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传统的沿z轴光纤传输光线的轨道角动量(orbital angular momentum, OAM)光束的制备方法共同之处都是从内部结构着想, 光束的主光线基本上不变, 只是波面在变. 但要获得携带高
$m\hbar $ 的光有一定的难度. 针对上述问题, 本文建立以波面不变, 光束主光线变化为基础的理论框架, 利用微分几何理论验证不沿z轴圆柱型光纤螺线圈传输的光线可以携带高$m\hbar $ OAM的理论设想. 研究发现: 利用流动坐标$(\alpha ,\beta ,\gamma )$ 计算光线在绕圆柱体的光纤中传输时光纤截面的衍射分布图呈现涡旋特征, 有高阶OAM模式. 当$\theta = {\theta _0}$ 时, 圆柱形轨道光纤过渡到直线轨道光纤. 计算光线沿直线传输时光纤截面的衍射分布图是Airy斑, 即圆孔衍射斑, 无高阶OAM模式.-
关键词:
- 光纤螺线圈 /
- 轨道角动量(OAM) /
- 微分几何
The common feature of traditional methods of preparing orbital angular momentum (OAM) light beams propagating along the z axis is that the wave-front phase is changed and the chief ray of beam is basically unchanged. But it is difficult to obtain a high$m\hbar $ OAM. To solve the above problem, we establish a theoretical framework based on the change of the chief ray of beam instead of the change of wave-front phase. The differential geometry theory is used to verify the theoretical assumption that the light transmitted by the cylindrical spiral wave-guide can carry high$m\hbar $ OAM. To measure the OAM optical fiber output, we use the diffraction method to detect the phase of vortex, that is, we can use a microscope to observe the phase distribution of optical fiber end face. We consider the output of linearly polarized light along the tangent direction of the fiber to observe its diffraction pattern. The transmission of optical fiber around the cylinder is the main light. The diameter of optical fiber is constant, and the light wave transmitting into the optical fiber is Bessel beam. For the linear fiber output, we need to consider only the linear fiber Bessel beam. The output cross section of the wave surface in the fiber is approximately that of plane wave. When$\theta > {\theta _0}$ , we use the flow coordinates$(\alpha,\beta, \gamma)$ to calculate the diffraction pattern of the cross section of the optical fiber when light travels in the optical fiber around the cylinder, which shows the characteristics of vortex. The optical field distribution carries a high-order OAM mode. When$\theta = {\theta _0}$ , cylindrical orbital optical fibers transit to linear orbital optical fibers. We calculate the diffraction pattern of the cross section of the optical fibers propagating in a straight line. It is an Airy spot, namely a circular aperture diffraction spot. The optical field distribution has no higher-order OAM mode. When the order of the output beam is small, the output shows certain uniformity and symmetry, when the order of the output beam increases gradually, the output beam shows some inhomogeneity and asymmetry.-
Keywords:
- wave-guide fiber /
- orbital angular momentum /
- differential geometry
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图 1 (a) 光沿圆柱型螺线圈传输; (b) OAM光场分布图; (c) 几何相位
Fig. 1. (a) Fiber propagation along cylindrical spiral wave-guide; (b) OAM light field distribution, (c) berry phase.
图 2 当
$k = 2$ ,$\psi (z) = {\rm{0}}{\rm{.5}}$ 时, (a) 路径矢量s, (b) 线动量密度P, (c) 角动量密度M的变化曲线Fig. 2. (a) Path vector s; (b) linear momentum density P; (c) angular momentum density M with
$k = 2$ ,$\psi (z) = {\rm{0}}{\rm{.5}}$ .
图 3 直线光纤传播, 光场分布是圆孔衍射斑
Fig. 3. There is no higher-order OAM mode in the cross section of the optical fibers propagating in a straight line, and the optical field distribution is a circular aperture diffraction spot.
图 4 圆柱形光纤传播有高阶OAM模式 (a)
$m = {\rm{1}}$ ; (b)$m = {\rm{2}}$ ; (c)$m = {\rm{4}}$ ; (d)$m = {\rm{16}}$ Fig. 4. The optical fiber cross section propagating in cylin-drical shape has a high-order OAM mode with: (a)
$m = {\rm{1}}$ ; (b)$m = {\rm{2}}$ ; (c)$m = {\rm{4}}$ ; (d)$m = {\rm{16}}$ . -
[1] Poynting J H 1909 Proc. R. Soc. London Ser. A 82 560
Google Scholar
[2] Beth R A 1936 Phys. Rev. 50 115
Google Scholar
[3] Allen L, Beijersbergen M W, Spreeuw R J C, Woerdman J P 1992 Phys. Rev. A 45 8185
Google Scholar
[4] Bozinovic N, Golowich S, Kristensen P, Ramachandran S 2012 Opt. Lett. 37 2451
Google Scholar
[5] Li S H, Mo Q, Hu X, Du C, Wang J 2015 Opt. Lett. 40 4376
Google Scholar
[6] Niederriter R D, Siemens M E, Gopinath J T 2016 Opt. Lett. 41 3213
Google Scholar
[7] Oemrawsingh S S R, van Houwelingen J A W, Eliel E R, Woerdman J P, Verstegen E J K, Kloosterboer J G, ’t Hooft G W 2004 Appl. Opt. 43 688
Google Scholar
[8] Marrucci L, Manzo C, Paparo D 2006 Phys. Rev. Lett. 96 163905
Google Scholar
[9] Gibson G, Courtical J, Padgett M J, Vasnetsov M, Pas’ko V, Barnett S M, Franke-Arnold S 2004 Opt. Express 12 5448
Google Scholar
[10] Xiao Q S, Klitis C, Li S M, Chen Y Y, Cai X L, Sorel M, Yu S Y 2016 Opt. Express 24 3168
Google Scholar
[11] Cai X L, Wang J W, Strain M J, Morris M J, Zhu J B, Sorel M, O’Brien J L, Thompson M G, Yu S Y 2012 Science 338 363
Google Scholar
[12] Yue F Y, Wen D D, Zhang C M, Gerardot B D, Wang W, Zhang S, Chen X Z 2017 Adv Mater. 29 1603838
Google Scholar
[13] Niederriter R D, Siemens M E, Gopinath J T 2016 Opt. Lett. 41 5736
Google Scholar
[14] Chen Y, Gao J, Jiao Z Q, Sun K, Shen W G, Qiao L F, Tang H, Lin X F, Jin X M 2018 Phys. Rev. Lett. 121 233602
Google Scholar
[15] Zhang W H, Wang J K, Li F S, Chen L X, Karimi E 2017 Laser Photonics Rev. 11 1600163
Google Scholar
[16] Fu C L, Liu S, Wang Y, Bai Z Y, He J, Liao C R, Zhang Y, Zhang F, Yu B, Gao S C, Li Z H, Wang Y P 2018 Opt. Lett. 43 1786
Google Scholar
[17] Zhou H L, Fu D Z, Dong J J, Zhang P, Chen D X, Cai X L, Li F L, Zhang X L 2017 Light-Sci. Appl. 6 e16251
Google Scholar
[18] Pan X Z, Yu S, Zhou Y F, Zhang K, Zhang K, Lv S C, Li S J, Wang W, Jing J T 2019 Phys. Rev. Lett. 123 070506
Google Scholar
[19] Zhou N, Zheng S, Cao X P, Zhao Y F, Gao S Q, Zhu Y T, He M B, Cai X L, Wang J 2019 Sci. Adv. 5 eaau9593
Google Scholar
[20] Wang J W, Zepf M, Rykovanov S G 2019 Nat. Commun. 10 5554
Google Scholar
[21] Fang X Y, Ren H R, Gu M 2020 Nat. Photonics 14 102
Google Scholar
[22] Yao A M, Padgett M J 2011 Adv. Opt. Photonics 3 161
Google Scholar
[23] Arnold S F, Allen L, Padgett M 2008 Laser Photonics Rev. 2 299
Google Scholar
[24] 梅向明, 黄敬之 2003 微分几何 (第3版) (北京: 高教出版社) 第51—53页
Mei X M, Huang J Z 2003 Differential Geometry (3rd Ed.) (Beijing: Higher Education Press) pp51−53 (in Chinese)
[25] Yariv A 2013 Quantum Electronics (3rd Ed.) (New York: Wiley India Press) pp512–515
[26] Schiff L I 1968 Quantum Mechanics (3rd Ed.) (New York: McGraw-Hill Book Company) pp24–25
[27] 柯熙政, 王姣著 2018 涡旋光束的产生、传输、检测及应用 (第1版) (北京: 科学出版社) 第194—196页
Ke X Z, Wang J 2018 Generation, Transmission, Detection and Application of Vortex Beam (1st Ed.) (Beijing: Science Press) pp194–196 (in Chinese)
[28] Born M, Wolf E 2001 Principles of Optics (7th Ed.) (Cambridge: World publishing Corporation) pp640–642
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