Search

Article

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

Nonreciprocal transmission of vortex beam in double Laguerre-Gaussian rotational cavity system

Zhu Xue-Song Liu Xing-Yu Zhang Yan

Citation:

Nonreciprocal transmission of vortex beam in double Laguerre-Gaussian rotational cavity system

Zhu Xue-Song, Liu Xing-Yu, Zhang Yan
PDF
HTML
Get Citation
  • By constructing an optorotational system composed of two linearly coupled Laguerre-Gaussian rotational cavities, we realize the nonreciprocal transmission of the vortex beam with the orbital angular momentum. Two vortex beam cavity modes driven by strong fields are coupled with a rotational mirror via the torsion, and two cavity modes interact with each other via the optical fiber. A weak probe field is incident from one side of the system for examining the optical response along one propagating direction. With the Hamiltonian of the system and the Heisenberg-Langevin equation, we can obtain the transmission of the output light field from the input-output theory. The result shows that the optical nonreciprocity of the vortex beam arises from the quantum interference between the optorotational interaction and the linear coupling interaction between two vortex beam modes, and the phase difference can be used to adjust the optical nonreciprocity. The phase difference can determine not only the occurrence of the nonreciprocity but also the direction of nonreciprocity. Moreover, the ratio of the topological charges carried by the two vortex beam fields has an influence on the transmission. Under an appropriate topological charge ratio, the unidirectional transmission of the vortex beam can be realized in such a system. It is found that whether the topological charge ratio is positive or negative, i.e. whether the vortex beam is left-hand beam or right-hand beam, does not affect the transmission; the influence of the topological charge on the transmission amplitude actually comes from the topological charge number carried by the vortex beam, due to the fact that the coupling strength between the rotating mirror mode and the cavity mode depends on the topological charge number. In addition, we also obtain the condition that the system damping rates should meet for realizing the perfect nonreciprocal propagation of the vortex beam. Finally, we can achieve the nonreciprocal group velocity of the slow light. The direction of the nonreciprocal slow light can be controlled via phase modulation. Our work provides a possible application in manipulating the vortex beam propagation. Furthermore, we extend the nonreciprocity of ordinary beams in the optomechanical system to the nonreciprocity of the vortex beam in the optorotational system. The results are expected to be applied to fabricating the ideal optical isolators for the vortex beam carrying the orbital angular momentum in optical communication.
      Corresponding author: Zhang Yan, zhangy345@nenu.edu.cn
    • Funds: Project supported by the National Natural Science Foundation of China (Grant No. 11704064), the Science Foundation of the Education Department of Jilin Province during the 14th Five-Year Plan Period, China (Grant No. JJKH20211279KJ), and the Fundamental Research Fund for the Central Universities, China (Grant No. 2412019FZ045).
    [1]

    Allen L, Beijersbergen M W, Spreeuw R J, Woerdman J P 1992 Phys. Rev. A 45 8185Google Scholar

    [2]

    Yao A M, Padgett M J 2011 Adv. Opt. Photonics 3 161Google Scholar

    [3]

    He H, Friese M E J, Heckenberg N R, Rubinsztein-Dunlop H 1995 Phys. Rev. Lett. 75 826Google Scholar

    [4]

    Andersen M F, Ryu C, Clade P, Natarajan V, Vaziri A, Helmerson K, Phillips W D 2006 Phys. Rev. Lett. 97 170406Google Scholar

    [5]

    Volpe G, Petrov D 2006 Phys. Rev. Lett. 97 210603Google Scholar

    [6]

    Bhattacharya M, Meystre P 2007 Phys. Rev. Lett. 99 153603Google Scholar

    [7]

    Liu Y M, Bai C H, Wang D Y, Wang T, Zheng M H, Wang H F, Zhu A D, Zhang S 2018 Opt. Express 26 6143Google Scholar

    [8]

    Peng J X, Chen Z, Yuan Q Z, Feng X L 2019 Phys. Rev. A 99 043817Google Scholar

    [9]

    Zhang Z, Wang Y P, Wang X 2021 Front. Phys. 16 32503Google Scholar

    [10]

    Kazemi S H, Mahmoudi M 2020 Phys. Scr. 95 045107Google Scholar

    [11]

    Bhattacharya M, Giscard P L, Meystre P 2008 Phys. Rev. A 77 013827Google Scholar

    [12]

    Cheng H J, Zhou S J, Peng J X, Kundu A, Li H X, Jin L, Feng X L 2021 J. Opt. Soc. Am. B 38 285Google Scholar

    [13]

    Xiong H, Huang Y M, Wu Y 2021 Phys. Rev. A 103 043506Google Scholar

    [14]

    Law C K 1995 Phys. Rev. A 51 2537Google Scholar

    [15]

    Xiong H, Si L G, Zheng A S, Yang X, Wu Y 2012 Phys. Rev. A 86 013815Google Scholar

    [16]

    Tian L 2013 Phys. Rev. Lett. 110 233602Google Scholar

    [17]

    Deng Z J, Habraken S J M, Marquardt F 2016 New. J. Phys. 18 063022Google Scholar

    [18]

    Deng Z J, Yan X B, Wang Y D, Wu C W 2016 Phys. Rev. A 93 033842Google Scholar

    [19]

    Yan X B 2017 Phys. Rev. A 96 053831Google Scholar

    [20]

    张秀龙, 鲍倩倩, 杨明珠, 田雪松 2018 物理学报 67 104203Google Scholar

    Zhang X L, Bao Q Q, Yang M Z, Tian X S 2018 Acta Phys. Sin. 67 104203Google Scholar

    [21]

    Agarwal G S, Huang S M 2010 Phys. Rev. A 81 041803Google Scholar

    [22]

    Shu J 2011 Chin. Phys. Lett. 28 104203Google Scholar

    [23]

    陈华俊, 米贤武 2011 物理学报 60 124206Google Scholar

    Chen H J, Mi X W 2011 Acta Phys. Sin. 60 124206Google Scholar

    [24]

    He B, Yang L, Lin Q, Xiao M 2017 Phys. Rev. Lett. 118 233604Google Scholar

    [25]

    Li Y, Wu L A, Wang Z D 2011 Phys. Rev. A 83 043804Google Scholar

    [26]

    Xiong H, Fan Y W, Yang X, Wu Y 2016 Appl. Phys. Lett. 109 061108Google Scholar

    [27]

    Chen Y T, Du L, Zhang Y, Wu J H 2021 Phys. Rev. A 103 053712Google Scholar

    [28]

    Ge Y Q, Chen Y T, Yin K, Zhang Y 2020 Phys. Lett. A 384 126836Google Scholar

    [29]

    Chen Y T, Du L, Liu Y M, Zhang Y 2020 Opt. Express 28 7095Google Scholar

    [30]

    Bi L, Hu J, Jiang P, Kim D H, Dionne G F, Kimerling L C, Ross C A 2011 Nat. Photonics 5 758Google Scholar

    [31]

    Aplet L J, Carson J W 1964 Appl. Opt. 3 544Google Scholar

    [32]

    Korneeva Y P, Vodolazov D Y, Semenov A V, Florya I N, Simonov N, Baeva E, Korneev A A, Goltsman G N, Klapwijk T M 2018 Phys. Rev. Appl. 9 064037Google Scholar

    [33]

    Shen Z, Zhang Y L, Chen Y, Zou C L, Xiao Y F, Zou X B, Sun F W, Guo G C, Dong C H 2016 Nat. Photonics 10 657Google Scholar

    [34]

    Maayani S, Dahan R, Kligerman Y, Moses E, Hassan A U, Jing H, Nori F, Christodoulides D N, Carmon T 2018 Nature 558 569Google Scholar

    [35]

    Li B, Huang R, Xu X W, Miranowicz A, Jing H 2019 Photonics Res. 7 630Google Scholar

    [36]

    Li Y, Huang Y Y, Zhang X Z, Tian L 2017 Opt. Express 25 018907Google Scholar

    [37]

    Mirza I M, Ge W C, Jing H 2019 Opt. Express 27 25515Google Scholar

    [38]

    Jiang C, Song L N, Li Y 2018 Phys. Rev. A 97 053812Google Scholar

    [39]

    Jiang C, Baowei J I, Cui Y S, Zuo F, Shi J, Chen G 2018 Opt. Express 26 15255Google Scholar

    [40]

    Jiang C, Song L N, Li Y 2019 Phys. Rev. A 99 023823Google Scholar

    [41]

    Xu X W, Li Y 2015 Phys. Rev. A 91 053854Google Scholar

    [42]

    Xu X W, Li Y, Chen A X, Liu Y X 2016 Phys. Rev. A 93 023827Google Scholar

    [43]

    Xu X W, Song L N, Zheng Q, Wang Z H, Li Y 2018 Phys. Rev. A 98 063845Google Scholar

    [44]

    Yan X B, Lu H L, Gao F, Yang L 2019 Front. Rhys. 14 52601Google Scholar

    [45]

    Xia C C, Yan X B, Tian X D, Gao F 2019 Opt. Commun. 451 197Google Scholar

    [46]

    张利巍, 李贤丽, 杨柳 2019 物理学报 68 170701Google Scholar

    Zhang L W, Li X L, Yang L 2019 Acta Phys. Sin. 68 170701Google Scholar

    [47]

    Agarwal G S, Huang S 2014 New J. Phys. 16 033023Google Scholar

    [48]

    Yan X B, Cui C L, Gu K H, Tian X D, Fu C B, Wu J H 2014 Opt. Express 22 4886Google Scholar

    [49]

    Safavi-Naeini A H, Mayer Alegre T P, Chan J, Eichenfield M, Winger M, Lin Q, Hill J T, Chang D E, Painter O 2011 Nature 472 69Google Scholar

    [50]

    Weis S, Riviere R, Deleglise S, Gavartin E, Arcizet O, Schliesser A, Kippenberg T J 2010 Science 330 1520Google Scholar

    [51]

    Oemrawsingh S S R, Eliel E R, Woerdman J P, Verstegen E J K, Kloosterboer J G, 't Hooft G W 2004 J. Opt. A: Pure Appl. Opt. 6 S228

    [52]

    Li L, Allen Y Y, Huang C, Grewell D A, Benatar A, Chen Y 2006 Opt. Eng. 45 113401Google Scholar

    [53]

    Shi H, Bhattacharya M 2016 J. Phys. B 49 153001Google Scholar

    [54]

    Shen Y, Campbell G T, Hage B, Zou H, Buchler B C, Lam P K 2013 J. Opt. 15 044005Google Scholar

  • 图 1  双拉盖尔-高斯旋转腔示意图, 两L-G腔场通过光旋转相互作用与中间的旋转腔镜耦合, 振幅为$ {\varepsilon _{\text{c}}} $$ {\varepsilon _{\text{d}}} $($ {\varepsilon _{\text{L}}} $$ {\varepsilon _{\text{R}}} $)的强驱动场(弱探测场)分别从两侧入射系统来驱动L-G腔模$ {c_1} $$ {c_{\text{2}}} $, 同时用光纤将两L-G腔模线性耦合. 旋转腔镜的平衡位置为$ {\phi _{\text{0}}} $, 在扭力作用下的角位移用$ \phi $角表示

    Figure 1.  Schematic diagram of double Laguerre-Gaussian (L-G) rotational-cavity. The two L-G cavity modes are coupled with a rotating cavity mirror in the middle via the optical rotation interaction. Two strong pump fields (weak probe fields) with amplitudes $ {\varepsilon _{\text{c}}} $ and $ {\varepsilon _{\text{d}}} $ ($ {\varepsilon _{\text{L}}} $ and $ {\varepsilon _{\text{R}}} $) are incident on the system from both sides to drive the L-G cavity modes $ {c_1} $ and $ {c_{\text{2}}} $, and the two L-G cavity modes are linearly coupled with an optical fiber. The equilibrium position of the rotational mirror is $ {\phi _{\text{0}}} $, and the angular displacement is indicated by angle $ \phi $ under the action of the torsion.

    图 2  传输振幅$ {T_{12}} $(红色实线)和$ {T_{21}} $(蓝色虚线)在不同非互易相位差$ \theta $下随标准化失谐$ x/{\kappa _1} $的演化 (a) $ \theta = 0 $; (b) $ \theta = - {\text{π }}/4 $; (c) $ \theta = {\text{π }}/4 $; (d) $ \theta = - {\text{π }}/2 $; (e) $ \theta = {\text{π }}/2 $. (f)在标准化失谐为零(x = 0)时, 传输振幅$ {T_{12}} $(红色实线)和$ {T_{21}} $(蓝色虚线)随非互易相位差$ \theta $的演化. 其他参数为$ {\kappa _1} = 1 $, $ {\kappa _2} = 1 $, $ \gamma = 1 $, $ {G_i} = \sqrt {{\kappa _i}\gamma } /2 $, $ J = \sqrt {{\kappa _1}{\kappa _2}} /2 $.

    Figure 2.  Transmission amplitudes $ {T_{12}} $ (red solid line) and $ {T_{21}} $ (blue dotted line) versus normalized detuning $ x/{\kappa _1} $ under different nonreciprocal phase difference: (a) $ \theta = 0 $; (b) $ \theta = - {\text{π }}/4 $; (c) $ \theta = {\text{π }}/4 $; (d) $ \theta = - {\text{π }}/2 $; (e) $ \theta = {\text{π }}/2 $. (f) Transmission amplitudes $ {T_{12}} $ (red solid line) and $ {T_{21}} $ (blue dotted line) versus nonreciprocal phase difference with $ x = 0 $. Other parameters are $ {\kappa _1} = 1 $, $ {\kappa _2} = 1 $, $ \gamma = 1 $, $ {G_i} = \sqrt {{\kappa _i}\gamma } /2 $, $ J = \sqrt {{\kappa _1}{\kappa _2}} /2 $.

    图 3  (a)传输振幅$ {T_{12}} $和(b)传输振幅$ {T_{{\text{21}}}} $作为标准化失谐$ x/{\kappa _1} $和旋转镜与腔$ {c_1} $耗散比$ \gamma /{\kappa _1} $的函数; (c)传输振幅$ {T_{12}} $和(d)传输振幅$ {T_{{\text{21}}}} $作为标准化失谐$ x/{\kappa _1} $和腔$ {c_2} $与腔$ {c_1} $耗散比$ {\kappa _2}/{\kappa _1} $的函数. 其他参数为$ \theta = {\text{π }}/2 $, $ {\kappa _1} = 1 $, $ {G_1} = {G_2} = J = 1/2 $

    Figure 3.  (a) Transmission amplitude $ {T_{12}} $ and (b) transmission amplitude $ {T_{21}} $ as a function of the normalized detuning $ x/{\kappa _1} $ and the dissipation ratio $ \gamma /{\kappa _1} $ of rotating mirror to cavity $ {c_1} $; (c) transmission amplitudes $ {T_{12}} $ and (d) transmission amplitudes $ {T_{21}} $ as a function of the normalized detuning $ x/{\kappa _1} $ and the dissipation ratio $ {\kappa _2}/{\kappa _1} $ of cavity $ {c_2} $ to cavity $ {c_1} $. Other parameters are $ \theta = {\text{π }}/2 $, $ {\kappa _1} = 1 $, $ {G_1} = {G_2} = J = 1/2 $.

    图 4  传输振幅$ {T_{12}} $(红色圆圈)和$ {T_{21}} $(蓝色圆圈)在不同非互易相位差$ \theta $下随两个涡旋光场所携带拓扑荷之比$ {\ell _2}/{\ell _1} $的演化 (a) $\theta = 0$; (b) $ \theta = - {\text{π }}/4 $; (c) $ \theta = {\text{π }}/4 $; (d) $ \theta = - {\text{π }}/2 $; (e) $ \theta = {\text{π }}/2 $; (f) $ \theta = {\text{π }} $. 其他参数为$ {\kappa _1} = 1 $, $ {\kappa _2} = 1 $, $ \gamma = 1 $, $ J = 2{G_1}{G_2}/\gamma $

    Figure 4.  Transmission amplitudes $ {T_{12}} $ (red circle) and $ {T_{21}} $ (blue circle) with ratio of topological charges carried by two vortex optical fields $ {\ell _2}/{\ell _1} $ under different nonreciprocal phase difference: (a) $ \theta = 0 $; (b)$ \theta = - {\text{π }}/4 $; (c)$ \theta = {\text{π }}/4 $; (d) $ \theta = - {\text{π }}/2 $; (e) $ \theta = {\text{π }}/2 $; (f) $ \theta = {\text{π }} $. Other parameters are $ {\kappa _1} = 1 $, $ {\kappa _2} = 1 $, $ \gamma = 1 $, $ J = 2{G_1}{G_2}/\gamma $.

    图 5  群延迟$ {\tau _{12}} $(红色圆圈)和$ {\tau _{21}} $(蓝色圆圈)在不同非互易相位差$ \theta $下随两个涡旋光场所携带拓扑荷比$ {\ell _2}/{\ell _1} $的演化 (a) $\theta = 0$; (b) $ \theta = - {\text{π }}/2 $; (c) $ \theta = {\text{π }}/2 $. 其他参数为$ {\kappa _1} = 1 $, $ {\kappa _2} = 1 $, $ \gamma = 1 $, $ J = 2{G_1}{G_2}/\gamma $

    Figure 5.  Group delay $ {\tau _{12}} $ (red circle) and $ {\tau _{21}} $ (blue circle) with ratio of topological charges carried by two vortex optical fields $ {\ell _2}/{\ell _1} $ under different nonreciprocal phase difference: (a) $ \theta = 0 $; (b) $ \theta = - {\text{π }}/2 $; (c) $ \theta = {\text{π }}/2 $. Other parameters are $ {\kappa _1} = 1 $, $ {\kappa _2} = 1 $, $ \gamma = 1 $, $ J = 2{G_1}{G_2}/\gamma $.

  • [1]

    Allen L, Beijersbergen M W, Spreeuw R J, Woerdman J P 1992 Phys. Rev. A 45 8185Google Scholar

    [2]

    Yao A M, Padgett M J 2011 Adv. Opt. Photonics 3 161Google Scholar

    [3]

    He H, Friese M E J, Heckenberg N R, Rubinsztein-Dunlop H 1995 Phys. Rev. Lett. 75 826Google Scholar

    [4]

    Andersen M F, Ryu C, Clade P, Natarajan V, Vaziri A, Helmerson K, Phillips W D 2006 Phys. Rev. Lett. 97 170406Google Scholar

    [5]

    Volpe G, Petrov D 2006 Phys. Rev. Lett. 97 210603Google Scholar

    [6]

    Bhattacharya M, Meystre P 2007 Phys. Rev. Lett. 99 153603Google Scholar

    [7]

    Liu Y M, Bai C H, Wang D Y, Wang T, Zheng M H, Wang H F, Zhu A D, Zhang S 2018 Opt. Express 26 6143Google Scholar

    [8]

    Peng J X, Chen Z, Yuan Q Z, Feng X L 2019 Phys. Rev. A 99 043817Google Scholar

    [9]

    Zhang Z, Wang Y P, Wang X 2021 Front. Phys. 16 32503Google Scholar

    [10]

    Kazemi S H, Mahmoudi M 2020 Phys. Scr. 95 045107Google Scholar

    [11]

    Bhattacharya M, Giscard P L, Meystre P 2008 Phys. Rev. A 77 013827Google Scholar

    [12]

    Cheng H J, Zhou S J, Peng J X, Kundu A, Li H X, Jin L, Feng X L 2021 J. Opt. Soc. Am. B 38 285Google Scholar

    [13]

    Xiong H, Huang Y M, Wu Y 2021 Phys. Rev. A 103 043506Google Scholar

    [14]

    Law C K 1995 Phys. Rev. A 51 2537Google Scholar

    [15]

    Xiong H, Si L G, Zheng A S, Yang X, Wu Y 2012 Phys. Rev. A 86 013815Google Scholar

    [16]

    Tian L 2013 Phys. Rev. Lett. 110 233602Google Scholar

    [17]

    Deng Z J, Habraken S J M, Marquardt F 2016 New. J. Phys. 18 063022Google Scholar

    [18]

    Deng Z J, Yan X B, Wang Y D, Wu C W 2016 Phys. Rev. A 93 033842Google Scholar

    [19]

    Yan X B 2017 Phys. Rev. A 96 053831Google Scholar

    [20]

    张秀龙, 鲍倩倩, 杨明珠, 田雪松 2018 物理学报 67 104203Google Scholar

    Zhang X L, Bao Q Q, Yang M Z, Tian X S 2018 Acta Phys. Sin. 67 104203Google Scholar

    [21]

    Agarwal G S, Huang S M 2010 Phys. Rev. A 81 041803Google Scholar

    [22]

    Shu J 2011 Chin. Phys. Lett. 28 104203Google Scholar

    [23]

    陈华俊, 米贤武 2011 物理学报 60 124206Google Scholar

    Chen H J, Mi X W 2011 Acta Phys. Sin. 60 124206Google Scholar

    [24]

    He B, Yang L, Lin Q, Xiao M 2017 Phys. Rev. Lett. 118 233604Google Scholar

    [25]

    Li Y, Wu L A, Wang Z D 2011 Phys. Rev. A 83 043804Google Scholar

    [26]

    Xiong H, Fan Y W, Yang X, Wu Y 2016 Appl. Phys. Lett. 109 061108Google Scholar

    [27]

    Chen Y T, Du L, Zhang Y, Wu J H 2021 Phys. Rev. A 103 053712Google Scholar

    [28]

    Ge Y Q, Chen Y T, Yin K, Zhang Y 2020 Phys. Lett. A 384 126836Google Scholar

    [29]

    Chen Y T, Du L, Liu Y M, Zhang Y 2020 Opt. Express 28 7095Google Scholar

    [30]

    Bi L, Hu J, Jiang P, Kim D H, Dionne G F, Kimerling L C, Ross C A 2011 Nat. Photonics 5 758Google Scholar

    [31]

    Aplet L J, Carson J W 1964 Appl. Opt. 3 544Google Scholar

    [32]

    Korneeva Y P, Vodolazov D Y, Semenov A V, Florya I N, Simonov N, Baeva E, Korneev A A, Goltsman G N, Klapwijk T M 2018 Phys. Rev. Appl. 9 064037Google Scholar

    [33]

    Shen Z, Zhang Y L, Chen Y, Zou C L, Xiao Y F, Zou X B, Sun F W, Guo G C, Dong C H 2016 Nat. Photonics 10 657Google Scholar

    [34]

    Maayani S, Dahan R, Kligerman Y, Moses E, Hassan A U, Jing H, Nori F, Christodoulides D N, Carmon T 2018 Nature 558 569Google Scholar

    [35]

    Li B, Huang R, Xu X W, Miranowicz A, Jing H 2019 Photonics Res. 7 630Google Scholar

    [36]

    Li Y, Huang Y Y, Zhang X Z, Tian L 2017 Opt. Express 25 018907Google Scholar

    [37]

    Mirza I M, Ge W C, Jing H 2019 Opt. Express 27 25515Google Scholar

    [38]

    Jiang C, Song L N, Li Y 2018 Phys. Rev. A 97 053812Google Scholar

    [39]

    Jiang C, Baowei J I, Cui Y S, Zuo F, Shi J, Chen G 2018 Opt. Express 26 15255Google Scholar

    [40]

    Jiang C, Song L N, Li Y 2019 Phys. Rev. A 99 023823Google Scholar

    [41]

    Xu X W, Li Y 2015 Phys. Rev. A 91 053854Google Scholar

    [42]

    Xu X W, Li Y, Chen A X, Liu Y X 2016 Phys. Rev. A 93 023827Google Scholar

    [43]

    Xu X W, Song L N, Zheng Q, Wang Z H, Li Y 2018 Phys. Rev. A 98 063845Google Scholar

    [44]

    Yan X B, Lu H L, Gao F, Yang L 2019 Front. Rhys. 14 52601Google Scholar

    [45]

    Xia C C, Yan X B, Tian X D, Gao F 2019 Opt. Commun. 451 197Google Scholar

    [46]

    张利巍, 李贤丽, 杨柳 2019 物理学报 68 170701Google Scholar

    Zhang L W, Li X L, Yang L 2019 Acta Phys. Sin. 68 170701Google Scholar

    [47]

    Agarwal G S, Huang S 2014 New J. Phys. 16 033023Google Scholar

    [48]

    Yan X B, Cui C L, Gu K H, Tian X D, Fu C B, Wu J H 2014 Opt. Express 22 4886Google Scholar

    [49]

    Safavi-Naeini A H, Mayer Alegre T P, Chan J, Eichenfield M, Winger M, Lin Q, Hill J T, Chang D E, Painter O 2011 Nature 472 69Google Scholar

    [50]

    Weis S, Riviere R, Deleglise S, Gavartin E, Arcizet O, Schliesser A, Kippenberg T J 2010 Science 330 1520Google Scholar

    [51]

    Oemrawsingh S S R, Eliel E R, Woerdman J P, Verstegen E J K, Kloosterboer J G, 't Hooft G W 2004 J. Opt. A: Pure Appl. Opt. 6 S228

    [52]

    Li L, Allen Y Y, Huang C, Grewell D A, Benatar A, Chen Y 2006 Opt. Eng. 45 113401Google Scholar

    [53]

    Shi H, Bhattacharya M 2016 J. Phys. B 49 153001Google Scholar

    [54]

    Shen Y, Campbell G T, Hage B, Zou H, Buchler B C, Lam P K 2013 J. Opt. 15 044005Google Scholar

  • [1] Fan Hai-Ling, Guo Zhi-Jian, Li Ming-Qiang, Zhuo Hong-Bin. Numerical study of self-focusing and filament formation of intense vortex beams in plasmas. Acta Physica Sinica, 2023, 72(1): 014206. doi: 10.7498/aps.72.20221232
    [2] Fan Yu-Ting, Zhu En-Xu, Zhao Chao-Ying, Tan Wei-Han. Dynamic generation of vortex beam based on partial phase modulation of electro-optical crystal plate. Acta Physica Sinica, 2022, 71(20): 207801. doi: 10.7498/aps.71.20220835
    [3] Liang De-Shan, Huang Hou-Bing, Zhao Ya-Nan, Liu Zhu-Hong, Wang Hao-Yu, Ma Xing-Qiao. Size effect of topological charge in disc-like nematic liquid crystal films. Acta Physica Sinica, 2021, 70(4): 044202. doi: 10.7498/aps.70.20201623
    [4] Chen Tian-Yu, Wang Chang-Shun, Pan Yu-Jia, Sun Li-Li. Recording optical vortices in azo polymer films by applying holographic method. Acta Physica Sinica, 2021, 70(5): 054204. doi: 10.7498/aps.70.20201496
    [5] Tian Bo-Yu, Zhong Zhe-Qiang, Sui Zhan, Zhang Bin, Yuan Xiao. Ultrafast azimuthal beam smoothing scheme based on vortex beam. Acta Physica Sinica, 2019, 68(2): 024207. doi: 10.7498/aps.68.20181361
    [6] Peng Yi-Ming, Xue Yu, Xiao Guang-Zong, Yu Tao, Xie Wen-Ke, Xia Hui, Liu Shuang, Chen Xin, Chen Fang-Lin, Sun Xue-Cheng. Spiral spectrum analysis and application ofcoherent synthetic vortex beams. Acta Physica Sinica, 2019, 68(21): 214206. doi: 10.7498/aps.68.20190880
    [7] Fu Shi-Yao, Gao Chun-Qing. Progress of detecting orbital angular momentum states of optical vortices through diffraction gratings. Acta Physica Sinica, 2018, 67(3): 034201. doi: 10.7498/aps.67.20171899
    [8] Yu Tao, Xia Hui, Fan Zhi-Hua, Xie Wen-Ke, Zhang Pan, Liu Jun-Sheng, Chen Xin. Generation of Bessel-Gaussian vortex beam by combining technology. Acta Physica Sinica, 2018, 67(13): 134203. doi: 10.7498/aps.67.20180325
    [9] Shi Jian-Zhen, Xu Tian, Zhou Qiao-Qiao, Ji Xian-Ming, Yin Jian-Ping. Generation of no-diffraction hollow vertex beams with adjustable angular momentum by wave plate phase plates. Acta Physica Sinica, 2015, 64(23): 234209. doi: 10.7498/aps.64.234209
    [10] Shi Jian-Zhen, Yang Shen, Zou Ya-Qi, Ji Xian-Ming, Yin Jian-Ping. Generation of vortex beams by the four-step phase plates. Acta Physica Sinica, 2015, 64(18): 184202. doi: 10.7498/aps.64.184202
    [11] Wang Ya-Dong, Gan Xue-Tao, Ju Pei, Pang Yan, Yuan Lin-Guang, Zhao Jian-Lin. Control of topological structure in high-order optical vortices by use of noncanonical helical phase. Acta Physica Sinica, 2015, 64(3): 034204. doi: 10.7498/aps.64.034204
    [12] Huang Su-Juan, Gu Ting-Ting, Miao Zhuang, He Chao, Wang Ting-Yun. Experimental study on multiple-ring vortex beams. Acta Physica Sinica, 2014, 63(24): 244103. doi: 10.7498/aps.63.244103
    [13] Wang Lin, Yuan Cao-Jin, Nie Shou-Ping, Li Chong-Guang, Zhang Hui-Li, Zhao Ying-Chun, Zhang Xiu-Ying, Feng Shao-Tong. Measuring topology charge of vortex beam using digital holography. Acta Physica Sinica, 2014, 63(24): 244202. doi: 10.7498/aps.63.244202
    [14] Zhang Jin, Zhou Xin-Xing, Luo Hai-Lu, Wen Shuang-Chun. Cross polarization effects of vortex beam in reflection. Acta Physica Sinica, 2013, 62(17): 174202. doi: 10.7498/aps.62.174202
    [15] Zhao Ji-Zhi, Jiang Yue-Song, Ou Jun, Ye Ji-Hai. Scattering of the focused Laguerre-Gaussian beams by a spherical particle. Acta Physica Sinica, 2012, 61(6): 064202. doi: 10.7498/aps.61.064202
    [16] Ding Pan-Feng, Pu Ji-Xiong. Change of the off-center Laguerre-Gaussian vortex beam while propagation. Acta Physica Sinica, 2012, 61(6): 064103. doi: 10.7498/aps.61.064103
    [17] Ou Jun, Jiang Yue-Song, Li Fang, Liu Li. Shifts of beam centroid of Laguerre-Gaussian beams reflected and refracted at a dielectric interface. Acta Physica Sinica, 2011, 60(11): 114203. doi: 10.7498/aps.60.114203
    [18] Feng Bo, Gan Xue-Tao, Liu Sheng, Zhao Jian-Lin. Transformation of multi-edge-dislocations to screw-dislocations in optical field. Acta Physica Sinica, 2011, 60(9): 094203. doi: 10.7498/aps.60.094203
    [19] Ding Pan-Feng, Pu Ji-Xiong. Propagation of Laguerre-Gaussian vortex beam. Acta Physica Sinica, 2011, 60(9): 094204. doi: 10.7498/aps.60.094204
    [20] Li Yang-Yue, Chen Zi-Yang, Liu Hui, Pu Ji-Xiong. Generation and interference of vortex beams. Acta Physica Sinica, 2010, 59(3): 1740-1748. doi: 10.7498/aps.59.1740
Metrics
  • Abstract views:  2722
  • PDF Downloads:  146
  • Cited By: 0
Publishing process
  • Received Date:  26 January 2022
  • Accepted Date:  19 April 2022
  • Available Online:  25 July 2022
  • Published Online:  05 August 2022

/

返回文章
返回