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部分相干多离轴涡旋矢量光束的传输特性

徐华锋 张兴宇 王仁杰

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部分相干多离轴涡旋矢量光束的传输特性

徐华锋, 张兴宇, 王仁杰

Propagation properties of partially coherent vector beam with multiple off-axis vortex phases

Xu Hua-Feng, Zhang Xing-Yu, Wang Ren-Jie
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  • 基于相干与偏振的统一理论, 采用傅里叶变换和卷积定理的方法, 研究了携带多个离轴涡旋相位的径向偏振矩形对称余弦-高斯关联结构光束的传输特性. 结果表明, 该光束因其独特的空间相干结构而具有自分裂特性, 可以分裂成4束完全相同的子波瓣. 更重要的是, 多离轴涡旋相位的调制可以作用在每个子波瓣上. 当相干度较大时, 通过调制光束的离轴涡旋数量N0和光束阶数可以在焦平面处产生具有三角形或正方形等多边形空心光强分布的光斑阵列, 并且每个子波瓣上对应的偏振态呈现倒三角形或斜正方形的椭圆分布. 当相干度较小时, 部分相干光束的空间相干性调控占主导作用, 多离轴涡旋相位的调制效果消失, 每个子波瓣的光强退化成高斯形式分布, 但其偏振态分布仍保持不变, 与光束阶数和相干长度无关. 此外, 当利用障碍物遮挡住其中一个离轴涡旋相位时, 光束仍具有一定的自修复能力. 然而, 若将其中一个离轴涡旋相位完全遮挡住, 此时每个子波瓣的强度分布和偏振态分布都遭到破坏, 会出现不同程度的“缺口”.
    In this paper, we investigate the propagation properties of radially polarized rectangular-symmetric cosine-Gaussian Schell-model (RCGSM) beam with multiple off-axis vortex phases by using Fourier transform and convolution method based on the unified theory of coherence and polarization. The results indicate that the radially polarized RCGSM beam has self-splitting properties and can be split into four identical lobes due to its unique spatial coherence structure. Furthermore, the modulation of multiple off-axis vortex phases can be acted on each lobe. For high coherence, the spot arrays with triangular or square hollow light intensity distribution can be generated in the focal plane by modulating the number of off-axis vortices (N0) and the beam order, and the corresponding state of polarization on each lobe presents an inverted triangular or oblique square elliptic distribution. However, for small coherence, the modulation effect of multiple off-axis vortex phases disappears and the light intensity of each lobe degenerates into a quasi-Gaussian distribution, whereas its state of polarization keeps invariant, which is independent of the beam order and coherence length. In addition, the beam still has a certain self-healing ability for one of the off-axis vortex phases partially blocked by an obstacle, but it will be destroyed for completely blocking, resulting in a notch on each lobe.
      通信作者: 徐华锋, xhfeng716@126.com
    • 基金项目: 安徽省高校自然科学研究项目(批准号: 2023AH051206)和安徽省高等学校省级质量工程项目(批准号: 2022xxkc028)资助的课题.
      Corresponding author: Xu Hua-Feng, xhfeng716@126.com
    • Funds: Project supported by the Natural Science Foundation of the Higher Education Institutions of Anhui Province, China (Grant No. 2023AH051206) and the Quality Engineering Project of Higher Education of Anhui Province, China (Grant No. 2022xxkc028).
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    Wang F, Yu J Y, Liu X L, Cai Y J 2018 Acta Phys. Sin. 67 184203Google Scholar

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    Peng D M, Huang Z F, Liu Y L, Chen Y H, Wang F, Ponomarenko S A, Cai Y J 2021 PhotoniX 2 6Google Scholar

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    Chen Y H, Wang F, Cai Y J 2022 Adv. Phys. X 7 2009742Google Scholar

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    许文慧, 宁守琮, 张福才 2021 物理学报 70 214201Google Scholar

    Xu W H, Ning S C, Zhang F C 2021 Acta Phys. Sin. 70 214201Google Scholar

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    Gori F, Santarsiero M 2007 Opt. Lett. 32 3531Google Scholar

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    Gori F, Ramírez-Sánchez V, Santarsiero M, Shirai T 2009 J. Opt. A: Pure Appl. Opt. 11 085706Google Scholar

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    Chen Y H, Gu J X, Wang F, Cai Y J 2015 Phys. Rev. A 91 013823Google Scholar

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    Mei Z R 2014 Opt. Lett. 39 347Google Scholar

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    Chen Y H, Cai Y J 2014 Opt. Lett. 39 2549Google Scholar

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    Mei Z R 2014 Opt. Express 22 13029Google Scholar

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    Liang C H, Wang F, Liu X L, Cai Y J, Korotkova O 2014 Opt. Lett. 39 769Google Scholar

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    Chen Y H, Wang F, Cai Y J 2015 物理学进展 35 51Google Scholar

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    陈亚红, 蔡阳健 2016 光学学报 36 1026002Google Scholar

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    曾军, 陈亚红, 刘显龙, 蔡阳健 2019 光学学报 39 1026004Google Scholar

    Zeng J, Chen Y H, Liu X L, Cai Y J 2019 Acta Opt. Sin. 39 1026004Google Scholar

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    Ginson G, Courtial J, Padgett M, Vasnetsov M, Pas'ko V, Barnett S, Franke-Arnold S 2004 Opt. Express 12 5448Google Scholar

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    陈康, 马志远, 张明明, 窦建态, 胡友友 2022 物理学报 71 014203Google Scholar

    Cheng K, Ma Z Y, Zhang M M, Dou J T, Hu Y Y 2022 Acta Phys. Sin. 71 014203Google Scholar

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  • 图 1  (a)源平面处第j个离轴涡旋中心与观察点的位置矢量关系; (b)—(d)携带3个离轴涡旋相位(拓扑荷数l = 1)的径向偏振RCGSM光束在源平面处的(b)离轴涡旋相位排列、(c)离轴涡旋相位分布和(d)光强分布

    Fig. 1.  (a) An illustration of the position vector relationship between the j-th off-axis vortex phase core and the observation point in the initial plane; (b) arrangement of three off-axis vortex phases, (c) phase distribution, and (d) intensity distribution of a radially polarized RCGSM beam carrying three off-axis vortices in the source plane, respectively.

    图 2  当光束阶数$ m = n = 5 $时, 携带3个离轴涡旋相位的径向偏振RCGSM光束通过薄透镜后的聚焦光强演化

    Fig. 2.  Evolution of the focused intensity of a radially polarized RCGSM beam carrying three off-axis vortex phases through a thin lens when the beam order $ m = n = 5 $.

    图 3  当光束阶数$ m = n = 5 $时, 携带4个离轴涡旋相位的径向偏振RCGSM光束的聚焦光强演化

    Fig. 3.  Evolution of the focused intensity of a radially polarized RCGSM beam carrying four off-axis vortex phases through a thin lens when the beam order $ m = n = 5 $.

    图 4  当光束阶数$ m = n = 5 $和相干长度$ {\delta _0} = 1.5{\kern 1 pt} {\kern 1 pt} {\kern 1 pt} {\kern 1 pt} {\kern 1 pt} {\text{mm}} $时, 携带4个离轴涡旋相位的径向偏振RCGSM光束通过扇形障碍物的聚焦光强演化

    Fig. 4.  Evolution of the focused intensity of a radially polarized RCGSM beam carrying four off-axis vortex phases after passing through a sector-shaped opaque obstacle when the beam order $ m = n = 5 $ and coherent length $ {\delta _0} = 1.5{\kern 1 pt} {\kern 1 pt} {\kern 1 pt} {\kern 1 pt} {\kern 1 pt} {\text{mm}} $.

    图 5  携带4个离轴涡旋相位的径向偏振RCGSM光束通过圆形障碍物后的聚焦光强演化($ m = n = 5 $, $ {\delta _0} = 1.5{\kern 1 pt} {\kern 1 pt} {\kern 1 pt} {\kern 1 pt} {\kern 1 pt} {\text{mm}} $)

    Fig. 5.  Evolution of the focused intensity of a radially polarized RCGSM beam carrying four off-axis vortex phases after passing through a circular obstacle when the beam order $ m = n = 5 $ and coherent length $ {\delta _0} = 1.5{\kern 1 pt} {\kern 1 pt} {\kern 1 pt} {\kern 1 pt} {\kern 1 pt} {\text{mm}} $.

    图 6  当光束阶数$ {m_0} = {n_0} = 5 $和相干长度$ {\delta _0} = 1.5{\kern 1 pt} {\kern 1 pt} {\kern 1 pt} {\kern 1 pt} {\kern 1 pt} {\text{mm}} $时, 携带多个离轴涡旋相位的径向偏振RCGSM光束通过薄透镜后的偏振态演化情况

    Fig. 6.  Evolution of the state of polarization of radially polarized RCGSM beams carrying multiple off-axis vortex phases through a thin lens when the beam order $ {m_0} = {n_0} = 5 $ and coherent length $ {\delta _0} = 1.5{\kern 1 pt} {\kern 1 pt} {\kern 1 pt} {\kern 1 pt} {\kern 1 pt} {\text{mm}} $.

    图 7  当相干长度$ {\delta _0} = 1.5{\kern 1 pt} {\kern 1 pt} {\kern 1 pt} {\kern 1 pt} {\kern 1 pt} {\text{mm}} $时, 光束阶数$ {m_0}, {n_0} $对携带多个离轴涡旋相位的径向偏振RCGSM光束在焦平面处偏振态分布的影响

    Fig. 7.  Influences of beam order $ {m_0}, {n_0} $ on the distribution of the state of polarization of radially polarized RCGSM beams carrying multiple off-axis vortex phases in the focal plane when the coherent length $ {\delta _0} = 1.5{\kern 1 pt} {\kern 1 pt} {\kern 1 pt} {\kern 1 pt} {\kern 1 pt} {\text{mm}} $.

    图 8  当光束阶数$ {m_0} = {n_0} = 2 $时, 相干长度$ {\delta _0} $对携带多个离轴涡旋相位的径向偏振RCGSM光束在焦平面处偏振态分布的影响

    Fig. 8.  Influence of coherent length $ {\delta _0} $ on the distribution of the state of polarization of radially polarized RCGSM beams carrying multiple off-axis vortex phases in the focal plane when the beam order $ {m_0} = {n_0} = 2 $.

    图 9  当光束阶数$ m = n = 2 $和相干长度$ {\delta _0} = 0.5{\text{mm}} $时, 携带多个离轴涡旋相位的径向偏振RCGSM光束通过扇形障碍物后在焦平面处的偏振态分布

    Fig. 9.  Distribution of the state of polarization in the focal plane for the radially polarized RCGSM beams carrying multiple off-axis vortex phases through a sector-shaped opaque when the beam order $ m = n = 2 $ and the coherent length $ {\delta _0} = 0.5{\kern 1 pt} {\kern 1 pt} {\kern 1 pt} {\kern 1 pt} {\kern 1 pt} {\text{mm}} $.

  • [1]

    Ricklin J C, Davidson F M 2002 J. Opt. Soc. Am. A 19 1794Google Scholar

    [2]

    Cai Y J 2011 Proc. SPIE 7924 792402Google Scholar

    [3]

    王飞, 余佳益, 刘显龙, 蔡阳健 2018 物理学报 67 184203Google Scholar

    Wang F, Yu J Y, Liu X L, Cai Y J 2018 Acta Phys. Sin. 67 184203Google Scholar

    [4]

    Peng D M, Huang Z F, Liu Y L, Chen Y H, Wang F, Ponomarenko S A, Cai Y J 2021 PhotoniX 2 6Google Scholar

    [5]

    Chen Y H, Wang F, Cai Y J 2022 Adv. Phys. X 7 2009742Google Scholar

    [6]

    许文慧, 宁守琮, 张福才 2021 物理学报 70 214201Google Scholar

    Xu W H, Ning S C, Zhang F C 2021 Acta Phys. Sin. 70 214201Google Scholar

    [7]

    Gori F, Santarsiero M 2007 Opt. Lett. 32 3531Google Scholar

    [8]

    Gori F, Ramírez-Sánchez V, Santarsiero M, Shirai T 2009 J. Opt. A: Pure Appl. Opt. 11 085706Google Scholar

    [9]

    Chen Y H, Gu J X, Wang F, Cai Y J 2015 Phys. Rev. A 91 013823Google Scholar

    [10]

    Mei Z R 2014 Opt. Lett. 39 347Google Scholar

    [11]

    Chen Y H, Cai Y J 2014 Opt. Lett. 39 2549Google Scholar

    [12]

    Mei Z R 2014 Opt. Express 22 13029Google Scholar

    [13]

    Liang C H, Wang F, Liu X L, Cai Y J, Korotkova O 2014 Opt. Lett. 39 769Google Scholar

    [14]

    Chen Y H, Wang F, Cai Y J 2015 物理学进展 35 51Google Scholar

    陈亚红, 王飞, 蔡阳健 2015 Prog. Phys. 35 51Google Scholar

    [15]

    陈亚红, 蔡阳健 2016 光学学报 36 1026002Google Scholar

    Chen Y H, Cai Y J 2016 Acta Opt. Sin. 36 1026002Google Scholar

    [16]

    曾军, 陈亚红, 刘显龙, 蔡阳健 2019 光学学报 39 1026004Google Scholar

    Zeng J, Chen Y H, Liu X L, Cai Y J 2019 Acta Opt. Sin. 39 1026004Google Scholar

    [17]

    Willner A E, Huang H, Yan Y, Ren Y, Ahmed N, Xie G 2015 Adv. Opt. Photonics 7 66Google Scholar

    [18]

    Ni J C, Wang C W, Zhang C C, Hu Y L, Yang L, Lao Z X, Xu B, Li J W, Wu D, Chu J R 2017 Light Sci. Appl. 6 e17011Google Scholar

    [19]

    Ginson G, Courtial J, Padgett M, Vasnetsov M, Pas'ko V, Barnett S, Franke-Arnold S 2004 Opt. Express 12 5448Google Scholar

    [20]

    陈康, 马志远, 张明明, 窦建态, 胡友友 2022 物理学报 71 014203Google Scholar

    Cheng K, Ma Z Y, Zhang M M, Dou J T, Hu Y Y 2022 Acta Phys. Sin. 71 014203Google Scholar

    [21]

    Zhang H, Zeng J, Lu X Y, Wang Z Y, Zhao C L, Cai Y J 2021 Nanophoto. 11 241Google Scholar

    [22]

    Ostrovsky A S, Rickenstorffparrao C, Arrizon V 2013 Opt. Lett. 38 534Google Scholar

    [23]

    李阳月, 陈子阳, 刘辉, 蒲继雄 2010 物理学报 59 1740Google Scholar

    Li Y Y, Chen Z Y, Liu H, Pu J X 2010 Acta Phys. Sin. 59 1740Google Scholar

    [24]

    Bekshaev A Y, Karamoch A I 2008 Opt. Commun. 281 3597Google Scholar

    [25]

    Wang X L, Zhu B W, Dong Y X, Wang S, Zhu Z Q, Bo F, Li X P 2017 Opt. Express 25 26844Google Scholar

    [26]

    Xu H F, Zhang R, Sheng Z Q, Qu J 2020 Opt. Express 28 28858Google Scholar

    [27]

    Mei Z R, Mao Y H, Wang J X, Shi X H 2023 Opt. Express 31 727Google Scholar

    [28]

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

    [29]

    刘森森, 宋华冬, 林伟强, 陈旭东, 蒲继雄 2019 物理学报 68 074201Google Scholar

    Liu S S, Song H D, Lin W Q, Chen X D, Pu J X 2019 Acta Phys. Sin. 68 074201Google Scholar

    [30]

    Wolf E 2003 Phys. Lett. A 312 263Google Scholar

    [31]

    Mei Z R 2017 IEEE Photon. J. 9 6102306Google Scholar

    [32]

    Wu G F, Tao C Y 2018 Opt. Commun. 424 86Google Scholar

    [33]

    Zhou Y Q, Cui Z W, Han Y P 2022 Opt. Express 30 23448Google Scholar

    [34]

    Peng X F, Wang H Y, Liu L, Wang F, Popov S, Cai Y J 2020 Opt. Express 28 31510Google Scholar

    [35]

    Liu X L, Peng X F, Liu L, Wu G F, Zhao C L, Wang F, Cai Y J 2017 Appl. Phys. Lett. 110 181104Google Scholar

    [36]

    Zeng J, Liang C H, Wang H Y, Wang F, Zhao C L, Gbur G, Cai Y J 2020 Opt. Express 28 11493Google Scholar

    [37]

    Korotkova O, Wolf E 2005 Opt. Commun. 246 35Google Scholar

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出版历程
  • 收稿日期:  2023-09-14
  • 修回日期:  2023-10-26
  • 上网日期:  2023-11-01
  • 刊出日期:  2024-02-05

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