柱矢量涡旋光束在自由空间中传输时角动量的全矢量特性

高雨洁; 李晋红; 王静; 刘晋宏; 尹晓金

doi:10.7498/aps.74.20241344

摘要

利用自旋-动量关系表征了柱矢量涡旋光束在自由空间中传输时的动量(P)、自旋角动量(SAM)、横向自旋角动量(t-SAM)、纵向自旋角动量(l-SAM)、轨道角动量以及矢量光场分布. 研究结果表明: P存在与光轴平行和垂直的分量, t-SAM, l-SAM和光场在拓扑荷m不为零时均存在与光轴平行和垂直的分量, 而SAM只存在与光轴垂直的分量, 不存在与光轴平行的分量. 使用自旋-动量关系, 对在自由空间中传输的柱矢量涡旋光束的光学参量进行全矢量的表征, 可以为分析结构光束在不同介质中传输时的角动量特性提供一定的理论基础.

关键词:

Abstract

The full vector properties of the optical parameters of cylindrical vector vortex beam (CVVB) propagating in free space, such as the momentum (P), spin angular momentum (SAM), transverse-type spin angular momentum (t-SAM), longitudinal-type spin angular momentum (l-SAM), and light field are characterized by using spin-momentum relation in this work. The research results show that P has x-, y-, and z- component, SAM has x- and y- components, but no z-component; t-SAM and l-SAM both have components which are parallel and perpendicular to the optical axis when the topological charge m is not 0; t-SAM has a longitudinal component which is related to the helical trajectory of photons; l-SAM has a transverse component in free space. Except for the angularly polarized vortex beam (APVB), which has no longitudinal field when the topological charge m is 0, both radially polarized vortex beam (RPVB) and APVB have longitudinal fields in free space. The vectorial characteristic of the angular momentum of CVVB in free space can provide a theoretical basis for analyzing the transmission of structured beams in different media.

Keywords:

作者及机构信息

1.
太原科技大学应用科学学院, 山西省光场调控与融合应用技术创新中心, 太原　030024

2.
太原工业学院理学系, 太原　030008

通信作者: 尹晓金, 2021013@tyust.edu.cn

基金项目: 国家自然科学基金(批准号: 62305238, 12104332)和山西省基础研究计划(批准号: 202203021211192)资助的课题.

Authors and contacts

1.
Shanxi Center of Technology Innovation for Light Manipulations and Applications, School of Applied Science, Taiyuan University of Science and Technology, Taiyuan 030024, China

2.
Department of Science, Taiyuan Institute of Technology, Taiyuan 030008, China

Corresponding author: YIN Xiaojin, 2021013@tyust.edu.cn

Funds: Project supported by the National Natural Science Foundation of China (Grant Nos. 62305238, 12104332) and the Fundamental Research Program of Shanxi Province, China (Grant No. 202203021211192).

[1]	Allen L, Beijersbergen M W, Spreeuw R J C, Woerdman J P 1992 Phys. Rev. A 45 8185 Google Scholar
[2]	Allen L, Padgett M J, Babiker M 1999 Prog. Opt. 39 291 Google Scholar
[3]	Fang X Y, Yang H C, Yao W Z, Wang T X, Zhang Y, Gu M, Xiao M 2021 Adv. Photon. 3 015001 Google Scholar
[4]	Bekshaev A, Bliokh K Y, Soskin M 2011 J. Opt. 13 053001 Google Scholar
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[6]	Bliokh K Y, Niv A, Kleiner V, Hasman E 2008 Nat. Photonics 2 748 Google Scholar
[7]	Bliokh K Y 2009 J. Opt. A: Pure Appl. Opt. 11 094009 Google Scholar
[8]	Lin J, Yuan X C, Tao S H, Burge R E 2007 Appl. Opt. 46 4680 Google Scholar
[9]	Wang J, Yang J Y, Fazal I M, Ahmed N, Yan Y, Huang H, Ren Y, Yue Y, Dolinar S, Tur M, Willner A E 2012 Nat. Photonics 6 488 Google Scholar
[10]	Lei T, Zhang M, Li Y R, Jia P, Liu G N, Xu X G, Li Z H, Min C J, Lin J, Yu C Y, Niu H B, Yuan X C 2015 Light Sci. Appl. 4 e257 Google Scholar
[11]	Gibson G, Courtial J, Padgett M J, Vasnetsov M, Pas'ko V, Barnett S M, Franke-Arnold S 2004 Opt. Express 12 5448 Google Scholar
[12]	Richardson D J, Fini J M, Nelson L E 2013 Nat. Photonics 7 354 Google Scholar
[13]	Labroille G, Barré N, Pinel O, Denolle B, Lengle K, Garcia L, Jaffres L, Jian P, Morizur J F 2017 Opt. Fiber Technol. 35 93 Google Scholar
[14]	Yang Y, Ren Y X, Chen M, Arita Y, Rosales-Guzman C 2021 Adv. Photon. 3 034001 Google Scholar
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[17]	Solntsev A S, Agarwal G S, Kivshar Y 2021 Nat. Photonics 15 327 Google Scholar
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[20]	Bliokh K Y, Bekshaev A Y, Nori F 2014 Nat. Commun. 5 3300 Google Scholar
[21]	付泽宇 2018 硕士学位论文(哈尔滨: 哈尔滨工业大学) Fu Z Y 2018 M. S. Thesis (Harbin: Harbin Institute of Technology
[22]	Bliokh K Y, Smirnova D, Nori F 2015 Science 348 1448 Google Scholar
[23]	Bliokh K Y, Rodríguez-Fortuño F J, Bekshaev A Y, Kivshar Y S, Nori F 2018 Opt. Lett. 43 963 Google Scholar
[24]	Shi P, Lei X, Zhang Q, Li H, Du L P, Yuan X C 2022 Phys. Rev. Lett. 128 213904 Google Scholar
[25]	Bekshaev A Y, Bliokh K Y, Nori F 2015 Phys. Rev. X. 5 011039 Google Scholar
[26]	Aiello A, Banzer P 2016 J. Opt. 18 085605 Google Scholar
[27]	Shi P, Li H, Du L P, Yuan X C 2022 ACS Photonics 10 2332 Google Scholar
[28]	Shi P, Du L P, Yang A, Yin X, Lei X, Yuan X C 2023 Commun. Phys. 6 283 Google Scholar
[29]	Yin X J, Shi P, Du L P, Yuan X C 2020 Appl. Phys. Lett. 116 241107 Google Scholar
[30]	Yu P P, Zhao Q, Hu X Y, Li Y M, Gong L 2018 Opt. Lett. 43 5677 Google Scholar
[31]	Li C C, Shi P, Du L P, Yuan X C 2020 Nanoscale 12 13674 Google Scholar
[32]	Alexeyev C N, Alexeyev A N, Lapin B P, Milione G, Yavorsky M A 2013 Phys. Rev. A. 88 63814 Google Scholar
[33]	Volyar A V, Zhilaıtis V Z, Shvedov V G 1998 Tech. Phys. Lett. 24 826 Google Scholar
[34]	Johnson S D, Ma Z, Padgett M J, Ramachandran S 2019 OSA Continuum. 2 2975 Google Scholar
[35]	Chakravarthy T P, Viswanathan N K 2019 OSA Continuum. 2 1576 Google Scholar
[36]	Bliokh K Y, Alonso M A, Ostrovskaya E A, Aiello A 2010 Phys. Rev. A 82 63825 Google Scholar
[37]	Bliokh K Y, Ostrovskaya E A, Alonso M A, Rodríguez-Herrera O G, Lara D, Dainty C 2011 Opt. Express 19 26132 Google Scholar
[38]	Yin X J, Li Y, Jin G L, Wang J, Liu J H, Li J H 2024 J. Opt. Soc. Am. A 41 2231 Google Scholar
[39]	Rodríguez-Fortuño F J, Marino G, Ginzburg P, O´Connor D, Martínez A, Wurtz G A, Zayats A V 2013 Science 340 328 Google Scholar
[40]	Petersen J, Volz J, Rauschenbeutel A 2014 Science 346 67 Google Scholar
[41]	Rodríguez-Fortuño F J, Barber-Sanz I, Puerto D, Griol A, Martinez A 2014 ACS Photonics 1 762 Google Scholar
[42]	赵春刚 2022 硕士学位论文(太原: 太原科技大学) Zhao C G 2022 M. S. Thesis (Taiyuan: Taiyuan University of Science and Technology

施引文献

图 1 拓扑荷m = 0, ±1, ±2时RPVB在自由空间距离源平面z处动量(P)的x, y, z分量, 带有不同拓扑荷m的RPVB的动量分量通过除以相应拓扑荷m下总光强的最大值进行归一化

Fig. 1. The x, y, z components of kinetic momentum (P) of RPVB in free space from the source plane z when the topological charge m = 0, ±1, ±2, the momentum components of RPVB with different topological charges are normalized by dividing by the maximum value of the total light intensity of the corresponding topological charge m.

下载: 全尺寸图片幻灯片

图 2 拓扑荷m = 0, ±1, ±2时RPVB在自由空间距离源平面z处总SAM的x, y, z分量, 带有不同拓扑荷m的RPVB的总SAM分量通过除以相应拓扑荷m下总光强的最大值进行归一化

Fig. 2. The x, y, z components of the total SAM of RPVB in free space from the source plane z when the topological charge m = 0, ±1, ±2, the total SAM component of RPVB with different topological charges is normalized by dividing by the maximum valve of the total light intensity of the corresponding topological charge m.

下载: 全尺寸图片幻灯片

图 3 拓扑荷m = 0, ±1, ±2时RPVB在自由空间距离源平面z处横向自旋(t-SAM)的x, y, z分量, 带有不同拓扑荷m的RPVB的t-SAM的分量通过除以相应拓扑荷m下总光强的最大值进行归一化

Fig. 3. The x, y, z components of the transverse-type spin (t-SAM) of RPVB in free space from the source plane z when the topological charge m = 0, ±1, ±2, the components of the t-SAM of RPVB with different topological charges are normalized by dividing by the maximum value of the total light intensity of the corresponding topological charge m.

下载: 全尺寸图片幻灯片

图 4 拓扑荷m = 0, ±1, ±2时RPVB在自由空间距离源平面z处纵向自旋(l-SAM)的x, y, z分量, 带有不同拓扑荷m的RPVB的l-SAM的分量通过除以相应拓扑荷m下总光强的最大值进行归一化

Fig. 4. The x, y, z components of the longitudinal-type spin (l-SAM) of RPVB in free space from the source plane z when the topological charge m = 0, ±1, ±2, the components of the l-SAM of RPVB with different topological charges are normalized by dividing by the maximum value of the total light intensity of the corresponding topological charge m.

下载: 全尺寸图片幻灯片

图 5 (a)拓扑荷m = 0, ±1, ±2时RPVB在自由空间距离源平面z处的横向场和纵向场光强, 带有不同拓扑荷m的RPVB的横向场和纵向场光强通过除以相应拓扑荷m下I₁ + I₂的最大值进行归一化; (b)拓扑荷m = 0, ±1, ±2时APVB在自由空间距离源平面z处的纵向场光强, 带有不同拓扑荷m的APVB的纵向场光强通过除以相应拓扑荷m下I₁ + I₂的最大值进行归一化

Fig. 5. (a) The transverse field and longitudinal field intensity of RPVB in free space from the source plane z when the topological charge m = 0, ±1, ±2. The transverse and longitudinal field light intensities of RPVB with different topological charges are normalized by dividing by the maximum value of I₁ + I₂ of the corresponding topological charge m; (b) the longitudinal field intensity of APVB in free space from the source plane z when the topological charge m = 0, ±1, ±2, the longitudinal field light intensity of APVB with different topological charges are normalized by dividing by the maximum value of I₁ + I₂ of the corresponding topological charge m.

下载: 全尺寸图片幻灯片

图 6 拓扑荷m = 0, ±1, ±2时RPVB在自由空间距离源平面z处的OAM, 带有不同拓扑荷m的RPVB的OAM通过除以相应拓扑荷m下I₁ + I₂的最大值进行归一化

Fig. 6. The OAM of RPVB in free space from the source plane z when the topological charge m = 0, ±1, ±2, the OAM of RPVB with different topological charges is normalized by dividing by the maximum value of I₁ + I₂ of the corresponding topological charge m.

下载: 全尺寸图片幻灯片

[1]	Allen L, Beijersbergen M W, Spreeuw R J C, Woerdman J P 1992 Phys. Rev. A 45 8185 Google Scholar
[2]	Allen L, Padgett M J, Babiker M 1999 Prog. Opt. 39 291 Google Scholar
[3]	Fang X Y, Yang H C, Yao W Z, Wang T X, Zhang Y, Gu M, Xiao M 2021 Adv. Photon. 3 015001 Google Scholar
[4]	Bekshaev A, Bliokh K Y, Soskin M 2011 J. Opt. 13 053001 Google Scholar
[5]	Shen Y J, Wang X J, Xie Z W, Min C J, Fu X, Liu Q, Gong M L, Yuan X C 2019 Light Sci. Appl. 8 90 Google Scholar
[6]	Bliokh K Y, Niv A, Kleiner V, Hasman E 2008 Nat. Photonics 2 748 Google Scholar
[7]	Bliokh K Y 2009 J. Opt. A: Pure Appl. Opt. 11 094009 Google Scholar
[8]	Lin J, Yuan X C, Tao S H, Burge R E 2007 Appl. Opt. 46 4680 Google Scholar
[9]	Wang J, Yang J Y, Fazal I M, Ahmed N, Yan Y, Huang H, Ren Y, Yue Y, Dolinar S, Tur M, Willner A E 2012 Nat. Photonics 6 488 Google Scholar
[10]	Lei T, Zhang M, Li Y R, Jia P, Liu G N, Xu X G, Li Z H, Min C J, Lin J, Yu C Y, Niu H B, Yuan X C 2015 Light Sci. Appl. 4 e257 Google Scholar
[11]	Gibson G, Courtial J, Padgett M J, Vasnetsov M, Pas'ko V, Barnett S M, Franke-Arnold S 2004 Opt. Express 12 5448 Google Scholar
[12]	Richardson D J, Fini J M, Nelson L E 2013 Nat. Photonics 7 354 Google Scholar
[13]	Labroille G, Barré N, Pinel O, Denolle B, Lengle K, Garcia L, Jaffres L, Jian P, Morizur J F 2017 Opt. Fiber Technol. 35 93 Google Scholar
[14]	Yang Y, Ren Y X, Chen M, Arita Y, Rosales-Guzman C 2021 Adv. Photon. 3 034001 Google Scholar
[15]	Li Y, Zhou L M, Zhao N 2021 Opt. Lett. 46 106 Google Scholar
[16]	Stav T, Faerman A, Maguid E, Oren D, Kleiner V, Hasman E, Segev M 2018 Science 361 1101 Google Scholar
[17]	Solntsev A S, Agarwal G S, Kivshar Y 2021 Nat. Photonics 15 327 Google Scholar
[18]	Chong A, Wan C, Chen J, Zhan Q 2020 Nat. Photonics 14 350 Google Scholar
[19]	Shi P, Du L P, Yuan X C 2021 Nanophotonics 10 3927 Google Scholar
[20]	Bliokh K Y, Bekshaev A Y, Nori F 2014 Nat. Commun. 5 3300 Google Scholar
[21]	付泽宇 2018 硕士学位论文(哈尔滨: 哈尔滨工业大学) Fu Z Y 2018 M. S. Thesis (Harbin: Harbin Institute of Technology
[22]	Bliokh K Y, Smirnova D, Nori F 2015 Science 348 1448 Google Scholar
[23]	Bliokh K Y, Rodríguez-Fortuño F J, Bekshaev A Y, Kivshar Y S, Nori F 2018 Opt. Lett. 43 963 Google Scholar
[24]	Shi P, Lei X, Zhang Q, Li H, Du L P, Yuan X C 2022 Phys. Rev. Lett. 128 213904 Google Scholar
[25]	Bekshaev A Y, Bliokh K Y, Nori F 2015 Phys. Rev. X. 5 011039 Google Scholar
[26]	Aiello A, Banzer P 2016 J. Opt. 18 085605 Google Scholar
[27]	Shi P, Li H, Du L P, Yuan X C 2022 ACS Photonics 10 2332 Google Scholar
[28]	Shi P, Du L P, Yang A, Yin X, Lei X, Yuan X C 2023 Commun. Phys. 6 283 Google Scholar
[29]	Yin X J, Shi P, Du L P, Yuan X C 2020 Appl. Phys. Lett. 116 241107 Google Scholar
[30]	Yu P P, Zhao Q, Hu X Y, Li Y M, Gong L 2018 Opt. Lett. 43 5677 Google Scholar
[31]	Li C C, Shi P, Du L P, Yuan X C 2020 Nanoscale 12 13674 Google Scholar
[32]	Alexeyev C N, Alexeyev A N, Lapin B P, Milione G, Yavorsky M A 2013 Phys. Rev. A. 88 63814 Google Scholar
[33]	Volyar A V, Zhilaıtis V Z, Shvedov V G 1998 Tech. Phys. Lett. 24 826 Google Scholar
[34]	Johnson S D, Ma Z, Padgett M J, Ramachandran S 2019 OSA Continuum. 2 2975 Google Scholar
[35]	Chakravarthy T P, Viswanathan N K 2019 OSA Continuum. 2 1576 Google Scholar
[36]	Bliokh K Y, Alonso M A, Ostrovskaya E A, Aiello A 2010 Phys. Rev. A 82 63825 Google Scholar
[37]	Bliokh K Y, Ostrovskaya E A, Alonso M A, Rodríguez-Herrera O G, Lara D, Dainty C 2011 Opt. Express 19 26132 Google Scholar
[38]	Yin X J, Li Y, Jin G L, Wang J, Liu J H, Li J H 2024 J. Opt. Soc. Am. A 41 2231 Google Scholar
[39]	Rodríguez-Fortuño F J, Marino G, Ginzburg P, O´Connor D, Martínez A, Wurtz G A, Zayats A V 2013 Science 340 328 Google Scholar
[40]	Petersen J, Volz J, Rauschenbeutel A 2014 Science 346 67 Google Scholar
[41]	Rodríguez-Fortuño F J, Barber-Sanz I, Puerto D, Griol A, Martinez A 2014 ACS Photonics 1 762 Google Scholar
[42]	赵春刚 2022 硕士学位论文(太原: 太原科技大学) Zhao C G 2022 M. S. Thesis (Taiyuan: Taiyuan University of Science and Technology

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