径聚焦特性的研究. 物理学报, 2012, 61(12): 124209. doi: 10.7498/aps.61.124209
    [19] 丁攀峰, 蒲继雄. 拉盖尔高斯涡旋光束的传输. 物理学报, 2011, 60(9): 094204. doi: 10.7498/aps.60.094204
    [20] 李阳月, 陈子阳, 刘辉, 蒲继雄. 涡旋光束的产生与干涉. 物理学报, 2010, 59(3): 1740-1748. doi: 10.7498/aps.59.1740
计量
  • 文章访问数:  3900
  • PDF下载量:  175
  • 被引次数: 0
出版历程
  • 收稿日期:  2023-03-01
  • 修回日期:  2023-04-03
  • 上网日期:  2023-04-26
  • 刊出日期:  2023-06-20

/

返回文章
返回