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Design and application of flat spiral phase plate

## Design and application of flat spiral phase plate

Wu Wen-Bing, Sheng Zong-Qiang, Wu Hong-Wei
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• #### Abstract

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.

#### References

 [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 Su Z K, Wang F Q, Lu Y Q, Jin R B, Liang R S, Liu S H 2008 Acta Phys. Sin. 57 3016 [3] Allen L, Beijersbergen M W, Spreeuw R J C, Woerdman J P 1992 Phys. Rev. A 45 8185 [4] 陈理想, 张远颖 2015 物理学报 64 164210 Chen L X, Zhang Y Y 2015 Acta Phys. Sin. 64 164210 [5] Grier D G 2003 Nature 424 810 [6] Andersen M F, Ryu C, Clade P, Natarajan V, Vaziri A, Helmerson K, Phillips W D 2006 Phys. Rev. Lett. 97 170406 [7] Gibson G, Courtial J, Padgett M J, Vasnetsov M, Pas'ko V, Barnett S M, Franke-Arnold S 2004 Opt. Express 12 5448 [8] Molina-Terriza G, Torres J P, Torner L 2007 Nature Phys. 3 305 [9] Torner L, Torres L P, Carrasco S 2005 Opt. Express 13 873 [10] Dholakia K, Cizmar T 2011 Nat. Photonics 5 335 [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 [13] Beijersbergen M W, Coerwinkel R P C, Kristensen M, Woerdman J P 1994 Opt. Commun. 112 321 [14] 范庆斌, 徐挺 2017 物理学报 66 144208 Fan Q B, Xu T 2017 Acta Phys. Sin. 66 144208 [15] 李明, 陈阳, 郭光灿, 任希峰 2017 物理学报 66 144202 Li M, Chen Y, Guo G C, Ren X F 2017 Acta Phys. Sin. 66 144202 [16] Chen L X, She W L 2009 Opt. Lett. 34 178 [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 [18] Kotlyar V V, Khonina S N, Kovalev A A, Soifer V A 2006 Opt. Lett. 31 1597 [19] Lee W M, Yuan X C, Cheong W C 2004 Opt. Lett. 29 1796 [20] Rotschild C, Zommer S, Moed S, Hershcovitz O, Lipson S G 2004 Appl. Opt. 43 2397 [21] 刘国昌, 李超, 邵金进, 方广有 2014 物理学报 63 154102 Liu G C, Li C, Shao J J, Fang G Y 2014 Acta Phys. Sin. 63 154102 [22] 汪会波, 罗孝阳, 董建峰 2015 物理学报 64 154102 Wang H B, Luo X Y, Dong J F 2015 Acta Phys. Sin. 64 154102 [23] Pendry J B, Schurig D, Smith D R 2006 Science 312 1780 [24] Lai Y, Chen H Y, Zhang Z Q, Chan C T 2009 Phys. Rev. Lett. 102 093901 [25] Li J, Pendry J B 2008 Phys. Rev. Lett. 101 203901 [26] Zhao J Z, Wang D L, Peng R W, Hu Q, Wang M 2011 Phys. Rev. E 84 046607 [27] Lai Y, Chen H, Zhang Z Q, Chan C T 2009 Phys. Rev. Lett. 102 253902 [28] Jiang W X, Ma H F, Cheng Q, Cui T J 2010 Appl. Phys. Lett. 96 121910 [29] Rahm M, Schurig D, Roberts D A, Cummer S A, Smith D R, Pendry J B 2008 Photonics Nanostruct. Fundam. Appl. 6 87 [30] Ma H F, Cui T J 2010 Nat. Commun. 1 124 [31] Smith D R, Mock J J, Starr A F, Schurig D 2005 Phys. Rev. E 71 036609 [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

#### Cited By

• 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)

Figure 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

Figure 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

Figure 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

Figure 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.

•  [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 Su Z K, Wang F Q, Lu Y Q, Jin R B, Liang R S, Liu S H 2008 Acta Phys. Sin. 57 3016 [3] Allen L, Beijersbergen M W, Spreeuw R J C, Woerdman J P 1992 Phys. Rev. A 45 8185 [4] 陈理想, 张远颖 2015 物理学报 64 164210 Chen L X, Zhang Y Y 2015 Acta Phys. Sin. 64 164210 [5] Grier D G 2003 Nature 424 810 [6] Andersen M F, Ryu C, Clade P, Natarajan V, Vaziri A, Helmerson K, Phillips W D 2006 Phys. Rev. Lett. 97 170406 [7] Gibson G, Courtial J, Padgett M J, Vasnetsov M, Pas'ko V, Barnett S M, Franke-Arnold S 2004 Opt. Express 12 5448 [8] Molina-Terriza G, Torres J P, Torner L 2007 Nature Phys. 3 305 [9] Torner L, Torres L P, Carrasco S 2005 Opt. Express 13 873 [10] Dholakia K, Cizmar T 2011 Nat. Photonics 5 335 [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 [13] Beijersbergen M W, Coerwinkel R P C, Kristensen M, Woerdman J P 1994 Opt. Commun. 112 321 [14] 范庆斌, 徐挺 2017 物理学报 66 144208 Fan Q B, Xu T 2017 Acta Phys. Sin. 66 144208 [15] 李明, 陈阳, 郭光灿, 任希峰 2017 物理学报 66 144202 Li M, Chen Y, Guo G C, Ren X F 2017 Acta Phys. Sin. 66 144202 [16] Chen L X, She W L 2009 Opt. Lett. 34 178 [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 [18] Kotlyar V V, Khonina S N, Kovalev A A, Soifer V A 2006 Opt. Lett. 31 1597 [19] Lee W M, Yuan X C, Cheong W C 2004 Opt. Lett. 29 1796 [20] Rotschild C, Zommer S, Moed S, Hershcovitz O, Lipson S G 2004 Appl. Opt. 43 2397 [21] 刘国昌, 李超, 邵金进, 方广有 2014 物理学报 63 154102 Liu G C, Li C, Shao J J, Fang G Y 2014 Acta Phys. Sin. 63 154102 [22] 汪会波, 罗孝阳, 董建峰 2015 物理学报 64 154102 Wang H B, Luo X Y, Dong J F 2015 Acta Phys. Sin. 64 154102 [23] Pendry J B, Schurig D, Smith D R 2006 Science 312 1780 [24] Lai Y, Chen H Y, Zhang Z Q, Chan C T 2009 Phys. Rev. Lett. 102 093901 [25] Li J, Pendry J B 2008 Phys. Rev. Lett. 101 203901 [26] Zhao J Z, Wang D L, Peng R W, Hu Q, Wang M 2011 Phys. Rev. E 84 046607 [27] Lai Y, Chen H, Zhang Z Q, Chan C T 2009 Phys. Rev. Lett. 102 253902 [28] Jiang W X, Ma H F, Cheng Q, Cui T J 2010 Appl. Phys. Lett. 96 121910 [29] Rahm M, Schurig D, Roberts D A, Cummer S A, Smith D R, Pendry J B 2008 Photonics Nanostruct. Fundam. Appl. 6 87 [30] Ma H F, Cui T J 2010 Nat. Commun. 1 124 [31] Smith D R, Mock J J, Starr A F, Schurig D 2005 Phys. Rev. E 71 036609 [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
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•  Citation:
##### Metrics
• Abstract views:  101
• Cited By: 0
##### Publishing process
• Received Date:  09 September 2018
• Accepted Date:  03 November 2018
• Available Online:  23 March 2019
• Published Online:  01 March 2019

## Design and application of flat spiral phase plate

###### Corresponding author: Wu Hong-Wei, hwwu@aust.edu.cn
• 1. School of Mechanics and Photoelectric Physics, Anhui University of Science and Technology, Huainan 232001, China
• 2. National Laboratory of Solid State Microstructures, Nanjing University, Nanjing 210093, China

Abstract: 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.

Reference (33)

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