# Orbital Angular Momentum Generation and Detection by Geometric-Phase Based Metasurfaces

^{1}

^{2}

^{3}

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Geometric Phase

## 3. Metasurfaces for OAM Generation

#### 3.1. Artifical PEC-PMC Metasurface

#### 3.2. Ultrathin Complementary Metasurface

#### 3.3. Metasurface Fork Gratings

#### 3.4. Metasurface for OAM-Carrying Vector Beams Generation

#### 3.5. Continuously Shaped Metasurfaces

_{3}) to a depth of 2.5-µm.

#### 3.6. Metasurfaces for Multiple OAM-Beam Generation

_{2}and were fabricated based on atomic layer deposition and electron beam lithography. In Figure 11b, the nanoantennas with different topological charge are interleaved randomly.

## 4. Holographic Metasurfaces for OAM Detection

## 5. Conclusions

## Acknowledgments

## Author Contributions

## Conflicts of Interest

## Abbreviations

OAM | Orbital angular momentum |

EM | Electromagnetic |

AM | Angular momentum |

SAM | Spin angular momentum |

LHCP | Left-handed circular polarization |

RHCP | Right-handed circular polarization |

LG | Laguerre-Gaussian |

CGH | Computer generated hologram |

SPP | Spiral phase plates |

FSS | Frequency selective surface |

RCP | Right circularly polarized |

LCP | Left circularly polarized |

SRR | Split-ring resonators |

PEC | Perfect electric conductor |

PMC | Perfect magnetic conductor |

PCB | Printed circuit board |

CSRR | Complementary split-ring resonators |

LC | Inductor-capacitor |

## References

- Bliokh, K.Y.; Bekshaev, A.Y.; Nori, F. Dual electromagnetism: Helicity, spin, momentum and angular momentum. New J. Phys.
**2013**, 15, 033126. [Google Scholar] [CrossRef] - Gibson, G.; Courtial, J.; Padgett, M.J.; Vasnetsov, M.; Pas’ko, V.; Barnett, S.M.; Franke-Arnold, S. Free-space information transfer using light beams carrying orbital angular momentum. Opt. Express
**2004**, 12, 5448–5456. [Google Scholar] [CrossRef] [PubMed] - Ren, Y.X.; Wang, Z.; Liao, P.C.; Li, L.; Xie, G.D.; Huang, H.; Zhao, Z.; Yan, Y.; Ahmed, N.; Willner, A.; et al. Experimental characterization of a 400 Gbit/s orbital angular momentum multiplexed free-space optical link over 120 m. Opt. Lett.
**2016**, 41, 622–625. [Google Scholar] [CrossRef] [PubMed] - Willner, A.E.; Huang, H.; Yan, Y.; Ren, Y.; Ahmed, N.; Xie, G.; Bao, C.; Li, L.; Cao, Y.; Zhao, Z.; et al. Optical communications using orbital angular momentum beams. Adv. Opt. Photonics
**2015**, 7, 66–106. [Google Scholar] [CrossRef] - Wang, J.; Yang, J.Y.; Fazal, I.M.; Ahmed, N.; Yan, Y.; Huang, H.; Ren, Y.X.; Yue, Y.; Dolinar, S.; Tur, M.; et al. Terabit free-space data transmission employing orbital angular momentum multiplexing. Nat. Photonics
**2012**, 6, 488–496. [Google Scholar] [CrossRef] - Thide, B.; Then, H.; Sjoholm, J.; Palmer, K.; Bergman, J.; Carozzi, T.D.; Istomin, Y.N.; Ibragimov, N.H.; Khamitova, R. Utilization of photon orbital angular momentum in the low-frequency radio domain. Phys. Rev. Lett.
**2007**, 99, 087701. [Google Scholar] [CrossRef] [PubMed] - Mahmouli, F.E.; Walker, S.D. 4-Gbps uncompressed video transmission over a 60-ghz orbital angular momentum wireless channel. IEEE Wirel. Commun. Lett.
**2013**, 2, 223–226. [Google Scholar] [CrossRef] - Yan, Y.; Xie, G.D.; Lavery, M.P.J.; Huang, H.; Ahmed, N.; Bao, C.J.; Ren, Y.X.; Cao, Y.W.; Li, L.; Zhao, Z.; et al. High-capacity millimetre-wave communications with orbital angular momentum multiplexing. Nat. Commun.
**2014**, 5. [Google Scholar] [CrossRef] [PubMed] - Hui, X.N.; Zheng, S.L.; Chen, Y.L.; Hu, Y.P.; Jin, X.F.; Chi, H.; Zhang, X.M. Multiplexed Millimeter Wave Communication with Dual Orbital Angular Momentum (OAM) Mode Antennas. Sci. Rep.
**2015**, 5, 10148. [Google Scholar] [CrossRef] [PubMed] - Bozinovic, N.; Yue, Y.; Ren, Y.X.; Tur, M.; Kristensen, P.; Huang, H.; Willner, A.E.; Ramachandran, S. Terabit-Scale Orbital Angular Momentum Mode Division Multiplexing in Fibers. Science
**2013**, 340, 1545–1548. [Google Scholar] [CrossRef] [PubMed] - Andersson, M.; Berglind, E.; Björk, G. Orbital angular momentum modes do not increase the channel capacity in communication links. New J. Phys.
**2015**, 17, 043040. [Google Scholar] [CrossRef] - Xie, G.D.; Li, L.; Ren, Y.X.; Huang, H.; Yan, Y.; Ahmed, N.; Zhao, Z.; Lavery, M.P.J.; Ashrafi, N.; Ashrafi, S.; et al. Performance metrics and design considerations for a free-space optical orbital-angular-momentum-multiplexed communication link. Optica
**2015**, 2, 357–365. [Google Scholar] [CrossRef] - Paterson, C. Atmospheric turbulence and orbital angular momentum of single photons for optical communication. Phys. Rev. Lett.
**2005**, 94, 153901. [Google Scholar] [CrossRef] [PubMed] - Zhao, S.M.; Leach, J.; Gong, L.Y.; Ding, J.; Zheng, B.Y. Aberration corrections for free-space optical communications in atmosphere turbulence using orbital angular momentum states. Opt. Express
**2012**, 20, 452–461. [Google Scholar] [CrossRef] [PubMed] - Oldoni, M.; Spinello, F.; Mari, E.; Parisi, G.; Someda, C.G.; Tamburini, F.; Romanato, F.; Ravanelli, R.A.; Coassini, P.; Thide, B. Space-Division Demultiplexing in Orbital-Angular-Momentum-Based MIMO Radio Systems. IEEE Trans. Antennas Propag.
**2015**, 63, 4582–4587. [Google Scholar] [CrossRef] - Tamburini, F.; Anzolin, G.; Umbriaco, G.; Bianchini, A.; Barbieri, C. Overcoming the Rayleigh criterion limit with optical vortices. Phys. Rev. Lett.
**2006**, 97, 163903. [Google Scholar] [CrossRef] [PubMed] - Liu, K.; Cheng, Y.Q.; Yang, Z.C.; Wang, H.Q.; Qin, Y.L.; Li, X. Orbital-Angular-Momentum-Based Electromagnetic Vortex Imaging. IEEE Antennas Wirel. Propag. Lett.
**2015**, 14, 711–714. [Google Scholar] [CrossRef] - Grier, D.G. A revolution in optical manipulation. Nature
**2003**, 424, 810–816. [Google Scholar] [CrossRef] [PubMed] - He, H.; Friese, M.E.J.; Heckenberg, N.R.; Rubinszteindunlop, H. Direct Observation of Transfer of Angular-Momentum to Absorptive Particles from a Laser-Beam with a Phase Singularity. Phys. Rev. Lett.
**1995**, 75, 826–829. [Google Scholar] [CrossRef] [PubMed] - Simpson, N.B.; Dholakia, K.; Allen, L.; Padgett, M.J. Mechanical equivalence of spin and orbital angular momentum of light: an optical spanner. Opt. Lett.
**1997**, 22, 52–54. [Google Scholar] [CrossRef] [PubMed] - Lavery, M.P.J.; Speirits, F.C.; Barnett, S.M.; Padgett, M.J. Detection of a Spinning Object Using Light’s Orbital Angular Momentum. Science
**2013**, 341, 537–540. [Google Scholar] [CrossRef] [PubMed] - Dada, A.C.; Leach, J.; Buller, G.S.; Padgett, M.J.; Andersson, E. Experimental high-dimensional two-photon entanglement and violations of generalized Bell inequalities. Nat. Phys.
**2011**, 7, 677–680. [Google Scholar] [CrossRef] - Leach, J.; Jack, B.; Romero, J.; Jha, A.K.; Yao, A.M.; Franke-Arnold, S.; Ireland, D.G.; Boyd, R.W.; Barnett, S.M.; Padgett, M.J. Quantum Correlations in Optical Angle-Orbital Angular Momentum Variables. Science
**2010**, 329, 662–665. [Google Scholar] [CrossRef] [PubMed] - Ren, H.R.; Li, X.P.; Zhang, Q.M.; Gu, M. On-chip noninterference angular momentum multiplexing of broadband light. Science
**2016**, 352, 805–809. [Google Scholar] [CrossRef] [PubMed] - Mei, S.T.; Huang, K.; Liu, H.; Qin, F.; Mehmood, M.Q.; Xu, Z.J.; Hong, M.H.; Zhang, D.H.; Teng, J.H.; Danner, A.; et al. On-chip discrimination of orbital angular momentum of light with plasmonic nanoslits. Nanoscale
**2016**, 8, 2227–2233. [Google Scholar] [CrossRef] [PubMed] - Molina-Terriza, G.; Torres, J.P.; Torner, L. Twisted photons. Nat. Phys.
**2007**, 3, 305–310. [Google Scholar] [CrossRef] - Vaziri, A.; Weihs, G.; Zeilinger, A. Superpositions of the orbital angular momentum for applications in quantum experiments. J. Opt. B
**2002**, 4, S47–S51. [Google Scholar] [CrossRef] - Allen, L.; Beijersbergen, M.W.; Spreeuw, R.J.C.; Woerdman, J.P. Orbital Angular-Momentum of Light and the Transformation of Laguerre-Gaussian Laser Modes. Phys. Rev. A
**1992**, 45, 8185–8189. [Google Scholar] [CrossRef] [PubMed] - Bazhenov, V.Y.; Vasnetsov, M.V.; Soskin, M.S. Laser-Beams with Screw Dislocations in Their Wave-Fronts. JETP Lett.
**1990**, 52, 429–431. [Google Scholar] - Beijersbergen, M.W.; Allen, L.; Vanderveen, H.E.L.O.; Woerdman, J.P. Astigmatic Laser Mode Converters and Transfer of Orbital Angular-Momentum. Opt. Commun.
**1993**, 96, 123–132. [Google Scholar] [CrossRef] - Beijersbergen, M.; Coerwinkel, R.; Kristensen, M.; Woerdman, J. Helical-wavefront laser beams produced with a spiral phaseplate. Opt. Commun.
**1994**, 112, 321–327. [Google Scholar] [CrossRef] - Marrucci, L.; Manzo, C.; Paparo, D. Optical spin-to-orbital angular momentum conversion in inhomogeneous anisotropic media. Phys. Rev. Lett.
**2006**, 96, 163905. [Google Scholar] [CrossRef] [PubMed] - Mohammadi, S.M.; Daldorff, L.K.S.; Bergman, J.E.S.; Karlsson, R.L.; Thide, B.; Forozesh, K.; Carozzi, T.D.; Isham, B. Orbital Angular Momentum in Radio-A System Study. IEEE Trans. Antennas Propag.
**2010**, 58, 565–572. [Google Scholar] [CrossRef] - Zheng, S.L.; Hui, X.N.; Jin, X.F.; Chi, H.; Zhang, X.M. Transmission Characteristics of a Twisted Radio Wave Based on Circular Traveling-Wave Antenna. IEEE Trans. Antennas Propag.
**2015**, 63, 1530–1536. [Google Scholar] [CrossRef] - Barbuto, M.; Trotta, F.; Bilotti, F.; Toscano, A. Circular Polarized Patch Antenna Generating Orbital Angular Momentum. Prog. Electromagn. Res.
**2014**, 148, 23–30. [Google Scholar] [CrossRef] - Yu, N.F.; Capasso, F. Flat optics with designer metasurfaces. Nat. Mater.
**2014**, 13, 139–150. [Google Scholar] [CrossRef] [PubMed] - Yu, N.F.; Genevet, P.; Kats, M.A.; Aieta, F.; Tetienne, J.P.; Capasso, F.; Gaburro, Z. Light Propagation with Phase Discontinuities: Generalized Laws of Reflection and Refraction. Science
**2011**, 334, 333–337. [Google Scholar] [CrossRef] [PubMed] - Genevet, P.; Yu, N.F.; Aieta, F.; Lin, J.; Kats, M.A.; Blanchard, R.; Scully, M.O.; Gaburro, Z.; Capasso, F. Ultra-thin plasmonic optical vortex plate based on phase discontinuities. Appl. Phys. Lett.
**2012**, 100, 013101. [Google Scholar] [CrossRef] - Yu, N.F.; Genevet, P.; Aieta, F.; Kats, M.A.; Blanchard, R.; Aoust, G.; Tetienne, J.P.; Gaburro, Z.; Capasso, F. Flat optics: Controlling wavefronts with optical antenna metasurfaces. IEEE J. Sel. Top. Quantum Electron.
**2013**, 19. [Google Scholar] [CrossRef] - Munk, B. Frequency Selective Surfaces: Theory and Design; John Wiley: New York, NY, USA, 2000. [Google Scholar]
- Kou, N.; Yu, S.X.; Li, L. Generation of high-order Bessel vortex beam carrying orbital angular momentum using multilayer amplitude-phase-modulated surfaces in radiofrequency domain. Appl. Phys. Express
**2017**, 10, 016701. [Google Scholar] [CrossRef] - Pfeiffer, C.; Grbic, A. Metamaterial Huygens’ Surfaces: Tailoring Wave Fronts with Reflectionless Sheets. Phys. Rev. Lett.
**2013**, 110, 197401. [Google Scholar] [CrossRef] [PubMed] - Niv, A.; Biener, G.; Kleiner, V.; Hasman, E. Spiral phase elements obtained by use of discrete space-variant subwavelength gratings. Opt. Commun.
**2005**, 251, 306–314. [Google Scholar] [CrossRef] - Turnbull, G.A.; Robertson, D.A.; Smith, G.M.; Allen, L.; Padgett, M.J. The generation of free-space Laguerre-Gaussian modes at millimetre-wave frequencies by use of a spiral phaseplate. Opt. Commun.
**1996**, 127, 183–188. [Google Scholar] [CrossRef] - Kotlyar, V.V.; Almazov, A.A.; Khonina, S.N.; Soifer, V.A.; Elfstrom, H.; Turunen, J. Generation of phase singularity through diffracting a plane or Gaussian beam by a spiral phase plate. J. Opt. Soc. Am. A
**2005**, 22, 849–861. [Google Scholar] [CrossRef] - Hui, X.N.; Zheng, S.L.; Hu, Y.P.; Xu, C.; Jin, X.F.; Chi, H.; Zhang, X.M. Ultralow Reflectivity Spiral Phase Plate for Generation of Millimeter-wave OAM Beam. IEEE Antennas Wirel. Propag. Lett.
**2015**, 14, 966–969. [Google Scholar] [CrossRef] - Cheng, L.; Hong, W.; Hao, Z.C. Generation of Electromagnetic Waves with Arbitrary Orbital Angular Momentum Modes. Sci. Rep.
**2014**, 4. [Google Scholar] [CrossRef] [PubMed] - Sun, J.B.; Wang, X.; Xu, T.B.Y.; Kudyshev, Z.A.; Cartwright, A.N.; Litchinitser, N.M. Spinning Light on the Nanoscale. Nano Lett.
**2014**, 14, 2726–2729. [Google Scholar] [CrossRef] [PubMed] - Carpentier, A.V.; Michinel, H.; Salgueiro, J.R.; Olivieri, D. Making optical vortices with computer-generated holograms. Am. J. Phys.
**2008**, 76, 916–921. [Google Scholar] [CrossRef] - Heckenberg, N.R.; Mcduff, R.; Smith, C.P.; White, A.G. Generation of Optical-Phase Singularities by Computer-Generated Holograms. Opt. Lett.
**1992**, 17, 221–223. [Google Scholar] [CrossRef] [PubMed] - Arlt, J.; Dholakia, K.; Allen, L.; Padgett, M.J. The production of multiringed Laguerre-Gaussian modes by computer-generated holograms. J. Mod. Opt.
**1998**, 45, 1231–1237. [Google Scholar] [CrossRef] - Moreno, I.; Davis, J.A.; Pascoguin, B.M.L.; Mitry, M.J.; Cottrell, D.M. Vortex sensing diffraction gratings. Opt. Lett.
**2009**, 34, 2927–2929. [Google Scholar] [CrossRef] [PubMed] - Liu, K.; Liu, H.Y.; Qin, Y.L.; Cheng, Y.Q.; Wang, S.N.; Li, X.; Wang, H.Q. Generation of OAM Beams Using Phased Array in the Microwave Band. IEEE Trans. Antennas Propag.
**2016**, 64, 3850–3857. [Google Scholar] [CrossRef] - Comite, D.; Valerio, G.; Albani, M.; Galli, A.; Casaletti, M.; Ettorre, M. Exciting Vorticity through Higher Order Bessel Beams with a Radial-Line Slot-Array Antenna. IEEE Trans. Antennas Propag.
**2017**, 65, 2123–2128. [Google Scholar] [CrossRef] - Xu, B.J.; Wu, C.; Wei, Z.Y.; Fan, Y.C.; Li, H.Q. Generating an orbital-angular-momentum beam with a metasurface of gradient reflective phase. Opt. Mater. Express
**2016**, 6, 3940–3945. [Google Scholar] [CrossRef] - Yu, S.X.; Li, L.; Shi, G.M.; Zhu, C.; Shi, Y. Generating multiple orbital angular momentum vortex beams using a metasurface in radio frequency domain. Appl. Phys. Lett.
**2016**, 108, 241901. [Google Scholar] [CrossRef] - Wang, L.Y.; Shi, H.Y.; Zhu, S.T.; Li, J.X.; Zhang, A.X.; Li, L.M. Generation of multiple modes microwave vortex beams using tunable metasurfacee. In Proceedings of the 7th IEEE International Symposium on Microwave, Antenna, Propagation and EMC Technologies, Xi’an, China, 24–27 October 2017; pp. 379–381. [Google Scholar]
- Maccalli, S.; Pisano, G.; Colafrancesco, S.; Maffei, B.; Ng, M.W.R.; Gray, M. Q-plate for millimeter-wave orbital angular momentum manipulation. Appl. Opt.
**2013**, 52, 635–639. [Google Scholar] [CrossRef] [PubMed] - Cardano, F.; Karimi, E.; Slussarenko, S.; Marrucci, L.; de Lisio, C.; Santamato, E. Polarization pattern of vector vortex beams generated by q-plates with different topological charges. Appl. Opt.
**2012**, 51, C1–C6. [Google Scholar] [CrossRef] [PubMed] - Bliokh, K.Y.; Rodriguez-Fortuno, F.J.; Nori, F.; Zayats, A.V. Spin-orbit interactions of light. Nat. Photonics
**2015**, 9, 796–808. [Google Scholar] [CrossRef] [Green Version] - Karimi, E.; Piccirillo, B.; Nagali, E.; Marrucci, L.; Santamato, E. Efficient generation and sorting of orbital angular momentum eigenmodes of light by thermally tuned q-plates. Appl. Phys. Lett.
**2009**, 94, 231124. [Google Scholar] [CrossRef] - Piccirillo, B.; D’Ambrosio, V.; Slussarenko, S.; Marrucci, L.; Santamato, E. Photon spin-to-orbital angular momentum conversion via an electrically tunable q-plate. Appl. Phys. Lett.
**2010**, 97, 241104. [Google Scholar] [CrossRef] - Kang, M.; Feng, T.H.; Wang, H.T.; Li, J.S. Wave front engineering from an array of thin aperture antennas. Opt. Express
**2012**, 20, 15882–15890. [Google Scholar] [CrossRef] [PubMed] - Xu, H.X.; Liu, H.; Ling, X.; Sun, Y.; Yuan, F. Broadband Vortex Beam Generation Using Multimode Pancharatnam-Berry Metasurface. IEEE Trans. Antennas Propag.
**2017**, 65, 7378–7382. [Google Scholar] [CrossRef] - Karimi, E.; Schulz, S.A.; De Leon, I.; Qassim, H.; Upham, J.; Boyd, R.W. Generating optical orbital angular momentum at visible wavelengths using a plasmonic metasurface. Light Sci. Appl.
**2014**, 3, e167. [Google Scholar] [CrossRef] - Tan, Q.L.; Guo, Q.H.; Liu, H.C.; Huang, G.; Zhang, S. Controlling the plasmonic orbital angular momentum by combining the geometric and dynamic phases. Nanoscale
**2017**, 9, 4944–4949. [Google Scholar] [CrossRef] [PubMed] - Li, G.X.; Kang, M.; Chen, S.M.; Zhang, S.; Pun, E.Y.B.; Cheah, K.W.; Li, J.S. Spin-enabled plasmonic metasurfaces for manipulating orbital angular momentum of light. Nano Lett.
**2013**, 13, 4148–4151. [Google Scholar] [CrossRef] [PubMed] - Mohammadi, S.M.; Daldorff, L.K.S.; Forozesh, K.; Thide, B.; Bergman, J.E.S.; Isham, B.; Karlsson, R.; Carozzi, T.D. Orbital angular momentum in radio: Measurement methods. Radio Sci.
**2010**, 45. [Google Scholar] [CrossRef] - Schulze, C.; Dudley, A.; Flamm, D.; Duparre, M.; Forbes, A. Measurement of the orbital angular momentum density of light by modal decomposition. New J. Phys.
**2013**, 15, 073025. [Google Scholar] [CrossRef] - Hui, X.N.; Zheng, S.L.; Zhang, W.T.; Jin, X.F.; Chi, H.; Zhang, X.M. Local topological charge analysis of electromagnetic vortex beam based on empirical mode decomposition. Opt. Express
**2016**, 24, 5423–5430. [Google Scholar] [CrossRef] [PubMed] - Zhang, C.; Lu, M. Detecting the orbital angular momentum of electro-magnetic waves using virtual rotational antenna. Sci. Rep.
**2017**, 7, 4585. [Google Scholar] [CrossRef] [PubMed] - Courtial, J.; Dholakia, K.; Robertson, D.A.; Allen, L.; Padgett, M.J. Measurement of the rotational frequency shift imparted to a rotating light beam possessing orbital angular momentum. Phys. Rev. Lett.
**1998**, 80, 3217–3219. [Google Scholar] [CrossRef] - Allen, L.; Babiker, M.; Power, W.L. Azimuthal Doppler-Shift in Light-Beams with Orbital Angular-Momentum. Opt. Commun.
**1994**, 112, 141–144. [Google Scholar] [CrossRef] - Genevet, P.; Lin, J.; Kats, M.A.; Capasso, F. Holographic detection of the orbital angular momentum of light with plasmonic photodiodes. Nat. Commun.
**2012**, 3, 1278. [Google Scholar] [CrossRef] [PubMed] [Green Version] - Tamburini, F.; Mari, E.; Sponselli, A.; Thide, B.; Bianchini, A.; Romanato, F. Encoding many channels on the same frequency through radio vorticity: first experimental test. New J. Phys.
**2012**, 14, 033001. [Google Scholar] [CrossRef] - Mair, A.; Vaziri, A.; Weihs, G.; Zeilinger, A. Entanglement of the orbital angular momentum states of photons. Nature
**2001**, 412, 313–316. [Google Scholar] [CrossRef] [PubMed] - Luo, W.J.; Xiao, S.Y.; He, Q.; Sun, S.L.; Zhou, L. Photonic Spin Hall Effect with Nearly Efficiency. Adv. Opt. Mater.
**2015**, 3, 1102–1108. [Google Scholar] [CrossRef] - Georgi, P.; Schlickriede, C.; Li, G.X.; Zhang, S.; Zentgraf, T. Rotational Doppler shift induced by spin-orbit coupling of light at spinning metasurfaces. Optica
**2017**, 4, 1000–1005. [Google Scholar] [CrossRef] - Bouchard, F.; De Leon, I.; Schulz, S.A.; Upham, J.; Karimi, E.; Boyd, R.W. Optical spin-to-orbital angular momentum conversion in ultra-thin metasurfaces with arbitrary topological charges. Appl. Phys. Lett.
**2014**, 105, 101905. [Google Scholar] [CrossRef] - Wang, W.; Li, Y.; Guo, Z.Y.; Li, R.Z.; Zhang, J.R.; Zhang, A.J.; Qu, S.L. Ultra-thin optical vortex phase plate based on the metasurface and the angular momentum transformation. J. Opt.
**2015**, 17, 045102. [Google Scholar] [CrossRef] - Jin, J.J.; Luo, J.; Zhang, X.H.; Gao, H.; Li, X.; Pu, M.B.; Gao, P.; Zhao, Z.Y.; Luo, X.G. Generation and detection of orbital angular momentum via metasurface. Sci. Rep.
**2016**, 6. [Google Scholar] [CrossRef] [PubMed] - Zelenchuk, D.; Fusco, V. Split-Ring FSS Spiral Phase Plate. IEEE Antennas Wirel. Propag. Lett.
**2013**, 12, 284–287. [Google Scholar] [CrossRef] [Green Version] - Tan, Y.H.; Li, L.L.; Ruan, H.X. An Efficient Approach to Generate Microwave Vector-Vortex Fields Based on Metasurface. Microw. Opt. Technol. Lett.
**2015**, 57, 1708–1713. [Google Scholar] [CrossRef] - Chen, M.L.N.; Jiang, L.J.; Sha, W.E.I. Artificial perfect electric conductor-perfect magnetic conductor anisotropic metasurface for generating orbital angular momentum of microwave with nearly perfect conversion efficiency. J. Appl. Phys.
**2016**, 119, 064506. [Google Scholar] [CrossRef] - Chen, M.L.L.N.; Jiang, L.J.; Sha, W.E.I. Ultrathin Complementary Metasurface for Orbital Angular Momentum Generation at Microwave Frequencies. IEEE Trans. Antennas Propag.
**2017**, 65, 396–400. [Google Scholar] [CrossRef] - Li, Y.; Li, X.; Chen, L.W.; Pu, M.B.; Jin, J.J.; Hong, M.H.; Luo, X.G. Orbital Angular Momentum Multiplexing and Demultiplexing by a Single Metasurface. Adv. Opt. Mater.
**2017**, 5. [Google Scholar] [CrossRef] - Guo, Y.H.; Pu, M.B.; Zhao, Z.Y.; Wang, Y.Q.; Jin, J.J.; Gao, P.; Li, X.; Ma, X.L.; Luo, X.G. Merging Geometric Phase and Plasmon Retardation Phase in Continuously Shaped Metasurfaces for Arbitrary Orbital Angular Momentum Generation. ACS Photonics
**2016**, 3, 2022–2029. [Google Scholar] [CrossRef] - Pu, M.B.; Li, X.; Ma, X.L.; Wang, Y.Q.; Zhao, Z.Y.; Wang, C.T.; Hu, C.G.; Gao, P.; Huang, C.; Ren, H.R.; et al. Catenary optics for achromatic generation of perfect optical angular momentum. Sci. Adv.
**2015**, 1, e1500396. [Google Scholar] [CrossRef] [PubMed] - Chen, M.; Jiang, L.J.; Wei, E. Detection of Orbital Angular Momentum with Metasurface at Microwave Band. IEEE Antennas Wirel. Propag. Lett.
**2017**. [Google Scholar] [CrossRef] - Devlin, R.C.; Ambrosio, A.; Wintz, D.; Oscurato, S.L.; Zhu, A.Y.; Khorasaninejad, M.; Oh, J.; Maddalena, P.; Capasso, F. Spin-to-orbital angular momentum conversion in dielectric metasurfaces. Opt. Express
**2017**, 25, 377–393. [Google Scholar] [CrossRef] [PubMed] - Dang, X.W.; Li, M.K.; Yang, F.; Xu, S.H. Quasi-periodic array modeling using reduced basis from elemental array. IEEE J. Multiscale Multiphys. Comput. Tech.
**2017**, 2, 202–208. [Google Scholar] [CrossRef] - Chen, S.M.; Cai, Y.; Li, G.X.; Zhang, S.; Cheah, K.W. Geometric metasurface fork gratings for vortex-beam generation and manipulation. Laser Photonics Rev.
**2016**, 10, 322–326. [Google Scholar] [CrossRef] - Kang, M.; Chen, J.; Wang, X.L.; Wang, H.T. Twisted vector field from an inhomogeneous and anisotropic metamaterial. J. Opt. Soc. Am. B
**2012**, 29, 572–576. [Google Scholar] [CrossRef] - Zhao, Z.; Wang, J.; Li, S.H.; Willner, A.E. Metamaterials-based broadband generation of orbital angular momentum carrying vector beams. Opt. Lett.
**2013**, 38, 932–934. [Google Scholar] [CrossRef] [PubMed] - Wang, J.; Du, J. Plasmonic and dielectric metasurfaces: Design, fabrication and applications. Appl. Sci.
**2016**, 6, 239. [Google Scholar] [CrossRef] - Biener, G.; Niv, A.; Kleiner, V.; Hasman, E. Formation of helical beams by use of Pancharatnam-Berry phase optical elements. Opt. Lett.
**2002**, 27, 1875–1877. [Google Scholar] [CrossRef] [PubMed] - Maguid, E.; Yulevich, I.; Veksler, D.; Kleiner, V.; Brongersma, M.L.; Hasman, E. Photonic spin-controlled multifunctional shared-aperture antenna array. Science
**2016**, 352, 1202–1206. [Google Scholar] [CrossRef] [PubMed]

**Figure 1.**Schematic pattern of the perfect electric conductor (PEC)-perfect magnetic conductor (PMC) anisotropic metasurface for orbital angular momentum (OAM) generation. With a nearly 100% conversion efficiency, the metasurface perfectly converts a left (right) circularly polarized plane wave carrying zero OAM to a right (left) circularly polarized vortex beam carrying $\pm 2\hslash $ OAM: (

**a**) Top view of the whole metasurface; (

**b**,

**c**) A scatterer in the metasurface. The scatterer is composed of artificial PEC (purple) and PMC (blue and red) surfaces. The period of the scatterer is $p=7$ mm. The permittivity and thickness of the dielectric substrate are set to ${\u03f5}_{r}=2.2$, ${d}_{1}=2$ mm and ${d}_{2}=3$ mm. For the artificial PEC surface (top-right inset), the width and gap for the strip is $t=1$ mm and $g=2.5$ mm, respectively. For the mushroom-based artificial PMC surface (bottom-right inset), the square patch size is $a=6$ mm. A metallic via with the radius of $r=0.25$ mm and height of ${d}_{1}=2$ mm connects the patch to the ground plane. Reproduced with permission from [84], Copyright AIP Publishing LLC, 2016.

**Figure 2.**The amplitude and phase distributions of reflected electric fields from the PEC-PMC metasurface at a transverse plane $z=20$ mm: (

**a**) Amplitude; (

**b**) Phase. Reproduced with permission from [84], Copyright AIP Publishing LLC, 2016.

**Figure 3.**The amplitude and phase distributions of reflected electric fields from the discrete PEC-PMC metasurface. For the generation of OAM of order −2, (

**a**) amplitude; (

**b**) phase at a transverse plane $z=40$ mm. For the generation of OAM of order −4, (

**c**) amplitude; (

**d**) phase at a transverse plane $z=100$ mm. Reproduced with permission from [84], Copyright AIP Publishing LLC, 2016.

**Figure 4.**Schematic and the response of the proposed unit cell: (

**a**) Schematic; (

**b**) Equivalent circuit model of one pair of complementary split-ring resonators (CSRRs) and simulated ${S}_{21}$. The purple and green curves are obtained by the translation of the original blue (magnitude) and red (phase) curves. The distance between the two layers is h = 1.25 mm. Characteristic impedance of free space is ${Z}_{0}=377\phantom{\rule{3.33333pt}{0ex}}\Omega $. The capacitance and inductance are ${C}_{0}=0.09$ pF and ${L}_{0}=1.03$ nH; (

**c**) Full-wave simulation results. The period of the unit cell is 7 × 7 mm

^{2}. Side lengths of the two types of square CSRRs are ${a}_{l}=5.2$ mm and ${a}_{s}=3.9$ mm. The length of the gap is $g=0.2$ mm. The width of the slots is $t=0.2$ mm. Reproduced with permission from [85], Copyright IEEE, 2017.

**Figure 5.**Geometric structure of the metasurface. Topological charge is (

**a**) $q=1$; (

**b**) $q=2$. The radius of the inner ring is ${r}_{1}=14$ mm and that of the outer ring is ${r}_{2}=21$ mm. Reproduced with permission from [85], Copyright IEEE, 2017.

**Figure 6.**Amplitude and phase distributions of the cross-circularly polarized component of electric field at a transverse plane of $z=10$ mm calculated from (

**a**) the equivalent dipole model with the aperture in Figure 5a; (

**b**) the equivalent dipole model with the aperture in Figure 5b; (

**c**) the full-wave simulation with the aperture in Figure 5a; (

**d**) the full-wave simulation with the aperture in Figure 5b. Reproduced with permission from [85], Copyright IEEE, 2017.

**Figure 7.**(

**a**) Phase distribution and the scanning electron images of metasurface fork gratings with topological charge of $q=2,3$; The plasmonic metasurfaces are fabricated on an 80-nm thick aluminum thin film by using focus ion beam method, consists of spatially variant nanoslits with a size of ∼50 nm by 210 nm. Scale bar: 3 µm. Reproduced with permission from [92], Copyright WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim, 2016; (

**b**) Schematics of off-axis incidence multi-OAM multiplexer and off-axis multi-OAM demultiplexer. Reproduced with permission from [86], Copyright WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim, 2016.

**Figure 8.**Geometry of a one-dimensional inhomogeneous anisotropic metamaterial composed of 10 rectangular holes with the orientation changed stepwisely from 0 to $\pi /2$. The inset is the geometry of the unit cell that is a square metal slab punched into a rectangular hole. Reproduced with permission from [93], Copyright The Optical Society, 2012.

**Figure 9.**Schematic structure of metamaterials for generating OAM-carrying vector beams and the spatial distributions of phase and polarization of generated OAM-carrying vector beams ($\sigma =-1$, right circularly polarized (RCP) input beam). Reproduced with permission from [94], Copyright The Optical Society, 2013.

**Figure 10.**(

**a**) The metasurface is constructed by drilling a silver film with multiple periods of annular rings, whose radius is defined as ${R}_{n}={R}_{1}+(n-1)P$, where n and P denote the number and the period of the apertures. The annular apertures can be taken as two-dimensional extensions of a set of nanoslits with spatially varying orientation. Reproduced with permission from [87], Copyright American Chemical Society, 2016; (

**b**) OAM generators based on catenary arrays. The topological charges from up to bottom are −3, −6, and 12 ($s=1$), respectively. The first column represents the scanning electron microscopy (SEM) images of the fabricated samples. The second column shows the spiral phase profiles. Reproduced with permission from [88], Copyright The American Association for the Advancement of Science, 2015; (

**c**) Top, geometry of the subwavelength gratings for four topological charges. Bottom, image of a typical grating profile taken with a scanning-electron microscope. Reproduced with permission from [96], Copyright Optical Society of America, 2002.

**Figure 11.**(

**a**) Schematic of the nanofins azimuthal distribution in the inner part of metasurface device with interleaved patterns that generate collinear beams having topological charges $\left|l\right|=5$ and $\left|l\right|=10$. The device has a 500 µm diameter and contains more than 700 interleaved radial rows of nanofins. Reproduced with permission from [90], Copyright Optical Society of America, 2017; (

**b**) Schematic of shared-aperture concepts using interleaved 1D phased arrays and the schematic far-field intensity distribution of wavefronts with positive (red) and negative (blue) helicities. Reproduced with permission from [97], Copyright The American Association for the Advancement of Science, 2016.

**Figure 12.**Schematic representation of multiple OAM-beam detection by a single metasurface. Reproduced with permission from [89], Copyright IEEE, 2017.

**Figure 13.**Full-wave simulated far-field power patterns when the incident wave carries OAM of order (

**a**) −2; (

**b**) −1; (

**c**) 0; (

**d**) 1; (

**e**) 2. (

**f**) Original and optimized far-field power patterns at $\theta $ = 40° for the five cases (

**a**–

**e**). Reproduced with permission from [89], Copyright IEEE, 2017.

© 2018 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

Chen, M.L.N.; Jiang, L.J.; Sha, W.E.I.
Orbital Angular Momentum Generation and Detection by Geometric-Phase Based Metasurfaces. *Appl. Sci.* **2018**, *8*, 362.
https://doi.org/10.3390/app8030362

**AMA Style**

Chen MLN, Jiang LJ, Sha WEI.
Orbital Angular Momentum Generation and Detection by Geometric-Phase Based Metasurfaces. *Applied Sciences*. 2018; 8(3):362.
https://doi.org/10.3390/app8030362

**Chicago/Turabian Style**

Chen, Menglin L. N., Li Jun Jiang, and Wei E. I. Sha.
2018. "Orbital Angular Momentum Generation and Detection by Geometric-Phase Based Metasurfaces" *Applied Sciences* 8, no. 3: 362.
https://doi.org/10.3390/app8030362