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传统的螺旋相位板是一种利用沿方位角方向介质材料高度递增实现对光束相位调控产生涡旋光束的光学器件, 由于这种特殊的几何结构特征使其不能通过相位板的叠加而调控出射光束所携带的角量子数. 本文基于坐标变换方法将介质材料沿方位角方向折射率不变而高度递增的传统螺旋相位板变换为一种介质材料沿方位角方向高度不变而折射率递增的平板式螺旋相位板. 通过理论分析与数值模拟, 发现本文所设计的平板式螺旋相位板不仅与传统螺旋相位板一样能够产生高质量的涡旋光束, 而且平板式螺旋相位板的高度和涡旋光束携带的角量子数可以根据介质材料的折射率选取而任意调节. 为了实际应用的需要, 可以通过叠加多层平板式螺旋相位板以获得不同角量子数的涡旋光束. 这种平板式螺旋相位板在光传输、光通信等领域具有广阔的潜在应用价值.Phase is an important characteristic of electromagnetic waves. It is well known that a beam with a helical wave front characterized by a phase of
$\exp({\rm{i}}l\theta )$ (which depends on azimuthal angle$\theta$ and topological charge l), has a momentum component along the azimuthal direction, resulting in an orbital angular momentum of per photon along the beam axis. Owing to its fascinating properties, the beam has received a great deal of attention and has provided novel applications in manipulation of particles or atoms, optical communication, optical data storage. In order to meet the needs of various applications, techniques for efficiently generating optical beams carrying orbital angular momentum are always required. Current schemes for generating the beams carrying orbital angular momentum include computer-generated holograms, spiral phase plates, spatial light modulators, and silicon integrated optical vortex emitters. Among the usual methods to produce helical beams, the traditional spiral phase plate is an optical device that utilizes the progressive increasing of height of a dielectric material along an azimuthal direction to produce a vortex beam for beam phase modulation with a high conversion efficiency. However, it is difficult to regulate the topological charge l of the outgoing beam through the superposition of the phase plates due to the special geometric feature. In this paper, the flat spiral phase plate is designed by compressing the height of traditional spiral phase plate, and inducing the refractive index to increase in the azimuthal direction based on coordinate transformation. By means of theoretical analysis and numerical simulation, it is found that the flat spiral phase plate can produce high quality vortex beams just as the traditional spiral phase plate can do. Particularly, the height of the flat spiral phase plate and the topological charge l carried by the vortex beams can be arbitrarily adjusted according to the refractive index selection of the dielectric material. In order to meet the needs of practical applications, the vortex beams with different topological charges can be obtained by stacking multiple layers of flat spiral phase plates. The flat spiral phase plate has broad potential applications in the fields of optical transmission and optical communication.[1] Padgett M, Courtial J, Allen L 2004 Phys. Today 57 35
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图 1 传统螺旋相位板和平板式螺旋相位板的结构示意图 (a)传统螺旋相位板; (b)平板式螺旋相位板(颜色深浅表示折射率的大小)
Fig. 1. Schematic diagram of a conventional spiral phase plate and a flat-plate spiral phase plate: (a) A conventional spiral phase plate; (b) a flat-plate spiral phase plate (the color depth indicates the size of the refractive index).
图 2 数值模拟结果 (a)平板式螺旋相位板产生的光束横截面场分布图; (b)平板式螺旋相位板横截面相位分布图; (c)设计的平板式螺旋相位板空间材料分布图; (d)高斯光束入射平板式螺旋相位板产生涡旋光束的xz截面图
Fig. 2. The simulation results: (a) Cross-sectional field distribution of the beam produced by the flat-plate spiral phase plate; (b) phase distribution of cross section of flat-plates piral phase plate; (c) designed flat-plate spiral phase plate space material distribution; (d) the Gaussian beam incident on the flat-plate spiral phase plate produces a xz cross-sectional view of the vortex beam.
图 3 数值模拟结果 (a)平板式螺旋相位板产生的光束横截面场分布图; (b)平板式螺旋相位板横截面相位分布图; (c)平板式螺旋相位板光强分布图; (d)设计的平板式螺旋相位板空间材料分布图; (e)传统的螺旋相位板产生的光束横截面场分布图
Fig. 3. The simulation results: (a) Cross-sectional field distribution of the beam produced by the flat-plate spiral phase plate; (b) phase distribution of cross section of flat-plates piral phase plate; (c) light intensity distribution of flat-plates piral phase plate; (d) designed flat-plate spiral phase plate space material distribution; (e) a cross-sectional field distribution diagram of a beam produced by a conventional spiral phase plate.
图 4 (a) 双层l = –1的平板式螺旋相位板叠加产生的光束横截面场分布图; (b)由三层l = –1的平板式螺旋相位板叠加产生的光束横截面场分布图
Fig. 4. (a) Cross-sectional field distribution of the beam produced by the superposition of a flat-plate spiral phase plate with a double layer l = –1; (b) the cross-sectional field distribution of the beam produced by the superposition of three layers of flat spiral phase plates with l = –1.
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[1] Padgett M, Courtial J, Allen L 2004 Phys. Today 57 35
[2] 苏志锟, 王发强, 路轶群, 金锐博, 梁瑞生, 刘颂豪 2008 物理学报 57 3016
Google Scholar
Su Z K, Wang F Q, Lu Y Q, Jin R B, Liang R S, Liu S H 2008 Acta Phys. Sin. 57 3016
Google Scholar
[3] Allen L, Beijersbergen M W, Spreeuw R J C, Woerdman J P 1992 Phys. Rev. A 45 8185
Google Scholar
[4] 陈理想, 张远颖 2015 物理学报 64 164210
Google Scholar
Chen L X, Zhang Y Y 2015 Acta Phys. Sin. 64 164210
Google Scholar
[5] Grier D G 2003 Nature 424 810
Google Scholar
[6] Andersen M F, Ryu C, Clade P, Natarajan V, Vaziri A, Helmerson K, Phillips W D 2006 Phys. Rev. Lett. 97 170406
Google Scholar
[7] 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
[8] Molina-Terriza G, Torres J P, Torner L 2007 Nature Phys. 3 305
Google Scholar
[9] Torner L, Torres L P, Carrasco S 2005 Opt. Express 13 873
Google Scholar
[10] Dholakia K, Cizmar T 2011 Nat. Photonics 5 335
Google Scholar
[11] Bazhenov V Y, Vasnetsov M V, Soskin M S 1990 JETP Lett. 52 429
[12] Heckenberg N R, McDuff R, Smith C P, White A G 1992 Opt. Lett. 17 221
Google Scholar
[13] Beijersbergen M W, Coerwinkel R P C, Kristensen M, Woerdman J P 1994 Opt. Commun. 112 321
Google Scholar
[14] 范庆斌, 徐挺 2017 物理学报 66 144208
Google Scholar
Fan Q B, Xu T 2017 Acta Phys. Sin. 66 144208
Google Scholar
[15] 李明, 陈阳, 郭光灿, 任希峰 2017 物理学报 66 144202
Google Scholar
Li M, Chen Y, Guo G C, Ren X F 2017 Acta Phys. Sin. 66 144202
Google Scholar
[16] Chen L X, She W L 2009 Opt. Lett. 34 178
Google Scholar
[17] Oemrawsingh S S R, van Houwelingen J A W, Eliel E R, Woerdman J P, Verstegen E J K, Kloosterboer J G, Hooft G W 't 2004 Appl. Opt. 43 688
Google Scholar
[18] Kotlyar V V, Khonina S N, Kovalev A A, Soifer V A 2006 Opt. Lett. 31 1597
Google Scholar
[19] Lee W M, Yuan X C, Cheong W C 2004 Opt. Lett. 29 1796
Google Scholar
[20] Rotschild C, Zommer S, Moed S, Hershcovitz O, Lipson S G 2004 Appl. Opt. 43 2397
Google Scholar
[21] 刘国昌, 李超, 邵金进, 方广有 2014 物理学报 63 154102
Google Scholar
Liu G C, Li C, Shao J J, Fang G Y 2014 Acta Phys. Sin. 63 154102
Google Scholar
[22] 汪会波, 罗孝阳, 董建峰 2015 物理学报 64 154102
Google Scholar
Wang H B, Luo X Y, Dong J F 2015 Acta Phys. Sin. 64 154102
Google Scholar
[23] Pendry J B, Schurig D, Smith D R 2006 Science 312 1780
Google Scholar
[24] Lai Y, Chen H Y, Zhang Z Q, Chan C T 2009 Phys. Rev. Lett. 102 093901
Google Scholar
[25] Li J, Pendry J B 2008 Phys. Rev. Lett. 101 203901
Google Scholar
[26] Zhao J Z, Wang D L, Peng R W, Hu Q, Wang M 2011 Phys. Rev. E 84 046607
Google Scholar
[27] Lai Y, Chen H, Zhang Z Q, Chan C T 2009 Phys. Rev. Lett. 102 253902
Google Scholar
[28] Jiang W X, Ma H F, Cheng Q, Cui T J 2010 Appl. Phys. Lett. 96 121910
Google Scholar
[29] Rahm M, Schurig D, Roberts D A, Cummer S A, Smith D R, Pendry J B 2008 Photonics Nanostruct. Fundam. Appl. 6 87
Google Scholar
[30] Ma H F, Cui T J 2010 Nat. Commun. 1 124
Google Scholar
[31] Smith D R, Mock J J, Starr A F, Schurig D 2005 Phys. Rev. E 71 036609
Google Scholar
[32] Mei Z L, Bai J, Cui T J 2010 Appl. Phys. 43 055404
[33] Ma H F, Cai B J, Zhang T X, Yang Y, Jiang W X, Cui T J 2013 IEEE Trans. Antennas Propag. 61 2561
Google Scholar
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