Abstract

Vortex beams are characterized by a helical wavefront and a phase singularity point on the propagation axis that results in a doughnut-like intensity profile. These beams carry orbital angular momentum proportional to the number of intertwined helices constituting the wavefront. Vortex beams have many applications in optics, such as optical trapping, quantum optics and microscopy. Although beams with such characteristics can be generated holographically, spin-to-orbital angular momentum conversion has attracted considerable interest as a tool to create vortex beams. In this process, the geometrical phase is exploited to create helical beams whose handedness is determined by the circular polarization (left/right) of the incident light, that is by its spin. Here we demonstrate high-efficiency Spin-to-Orbital angular momentum-Converters (SOCs) at visible wavelengths based on dielectric metasurfaces. With these SOCs we generate vortex beams with high and fractional topological charge and show for the first time the simultaneous generation of collinear helical beams with different and arbitrary orbital angular momentum. This versatile method of creating vortex beams, which circumvents the limitations of liquid crystal SOCs and adds new functionalities, should significantly expand the applications of these beams.

© 2017 Optical Society of America

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Corrections

Robert Charles Devlin, Antonio Ambrosio, Daniel Wintz, Stefano Luigi Oscurato, Alexander Yutong Zhu, Mohammadreza Khorasaninejad, Jaewon Oh, Pasqualino Maddalena, and Federico Capasso, "Spin-to-orbital angular momentum conversion in dielectric metasurfaces: erratum," Opt. Express 25, 4239-4239 (2017)
https://www.osapublishing.org/oe/abstract.cfm?uri=oe-25-4-4239

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References

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2016 (3)

M. Q. Mehmood, S. Mei, S. Hussain, K. Huang, S. Y. Siew, L. Zhang, T. Zhang, X. Ling, H. Liu, J. Teng, A. Danner, S. Zhang, and C.-W. Qiu, “Visible-frequency metasurface for structuring and spatially multiplexing optical vortices,” Adv. Mater. 28(13), 2533–2539 (2016).
[Crossref] [PubMed]

M. Khorasaninejad, A. Ambrosio, P. Kanhaiya, and F. Capasso, “Dispersion-compensated meta-holograms based on detour phase,” Sci. Adv. 2, e1501258 (2016).
[Crossref] [PubMed]

R. C. Devlin, M. Khorasaninejad, W.-T. Chen, J. Oh, and F. Capasso, “Broadband high-efficiency dielectric metasurfaces for the visible spectrum,” Proc. Natl. Acad. Sci. U.S.A. 113(38), 10473–10478 (2016).
[Crossref] [PubMed]

2015 (9)

T. Bauer, P. Banzer, E. Karimi, S. Orlov, A. Rubano, L. Marrucci, E. Santamato, R. W. Boyd, and G. Leuchs, “Observation of optical polarization Möbius strips,” Science 347(6225), 964–966 (2015).
[Crossref] [PubMed]

L. Yan, P. Gregg, E. Karimi, A. Rubano, L. Marrucci, R. W. Boyd, and S. Ramachandran, “Q-plate enabled spectrally diverse orbital-angular-momentum conversion for stimulated emission depletion microscopy,” Optica 2(10), 900 (2015).
[Crossref]

A. Arbabi, Y. Horie, A. J. Ball, M. Bagheri, and A. Faraon, “Subwavelength-thick lenses with high numerical apertures and large efficiency based on high-contrast transmitarrays,” Nat. Commun. 6, 7069 (2015).
[Crossref] [PubMed]

A. Arbabi, Y. Horie, M. Bagheri, and A. Faraon, “Dielectric metasurfaces for complete control of phase and polarization with subwavelength spatial resolution and high transmission,” Nat. Nanotechnol. 10(11), 937–943 (2015).
[Crossref] [PubMed]

M. Pu, X. Li, X. Ma, Y. Wang, Z. Zhao, C. Wang, C. Hu, P. Gao, C. Huang, H. Ren, X. Li, F. Qin, J. Yang, M. Gu, M. Hong, and X. Luo, “Catenary optics for achromatic generation of perfect optical angular momentum,” Sci. Adv. 1(9), e1500396 (2015).
[Crossref] [PubMed]

D. Hakobyan, H. Magallanes, G. Seniutinas, S. Juodkazis, and E. Brasselet, “Tailoring orbital angular momentum of light in the visible domain with metallic metasurfaces,” Adv. Optical Mater. 4(2), 306 (2015).

M. I. Shalaev, J. Sun, A. Tsukernik, A. Pandey, K. Nikolskiy, and N. M. Litchinitser, “High-Efficiency all-dielectric metasurfaces for ultracompact beam manipulation in transmission mode,” Nano Lett. 15(9), 6261–6266 (2015).
[Crossref] [PubMed]

G. Milione, M. P. J. Lavery, H. Huang, Y. Ren, G. Xie, T. A. Nguyen, E. Karimi, L. Marrucci, D. A. Nolan, R. R. Alfano, and A. E. Willner, “4 × 20 Gbit/s mode division multiplexing over free space using vector modes and a q-plate mode (de)multiplexer,” Opt. Lett. 40(9), 1980–1983 (2015).
[Crossref] [PubMed]

H. Huang, G. Milione, M. P. J. Lavery, G. Xie, Y. Ren, Y. Cao, N. Ahmed, T. An Nguyen, D. A. Nolan, M.-J. Li, M. Tur, R. R. Alfano, and A. E. Willner, “Mode division multiplexing using an orbital angular momentum mode sorter and MIMO-DSP over a graded-index few-mode optical fibre,” Sci. Rep. 5, 14931 (2015).
[Crossref] [PubMed]

2014 (6)

N. Yu and F. Capasso, “Flat optics with designer metasurfaces,” Nat. Mater. 13(2), 139–150 (2014).
[Crossref] [PubMed]

D. Lin, P. Fan, E. Hasman, and M. L. Brongersma, “Dielectric gradient metasurface optical elements,” Science 345(6194), 298–302 (2014).
[Crossref] [PubMed]

F. Bouchard, I. De Leon, S. A. Schulz, J. Upham, E. Karimi, and R. W. Boyd, “Optical spin-to-orbital momentum conversion in ultra-thin metasurfaces with arbitrary topological charges,” Appl. Phys. Lett. 105(10), 101905 (2014).
[Crossref]

E. Karimi, S. A. Schulz, I. De Leon, H. Qassim, J. Upham, and R. W. Boyd, “Generating optical orbital angular momentum at visible wavelengths using a plasmonic metasurface,” Light Sci. Appl. 3(5), e167 (2014).
[Crossref]

F. Bouchard, H. Mand, M. Mirhosseini, E. Karimi, and R. W. Boyd, “Achromatic orbital angular momentum generator,” New J. Phys. 16(12), 123006 (2014).
[Crossref]

M. Khorasaninejad and K. B. Crozier, “Silicon nanofin grating as a miniature chirality-distinguishing beam-splitter,” Nat. Commun. 5, 5386 (2014).
[Crossref] [PubMed]

2013 (3)

V. D’Ambrosio, N. Spagnolo, L. Del Re, S. Slussarenko, Y. Li, L. C. Kwek, L. Marrucci, S. P. Walborn, L. Aolita, and F. Sciarrino, “Photonic polarization gears for ultra-sensitive angular measurements,” Nat. Commun. 4, 2432 (2013).
[Crossref] [PubMed]

J. Lin, P. Genevet, M. A. Kats, N. Antoniou, and F. Capasso, “Nanostructured holograms for broadband manipulation of vector beams,” Nano Lett. 13(9), 4269–4274 (2013).
[Crossref] [PubMed]

G. Li, M. Kang, S. Chen, S. Zhang, E. Y. Pun, K. W. Cheah, and J. Li, “Spin-enabled plasmonic metasurfaces for manipulating orbital angular momentum of light,” Nano Lett. 13(9), 4148–4151 (2013).
[Crossref] [PubMed]

2012 (1)

A. Ambrosio, L. Marrucci, F. Borbone, A. Roviello, and P. Maddalena, “Light-induced spiral mass transport in azo-polymer films under vortex-beam illumination,” Nat. Commun. 3, 989 (2012).
[Crossref] [PubMed]

2011 (5)

G. Milione, H. I. Sztul, D. A. Nolan, and R. R. Alfano, “Higher-order Poincaré sphere, stokes parameters, and the angular momentum of light,” Phys. Rev. Lett. 107(5), 053601 (2011).
[Crossref] [PubMed]

M. J. Padgett and R. Bowman, “Tweezers with a twist,” Nat. Photonics 5(6), 343–348 (2011).
[Crossref]

N. Yu, P. Genevet, M. A. Kats, F. Aieta, J.-P. Tetienne, F. Capasso, and Z. Gaburro, “Light propagation with phase discontinuities: generalized laws of reflection and refraction,” Science 334(6054), 333–337 (2011).
[Crossref] [PubMed]

S. Slussarenko, A. Murauski, T. Du, V. Chigrinov, L. Marrucci, and E. Santamato, “Tunable liquid crystal q-plates with arbitrary topological charge,” Opt. Express 19(5), 4085–4090 (2011).
[Crossref] [PubMed]

D. Giovannini, E. Nagali, L. Marrucci, and F. Sciarrino, “Resilience of orbital-angular-momentum photonic qubits and effects on hybrid entanglement,” Phys. Rev. A 83(4), 042338 (2011).
[Crossref]

2009 (2)

E. Nagali, L. Sansoni, F. Sciarrino, F. De Martini, L. Marrucci, B. Piccirillo, E. Karimi, and E. Santamato, “Optimal quantum cloning of orbital angular momentum photon qubits through Hong–Ou–Mandel coalescence,” Nat. Photonics 3(12), 720–723 (2009).
[Crossref]

M. R. Dennis, K. O’Holleran, and M. J. Padgett, “Singular Optics: Optical Vortices and Polarization Singularities,” Prog. Opt. 53, 293–363 (2009).
[Crossref]

2008 (1)

2007 (1)

J. B. Götte, S. Franke-Arnold, R. Zambrini, and S. M. Barnett, “Quantum formulation of fractional orbital angular momentum,” J. Mod. Opt. 54(12), 1723–1738 (2007).
[Crossref]

2006 (3)

L. Marrucci, C. Manzo, and D. Paparo, “Pancharatnam-Berry phase optical elements for wave front shaping,” Appl. Phys. Lett. 88(22), 221102 (2006).
[Crossref]

Y. Gorodetski, G. Biener, A. Niv, V. Kleiner, and E. Hasman, “Optical properties of polarization-dependent geometric phase elements with partially polarized light,” Opt. Commun. 266(2), 365–375 (2006).
[Crossref]

L. Marrucci, C. Manzo, and D. Paparo, “Optical spin-to-orbital angular momentum conversion in inhomogeneous anisotropic media,” Phys. Rev. Lett. 96(16), 163905 (2006).
[Crossref] [PubMed]

2005 (3)

A. Niv, G. Biener, V. Kleiner, and E. Hasman, “Spiral phase elements obtained by use of discrete space-variant subwavelength gratings,” Opt. Commun. 251(4-6), 306–314 (2005).
[Crossref]

S. S. R. Oemrawsingh, X. Ma, D. Voigt, A. Aiello, E. R. Eliel, G. W. ’t Hooft, and J. P. Woerdman, “Experimental demonstration of fractional orbital angular momentum entanglement of two photons,” Phys. Rev. Lett. 95(24), 240501 (2005).
[Crossref] [PubMed]

M. Menro, J. Liu, W. Rudolph, D. Ristau, and K. Starke, “Scaling laws of femtosecond laser pulse induced breakdown in oxide films,” Phys. Rev. B 71(11), 115109 (2005).
[Crossref]

2004 (4)

S. S. R. Oemrawsingh, A. Aiello, E. R. Eliel, G. Nienhuis, and J. P. Woerdman, “How to observe high-dimensional two-photon entanglement with only two detectors,” Phys. Rev. Lett. 92(21), 217901 (2004).
[Crossref] [PubMed]

M. V. Berry, “Optical vortices evolving from helicoidal integer and fractional phase steps,” J. Opt. A, Pure Appl. Opt. 6(2), 259–268 (2004).
[Crossref]

J. Leach, E. Yao, and M. J. Padgett, “Observation of the vortex structure of a non-integer vortex beam,” New J. Phys. 6, 71 (2004).
[Crossref]

A. Ambrosio, B. Piccirillo, A. Sasso, and E. Santamato, “Experimental and theoretical study of the transient rotation of isotropic transparent microparticles in astigmatic optical tweezers,” Opt. Commun. 230(4-6), 337–345 (2004).
[Crossref]

2002 (2)

G. Biener, A. Niv, V. Kleiner, and E. Hasman, “Formation of helical beams by use of Pancharatnam-Berry phase optical elements,” Opt. Lett. 27(21), 1875–1877 (2002).
[Crossref] [PubMed]

G. Machavariani, N. Davidson, E. Hasman, S. Blit, A. A. Ishaaya, and A. A. Friesem, “Efficient conversion of a Gaussian beam to a high purity helical beam,” Opt. Commun. 209(4-6), 265–271 (2002).
[Crossref]

2001 (1)

A. Mair, A. Vaziri, G. Weihs, and A. Zeilinger, “Entanglement of the orbital angular momentum states of photons,” Nature 412(6844), 313–316 (2001).
[Crossref] [PubMed]

1997 (1)

1996 (1)

M. E. J. Friese, J. Enger, H. Rubinsztein-Dunlop, and N. R. Heckenberg, “Optical angular-momentum transfer to trapped absorbing particles,” Phys. Rev. A 54(2), 1593–1596 (1996).
[Crossref] [PubMed]

1992 (1)

L. Allen, M. W. Beijersbergen, R. J. C. Spreeuw, and J. P. Woerdman, “Orbital angular momentum of light and the transformation of Laguerre-Gaussian laser modes,” Phys. Rev. A 45(11), 8185–8189 (1992).
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1984 (1)

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J. Lin, P. Genevet, M. A. Kats, N. Antoniou, and F. Capasso, “Nanostructured holograms for broadband manipulation of vector beams,” Nano Lett. 13(9), 4269–4274 (2013).
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A. Arbabi, Y. Horie, M. Bagheri, and A. Faraon, “Dielectric metasurfaces for complete control of phase and polarization with subwavelength spatial resolution and high transmission,” Nat. Nanotechnol. 10(11), 937–943 (2015).
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A. Arbabi, Y. Horie, M. Bagheri, and A. Faraon, “Dielectric metasurfaces for complete control of phase and polarization with subwavelength spatial resolution and high transmission,” Nat. Nanotechnol. 10(11), 937–943 (2015).
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A. Arbabi, Y. Horie, A. J. Ball, M. Bagheri, and A. Faraon, “Subwavelength-thick lenses with high numerical apertures and large efficiency based on high-contrast transmitarrays,” Nat. Commun. 6, 7069 (2015).
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A. Arbabi, Y. Horie, A. J. Ball, M. Bagheri, and A. Faraon, “Subwavelength-thick lenses with high numerical apertures and large efficiency based on high-contrast transmitarrays,” Nat. Commun. 6, 7069 (2015).
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Bauer, T.

T. Bauer, P. Banzer, E. Karimi, S. Orlov, A. Rubano, L. Marrucci, E. Santamato, R. W. Boyd, and G. Leuchs, “Observation of optical polarization Möbius strips,” Science 347(6225), 964–966 (2015).
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L. Allen, M. W. Beijersbergen, R. J. C. Spreeuw, and J. P. Woerdman, “Orbital angular momentum of light and the transformation of Laguerre-Gaussian laser modes,” Phys. Rev. A 45(11), 8185–8189 (1992).
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M. V. Berry, “Optical vortices evolving from helicoidal integer and fractional phase steps,” J. Opt. A, Pure Appl. Opt. 6(2), 259–268 (2004).
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M. V. Berry, “Quantal phase factors accompanying adiabatic changes,” Proc. R. Soc. Lond. A Math. Phys. Sci. 392(1802), 45–57 (1984).
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J. F. Nye and M. V. Berry, “Dislocations in wave train,” Proc. R. Soc. Lond. A Math. Phys. Sci. 336(1605), 165–190 (1974).
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Biener, G.

Y. Gorodetski, G. Biener, A. Niv, V. Kleiner, and E. Hasman, “Optical properties of polarization-dependent geometric phase elements with partially polarized light,” Opt. Commun. 266(2), 365–375 (2006).
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A. Niv, G. Biener, V. Kleiner, and E. Hasman, “Spiral phase elements obtained by use of discrete space-variant subwavelength gratings,” Opt. Commun. 251(4-6), 306–314 (2005).
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G. Biener, A. Niv, V. Kleiner, and E. Hasman, “Formation of helical beams by use of Pancharatnam-Berry phase optical elements,” Opt. Lett. 27(21), 1875–1877 (2002).
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G. Machavariani, N. Davidson, E. Hasman, S. Blit, A. A. Ishaaya, and A. A. Friesem, “Efficient conversion of a Gaussian beam to a high purity helical beam,” Opt. Commun. 209(4-6), 265–271 (2002).
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A. Ambrosio, L. Marrucci, F. Borbone, A. Roviello, and P. Maddalena, “Light-induced spiral mass transport in azo-polymer films under vortex-beam illumination,” Nat. Commun. 3, 989 (2012).
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F. Bouchard, H. Mand, M. Mirhosseini, E. Karimi, and R. W. Boyd, “Achromatic orbital angular momentum generator,” New J. Phys. 16(12), 123006 (2014).
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F. Bouchard, I. De Leon, S. A. Schulz, J. Upham, E. Karimi, and R. W. Boyd, “Optical spin-to-orbital momentum conversion in ultra-thin metasurfaces with arbitrary topological charges,” Appl. Phys. Lett. 105(10), 101905 (2014).
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T. Bauer, P. Banzer, E. Karimi, S. Orlov, A. Rubano, L. Marrucci, E. Santamato, R. W. Boyd, and G. Leuchs, “Observation of optical polarization Möbius strips,” Science 347(6225), 964–966 (2015).
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L. Yan, P. Gregg, E. Karimi, A. Rubano, L. Marrucci, R. W. Boyd, and S. Ramachandran, “Q-plate enabled spectrally diverse orbital-angular-momentum conversion for stimulated emission depletion microscopy,” Optica 2(10), 900 (2015).
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F. Bouchard, H. Mand, M. Mirhosseini, E. Karimi, and R. W. Boyd, “Achromatic orbital angular momentum generator,” New J. Phys. 16(12), 123006 (2014).
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F. Bouchard, I. De Leon, S. A. Schulz, J. Upham, E. Karimi, and R. W. Boyd, “Optical spin-to-orbital momentum conversion in ultra-thin metasurfaces with arbitrary topological charges,” Appl. Phys. Lett. 105(10), 101905 (2014).
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D. Hakobyan, H. Magallanes, G. Seniutinas, S. Juodkazis, and E. Brasselet, “Tailoring orbital angular momentum of light in the visible domain with metallic metasurfaces,” Adv. Optical Mater. 4(2), 306 (2015).

Brongersma, M. L.

D. Lin, P. Fan, E. Hasman, and M. L. Brongersma, “Dielectric gradient metasurface optical elements,” Science 345(6194), 298–302 (2014).
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H. Huang, G. Milione, M. P. J. Lavery, G. Xie, Y. Ren, Y. Cao, N. Ahmed, T. An Nguyen, D. A. Nolan, M.-J. Li, M. Tur, R. R. Alfano, and A. E. Willner, “Mode division multiplexing using an orbital angular momentum mode sorter and MIMO-DSP over a graded-index few-mode optical fibre,” Sci. Rep. 5, 14931 (2015).
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R. C. Devlin, M. Khorasaninejad, W.-T. Chen, J. Oh, and F. Capasso, “Broadband high-efficiency dielectric metasurfaces for the visible spectrum,” Proc. Natl. Acad. Sci. U.S.A. 113(38), 10473–10478 (2016).
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M. Khorasaninejad, A. Ambrosio, P. Kanhaiya, and F. Capasso, “Dispersion-compensated meta-holograms based on detour phase,” Sci. Adv. 2, e1501258 (2016).
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N. Yu and F. Capasso, “Flat optics with designer metasurfaces,” Nat. Mater. 13(2), 139–150 (2014).
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J. Lin, P. Genevet, M. A. Kats, N. Antoniou, and F. Capasso, “Nanostructured holograms for broadband manipulation of vector beams,” Nano Lett. 13(9), 4269–4274 (2013).
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N. Yu, P. Genevet, M. A. Kats, F. Aieta, J.-P. Tetienne, F. Capasso, and Z. Gaburro, “Light propagation with phase discontinuities: generalized laws of reflection and refraction,” Science 334(6054), 333–337 (2011).
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R. C. Devlin, M. Khorasaninejad, W.-T. Chen, J. Oh, and F. Capasso, “Broadband high-efficiency dielectric metasurfaces for the visible spectrum,” Proc. Natl. Acad. Sci. U.S.A. 113(38), 10473–10478 (2016).
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G. Machavariani, N. Davidson, E. Hasman, S. Blit, A. A. Ishaaya, and A. A. Friesem, “Efficient conversion of a Gaussian beam to a high purity helical beam,” Opt. Commun. 209(4-6), 265–271 (2002).
[Crossref]

De Leon, I.

F. Bouchard, I. De Leon, S. A. Schulz, J. Upham, E. Karimi, and R. W. Boyd, “Optical spin-to-orbital momentum conversion in ultra-thin metasurfaces with arbitrary topological charges,” Appl. Phys. Lett. 105(10), 101905 (2014).
[Crossref]

E. Karimi, S. A. Schulz, I. De Leon, H. Qassim, J. Upham, and R. W. Boyd, “Generating optical orbital angular momentum at visible wavelengths using a plasmonic metasurface,” Light Sci. Appl. 3(5), e167 (2014).
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E. Nagali, L. Sansoni, F. Sciarrino, F. De Martini, L. Marrucci, B. Piccirillo, E. Karimi, and E. Santamato, “Optimal quantum cloning of orbital angular momentum photon qubits through Hong–Ou–Mandel coalescence,” Nat. Photonics 3(12), 720–723 (2009).
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R. C. Devlin, M. Khorasaninejad, W.-T. Chen, J. Oh, and F. Capasso, “Broadband high-efficiency dielectric metasurfaces for the visible spectrum,” Proc. Natl. Acad. Sci. U.S.A. 113(38), 10473–10478 (2016).
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Dholakia, K.

Du, T.

Eliel, E. R.

S. S. R. Oemrawsingh, X. Ma, D. Voigt, A. Aiello, E. R. Eliel, G. W. ’t Hooft, and J. P. Woerdman, “Experimental demonstration of fractional orbital angular momentum entanglement of two photons,” Phys. Rev. Lett. 95(24), 240501 (2005).
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S. S. R. Oemrawsingh, A. Aiello, E. R. Eliel, G. Nienhuis, and J. P. Woerdman, “How to observe high-dimensional two-photon entanglement with only two detectors,” Phys. Rev. Lett. 92(21), 217901 (2004).
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M. E. J. Friese, J. Enger, H. Rubinsztein-Dunlop, and N. R. Heckenberg, “Optical angular-momentum transfer to trapped absorbing particles,” Phys. Rev. A 54(2), 1593–1596 (1996).
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Fan, P.

D. Lin, P. Fan, E. Hasman, and M. L. Brongersma, “Dielectric gradient metasurface optical elements,” Science 345(6194), 298–302 (2014).
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Faraon, A.

A. Arbabi, Y. Horie, A. J. Ball, M. Bagheri, and A. Faraon, “Subwavelength-thick lenses with high numerical apertures and large efficiency based on high-contrast transmitarrays,” Nat. Commun. 6, 7069 (2015).
[Crossref] [PubMed]

A. Arbabi, Y. Horie, M. Bagheri, and A. Faraon, “Dielectric metasurfaces for complete control of phase and polarization with subwavelength spatial resolution and high transmission,” Nat. Nanotechnol. 10(11), 937–943 (2015).
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Franke-Arnold, S.

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M. E. J. Friese, J. Enger, H. Rubinsztein-Dunlop, and N. R. Heckenberg, “Optical angular-momentum transfer to trapped absorbing particles,” Phys. Rev. A 54(2), 1593–1596 (1996).
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G. Machavariani, N. Davidson, E. Hasman, S. Blit, A. A. Ishaaya, and A. A. Friesem, “Efficient conversion of a Gaussian beam to a high purity helical beam,” Opt. Commun. 209(4-6), 265–271 (2002).
[Crossref]

Gaburro, Z.

N. Yu, P. Genevet, M. A. Kats, F. Aieta, J.-P. Tetienne, F. Capasso, and Z. Gaburro, “Light propagation with phase discontinuities: generalized laws of reflection and refraction,” Science 334(6054), 333–337 (2011).
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Gao, P.

M. Pu, X. Li, X. Ma, Y. Wang, Z. Zhao, C. Wang, C. Hu, P. Gao, C. Huang, H. Ren, X. Li, F. Qin, J. Yang, M. Gu, M. Hong, and X. Luo, “Catenary optics for achromatic generation of perfect optical angular momentum,” Sci. Adv. 1(9), e1500396 (2015).
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Genevet, P.

J. Lin, P. Genevet, M. A. Kats, N. Antoniou, and F. Capasso, “Nanostructured holograms for broadband manipulation of vector beams,” Nano Lett. 13(9), 4269–4274 (2013).
[Crossref] [PubMed]

N. Yu, P. Genevet, M. A. Kats, F. Aieta, J.-P. Tetienne, F. Capasso, and Z. Gaburro, “Light propagation with phase discontinuities: generalized laws of reflection and refraction,” Science 334(6054), 333–337 (2011).
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D. Giovannini, E. Nagali, L. Marrucci, and F. Sciarrino, “Resilience of orbital-angular-momentum photonic qubits and effects on hybrid entanglement,” Phys. Rev. A 83(4), 042338 (2011).
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Y. Gorodetski, G. Biener, A. Niv, V. Kleiner, and E. Hasman, “Optical properties of polarization-dependent geometric phase elements with partially polarized light,” Opt. Commun. 266(2), 365–375 (2006).
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Gregg, P.

Gu, M.

M. Pu, X. Li, X. Ma, Y. Wang, Z. Zhao, C. Wang, C. Hu, P. Gao, C. Huang, H. Ren, X. Li, F. Qin, J. Yang, M. Gu, M. Hong, and X. Luo, “Catenary optics for achromatic generation of perfect optical angular momentum,” Sci. Adv. 1(9), e1500396 (2015).
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Hakobyan, D.

D. Hakobyan, H. Magallanes, G. Seniutinas, S. Juodkazis, and E. Brasselet, “Tailoring orbital angular momentum of light in the visible domain with metallic metasurfaces,” Adv. Optical Mater. 4(2), 306 (2015).

Hasman, E.

D. Lin, P. Fan, E. Hasman, and M. L. Brongersma, “Dielectric gradient metasurface optical elements,” Science 345(6194), 298–302 (2014).
[Crossref] [PubMed]

Y. Gorodetski, G. Biener, A. Niv, V. Kleiner, and E. Hasman, “Optical properties of polarization-dependent geometric phase elements with partially polarized light,” Opt. Commun. 266(2), 365–375 (2006).
[Crossref]

A. Niv, G. Biener, V. Kleiner, and E. Hasman, “Spiral phase elements obtained by use of discrete space-variant subwavelength gratings,” Opt. Commun. 251(4-6), 306–314 (2005).
[Crossref]

G. Machavariani, N. Davidson, E. Hasman, S. Blit, A. A. Ishaaya, and A. A. Friesem, “Efficient conversion of a Gaussian beam to a high purity helical beam,” Opt. Commun. 209(4-6), 265–271 (2002).
[Crossref]

G. Biener, A. Niv, V. Kleiner, and E. Hasman, “Formation of helical beams by use of Pancharatnam-Berry phase optical elements,” Opt. Lett. 27(21), 1875–1877 (2002).
[Crossref] [PubMed]

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M. E. J. Friese, J. Enger, H. Rubinsztein-Dunlop, and N. R. Heckenberg, “Optical angular-momentum transfer to trapped absorbing particles,” Phys. Rev. A 54(2), 1593–1596 (1996).
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M. Pu, X. Li, X. Ma, Y. Wang, Z. Zhao, C. Wang, C. Hu, P. Gao, C. Huang, H. Ren, X. Li, F. Qin, J. Yang, M. Gu, M. Hong, and X. Luo, “Catenary optics for achromatic generation of perfect optical angular momentum,” Sci. Adv. 1(9), e1500396 (2015).
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A. Arbabi, Y. Horie, M. Bagheri, and A. Faraon, “Dielectric metasurfaces for complete control of phase and polarization with subwavelength spatial resolution and high transmission,” Nat. Nanotechnol. 10(11), 937–943 (2015).
[Crossref] [PubMed]

A. Arbabi, Y. Horie, A. J. Ball, M. Bagheri, and A. Faraon, “Subwavelength-thick lenses with high numerical apertures and large efficiency based on high-contrast transmitarrays,” Nat. Commun. 6, 7069 (2015).
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M. Pu, X. Li, X. Ma, Y. Wang, Z. Zhao, C. Wang, C. Hu, P. Gao, C. Huang, H. Ren, X. Li, F. Qin, J. Yang, M. Gu, M. Hong, and X. Luo, “Catenary optics for achromatic generation of perfect optical angular momentum,” Sci. Adv. 1(9), e1500396 (2015).
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M. Pu, X. Li, X. Ma, Y. Wang, Z. Zhao, C. Wang, C. Hu, P. Gao, C. Huang, H. Ren, X. Li, F. Qin, J. Yang, M. Gu, M. Hong, and X. Luo, “Catenary optics for achromatic generation of perfect optical angular momentum,” Sci. Adv. 1(9), e1500396 (2015).
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Huang, H.

H. Huang, G. Milione, M. P. J. Lavery, G. Xie, Y. Ren, Y. Cao, N. Ahmed, T. An Nguyen, D. A. Nolan, M.-J. Li, M. Tur, R. R. Alfano, and A. E. Willner, “Mode division multiplexing using an orbital angular momentum mode sorter and MIMO-DSP over a graded-index few-mode optical fibre,” Sci. Rep. 5, 14931 (2015).
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G. Milione, M. P. J. Lavery, H. Huang, Y. Ren, G. Xie, T. A. Nguyen, E. Karimi, L. Marrucci, D. A. Nolan, R. R. Alfano, and A. E. Willner, “4 × 20 Gbit/s mode division multiplexing over free space using vector modes and a q-plate mode (de)multiplexer,” Opt. Lett. 40(9), 1980–1983 (2015).
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M. Pu, X. Li, X. Ma, Y. Wang, Z. Zhao, C. Wang, C. Hu, P. Gao, C. Huang, H. Ren, X. Li, F. Qin, J. Yang, M. Gu, M. Hong, and X. Luo, “Catenary optics for achromatic generation of perfect optical angular momentum,” Sci. Adv. 1(9), e1500396 (2015).
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Pun, E. Y.

G. Li, M. Kang, S. Chen, S. Zhang, E. Y. Pun, K. W. Cheah, and J. Li, “Spin-enabled plasmonic metasurfaces for manipulating orbital angular momentum of light,” Nano Lett. 13(9), 4148–4151 (2013).
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Qassim, H.

E. Karimi, S. A. Schulz, I. De Leon, H. Qassim, J. Upham, and R. W. Boyd, “Generating optical orbital angular momentum at visible wavelengths using a plasmonic metasurface,” Light Sci. Appl. 3(5), e167 (2014).
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Qin, F.

M. Pu, X. Li, X. Ma, Y. Wang, Z. Zhao, C. Wang, C. Hu, P. Gao, C. Huang, H. Ren, X. Li, F. Qin, J. Yang, M. Gu, M. Hong, and X. Luo, “Catenary optics for achromatic generation of perfect optical angular momentum,” Sci. Adv. 1(9), e1500396 (2015).
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Qiu, C.-W.

M. Q. Mehmood, S. Mei, S. Hussain, K. Huang, S. Y. Siew, L. Zhang, T. Zhang, X. Ling, H. Liu, J. Teng, A. Danner, S. Zhang, and C.-W. Qiu, “Visible-frequency metasurface for structuring and spatially multiplexing optical vortices,” Adv. Mater. 28(13), 2533–2539 (2016).
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Ramachandran, S.

Ren, H.

M. Pu, X. Li, X. Ma, Y. Wang, Z. Zhao, C. Wang, C. Hu, P. Gao, C. Huang, H. Ren, X. Li, F. Qin, J. Yang, M. Gu, M. Hong, and X. Luo, “Catenary optics for achromatic generation of perfect optical angular momentum,” Sci. Adv. 1(9), e1500396 (2015).
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Ren, Y.

H. Huang, G. Milione, M. P. J. Lavery, G. Xie, Y. Ren, Y. Cao, N. Ahmed, T. An Nguyen, D. A. Nolan, M.-J. Li, M. Tur, R. R. Alfano, and A. E. Willner, “Mode division multiplexing using an orbital angular momentum mode sorter and MIMO-DSP over a graded-index few-mode optical fibre,” Sci. Rep. 5, 14931 (2015).
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G. Milione, M. P. J. Lavery, H. Huang, Y. Ren, G. Xie, T. A. Nguyen, E. Karimi, L. Marrucci, D. A. Nolan, R. R. Alfano, and A. E. Willner, “4 × 20 Gbit/s mode division multiplexing over free space using vector modes and a q-plate mode (de)multiplexer,” Opt. Lett. 40(9), 1980–1983 (2015).
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Ristau, D.

M. Menro, J. Liu, W. Rudolph, D. Ristau, and K. Starke, “Scaling laws of femtosecond laser pulse induced breakdown in oxide films,” Phys. Rev. B 71(11), 115109 (2005).
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Roviello, A.

A. Ambrosio, L. Marrucci, F. Borbone, A. Roviello, and P. Maddalena, “Light-induced spiral mass transport in azo-polymer films under vortex-beam illumination,” Nat. Commun. 3, 989 (2012).
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Rubano, A.

L. Yan, P. Gregg, E. Karimi, A. Rubano, L. Marrucci, R. W. Boyd, and S. Ramachandran, “Q-plate enabled spectrally diverse orbital-angular-momentum conversion for stimulated emission depletion microscopy,” Optica 2(10), 900 (2015).
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T. Bauer, P. Banzer, E. Karimi, S. Orlov, A. Rubano, L. Marrucci, E. Santamato, R. W. Boyd, and G. Leuchs, “Observation of optical polarization Möbius strips,” Science 347(6225), 964–966 (2015).
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M. E. J. Friese, J. Enger, H. Rubinsztein-Dunlop, and N. R. Heckenberg, “Optical angular-momentum transfer to trapped absorbing particles,” Phys. Rev. A 54(2), 1593–1596 (1996).
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M. Menro, J. Liu, W. Rudolph, D. Ristau, and K. Starke, “Scaling laws of femtosecond laser pulse induced breakdown in oxide films,” Phys. Rev. B 71(11), 115109 (2005).
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Sansoni, L.

E. Nagali, L. Sansoni, F. Sciarrino, F. De Martini, L. Marrucci, B. Piccirillo, E. Karimi, and E. Santamato, “Optimal quantum cloning of orbital angular momentum photon qubits through Hong–Ou–Mandel coalescence,” Nat. Photonics 3(12), 720–723 (2009).
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Santamato, E.

T. Bauer, P. Banzer, E. Karimi, S. Orlov, A. Rubano, L. Marrucci, E. Santamato, R. W. Boyd, and G. Leuchs, “Observation of optical polarization Möbius strips,” Science 347(6225), 964–966 (2015).
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S. Slussarenko, A. Murauski, T. Du, V. Chigrinov, L. Marrucci, and E. Santamato, “Tunable liquid crystal q-plates with arbitrary topological charge,” Opt. Express 19(5), 4085–4090 (2011).
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E. Nagali, L. Sansoni, F. Sciarrino, F. De Martini, L. Marrucci, B. Piccirillo, E. Karimi, and E. Santamato, “Optimal quantum cloning of orbital angular momentum photon qubits through Hong–Ou–Mandel coalescence,” Nat. Photonics 3(12), 720–723 (2009).
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A. Ambrosio, B. Piccirillo, A. Sasso, and E. Santamato, “Experimental and theoretical study of the transient rotation of isotropic transparent microparticles in astigmatic optical tweezers,” Opt. Commun. 230(4-6), 337–345 (2004).
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A. Ambrosio, B. Piccirillo, A. Sasso, and E. Santamato, “Experimental and theoretical study of the transient rotation of isotropic transparent microparticles in astigmatic optical tweezers,” Opt. Commun. 230(4-6), 337–345 (2004).
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Schulz, S. A.

E. Karimi, S. A. Schulz, I. De Leon, H. Qassim, J. Upham, and R. W. Boyd, “Generating optical orbital angular momentum at visible wavelengths using a plasmonic metasurface,” Light Sci. Appl. 3(5), e167 (2014).
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F. Bouchard, I. De Leon, S. A. Schulz, J. Upham, E. Karimi, and R. W. Boyd, “Optical spin-to-orbital momentum conversion in ultra-thin metasurfaces with arbitrary topological charges,” Appl. Phys. Lett. 105(10), 101905 (2014).
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Sciarrino, F.

V. D’Ambrosio, N. Spagnolo, L. Del Re, S. Slussarenko, Y. Li, L. C. Kwek, L. Marrucci, S. P. Walborn, L. Aolita, and F. Sciarrino, “Photonic polarization gears for ultra-sensitive angular measurements,” Nat. Commun. 4, 2432 (2013).
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D. Giovannini, E. Nagali, L. Marrucci, and F. Sciarrino, “Resilience of orbital-angular-momentum photonic qubits and effects on hybrid entanglement,” Phys. Rev. A 83(4), 042338 (2011).
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E. Nagali, L. Sansoni, F. Sciarrino, F. De Martini, L. Marrucci, B. Piccirillo, E. Karimi, and E. Santamato, “Optimal quantum cloning of orbital angular momentum photon qubits through Hong–Ou–Mandel coalescence,” Nat. Photonics 3(12), 720–723 (2009).
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Seniutinas, G.

D. Hakobyan, H. Magallanes, G. Seniutinas, S. Juodkazis, and E. Brasselet, “Tailoring orbital angular momentum of light in the visible domain with metallic metasurfaces,” Adv. Optical Mater. 4(2), 306 (2015).

Shalaev, M. I.

M. I. Shalaev, J. Sun, A. Tsukernik, A. Pandey, K. Nikolskiy, and N. M. Litchinitser, “High-Efficiency all-dielectric metasurfaces for ultracompact beam manipulation in transmission mode,” Nano Lett. 15(9), 6261–6266 (2015).
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Siew, S. Y.

M. Q. Mehmood, S. Mei, S. Hussain, K. Huang, S. Y. Siew, L. Zhang, T. Zhang, X. Ling, H. Liu, J. Teng, A. Danner, S. Zhang, and C.-W. Qiu, “Visible-frequency metasurface for structuring and spatially multiplexing optical vortices,” Adv. Mater. 28(13), 2533–2539 (2016).
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Simpson, N. B.

Slussarenko, S.

V. D’Ambrosio, N. Spagnolo, L. Del Re, S. Slussarenko, Y. Li, L. C. Kwek, L. Marrucci, S. P. Walborn, L. Aolita, and F. Sciarrino, “Photonic polarization gears for ultra-sensitive angular measurements,” Nat. Commun. 4, 2432 (2013).
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S. Slussarenko, A. Murauski, T. Du, V. Chigrinov, L. Marrucci, and E. Santamato, “Tunable liquid crystal q-plates with arbitrary topological charge,” Opt. Express 19(5), 4085–4090 (2011).
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Spagnolo, N.

V. D’Ambrosio, N. Spagnolo, L. Del Re, S. Slussarenko, Y. Li, L. C. Kwek, L. Marrucci, S. P. Walborn, L. Aolita, and F. Sciarrino, “Photonic polarization gears for ultra-sensitive angular measurements,” Nat. Commun. 4, 2432 (2013).
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L. Allen, M. W. Beijersbergen, R. J. C. Spreeuw, and J. P. Woerdman, “Orbital angular momentum of light and the transformation of Laguerre-Gaussian laser modes,” Phys. Rev. A 45(11), 8185–8189 (1992).
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Starke, K.

M. Menro, J. Liu, W. Rudolph, D. Ristau, and K. Starke, “Scaling laws of femtosecond laser pulse induced breakdown in oxide films,” Phys. Rev. B 71(11), 115109 (2005).
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Sun, J.

M. I. Shalaev, J. Sun, A. Tsukernik, A. Pandey, K. Nikolskiy, and N. M. Litchinitser, “High-Efficiency all-dielectric metasurfaces for ultracompact beam manipulation in transmission mode,” Nano Lett. 15(9), 6261–6266 (2015).
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G. Milione, H. I. Sztul, D. A. Nolan, and R. R. Alfano, “Higher-order Poincaré sphere, stokes parameters, and the angular momentum of light,” Phys. Rev. Lett. 107(5), 053601 (2011).
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M. Q. Mehmood, S. Mei, S. Hussain, K. Huang, S. Y. Siew, L. Zhang, T. Zhang, X. Ling, H. Liu, J. Teng, A. Danner, S. Zhang, and C.-W. Qiu, “Visible-frequency metasurface for structuring and spatially multiplexing optical vortices,” Adv. Mater. 28(13), 2533–2539 (2016).
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Tetienne, J.-P.

N. Yu, P. Genevet, M. A. Kats, F. Aieta, J.-P. Tetienne, F. Capasso, and Z. Gaburro, “Light propagation with phase discontinuities: generalized laws of reflection and refraction,” Science 334(6054), 333–337 (2011).
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Tsukernik, A.

M. I. Shalaev, J. Sun, A. Tsukernik, A. Pandey, K. Nikolskiy, and N. M. Litchinitser, “High-Efficiency all-dielectric metasurfaces for ultracompact beam manipulation in transmission mode,” Nano Lett. 15(9), 6261–6266 (2015).
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H. Huang, G. Milione, M. P. J. Lavery, G. Xie, Y. Ren, Y. Cao, N. Ahmed, T. An Nguyen, D. A. Nolan, M.-J. Li, M. Tur, R. R. Alfano, and A. E. Willner, “Mode division multiplexing using an orbital angular momentum mode sorter and MIMO-DSP over a graded-index few-mode optical fibre,” Sci. Rep. 5, 14931 (2015).
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Upham, J.

F. Bouchard, I. De Leon, S. A. Schulz, J. Upham, E. Karimi, and R. W. Boyd, “Optical spin-to-orbital momentum conversion in ultra-thin metasurfaces with arbitrary topological charges,” Appl. Phys. Lett. 105(10), 101905 (2014).
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E. Karimi, S. A. Schulz, I. De Leon, H. Qassim, J. Upham, and R. W. Boyd, “Generating optical orbital angular momentum at visible wavelengths using a plasmonic metasurface,” Light Sci. Appl. 3(5), e167 (2014).
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A. Mair, A. Vaziri, G. Weihs, and A. Zeilinger, “Entanglement of the orbital angular momentum states of photons,” Nature 412(6844), 313–316 (2001).
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S. S. R. Oemrawsingh, X. Ma, D. Voigt, A. Aiello, E. R. Eliel, G. W. ’t Hooft, and J. P. Woerdman, “Experimental demonstration of fractional orbital angular momentum entanglement of two photons,” Phys. Rev. Lett. 95(24), 240501 (2005).
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Walborn, S. P.

V. D’Ambrosio, N. Spagnolo, L. Del Re, S. Slussarenko, Y. Li, L. C. Kwek, L. Marrucci, S. P. Walborn, L. Aolita, and F. Sciarrino, “Photonic polarization gears for ultra-sensitive angular measurements,” Nat. Commun. 4, 2432 (2013).
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Wang, C.

M. Pu, X. Li, X. Ma, Y. Wang, Z. Zhao, C. Wang, C. Hu, P. Gao, C. Huang, H. Ren, X. Li, F. Qin, J. Yang, M. Gu, M. Hong, and X. Luo, “Catenary optics for achromatic generation of perfect optical angular momentum,” Sci. Adv. 1(9), e1500396 (2015).
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M. Pu, X. Li, X. Ma, Y. Wang, Z. Zhao, C. Wang, C. Hu, P. Gao, C. Huang, H. Ren, X. Li, F. Qin, J. Yang, M. Gu, M. Hong, and X. Luo, “Catenary optics for achromatic generation of perfect optical angular momentum,” Sci. Adv. 1(9), e1500396 (2015).
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A. Mair, A. Vaziri, G. Weihs, and A. Zeilinger, “Entanglement of the orbital angular momentum states of photons,” Nature 412(6844), 313–316 (2001).
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Willner, A. E.

H. Huang, G. Milione, M. P. J. Lavery, G. Xie, Y. Ren, Y. Cao, N. Ahmed, T. An Nguyen, D. A. Nolan, M.-J. Li, M. Tur, R. R. Alfano, and A. E. Willner, “Mode division multiplexing using an orbital angular momentum mode sorter and MIMO-DSP over a graded-index few-mode optical fibre,” Sci. Rep. 5, 14931 (2015).
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G. Milione, M. P. J. Lavery, H. Huang, Y. Ren, G. Xie, T. A. Nguyen, E. Karimi, L. Marrucci, D. A. Nolan, R. R. Alfano, and A. E. Willner, “4 × 20 Gbit/s mode division multiplexing over free space using vector modes and a q-plate mode (de)multiplexer,” Opt. Lett. 40(9), 1980–1983 (2015).
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S. S. R. Oemrawsingh, X. Ma, D. Voigt, A. Aiello, E. R. Eliel, G. W. ’t Hooft, and J. P. Woerdman, “Experimental demonstration of fractional orbital angular momentum entanglement of two photons,” Phys. Rev. Lett. 95(24), 240501 (2005).
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S. S. R. Oemrawsingh, A. Aiello, E. R. Eliel, G. Nienhuis, and J. P. Woerdman, “How to observe high-dimensional two-photon entanglement with only two detectors,” Phys. Rev. Lett. 92(21), 217901 (2004).
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L. Allen, M. W. Beijersbergen, R. J. C. Spreeuw, and J. P. Woerdman, “Orbital angular momentum of light and the transformation of Laguerre-Gaussian laser modes,” Phys. Rev. A 45(11), 8185–8189 (1992).
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Xie, G.

H. Huang, G. Milione, M. P. J. Lavery, G. Xie, Y. Ren, Y. Cao, N. Ahmed, T. An Nguyen, D. A. Nolan, M.-J. Li, M. Tur, R. R. Alfano, and A. E. Willner, “Mode division multiplexing using an orbital angular momentum mode sorter and MIMO-DSP over a graded-index few-mode optical fibre,” Sci. Rep. 5, 14931 (2015).
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G. Milione, M. P. J. Lavery, H. Huang, Y. Ren, G. Xie, T. A. Nguyen, E. Karimi, L. Marrucci, D. A. Nolan, R. R. Alfano, and A. E. Willner, “4 × 20 Gbit/s mode division multiplexing over free space using vector modes and a q-plate mode (de)multiplexer,” Opt. Lett. 40(9), 1980–1983 (2015).
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Yan, L.

Yang, J.

M. Pu, X. Li, X. Ma, Y. Wang, Z. Zhao, C. Wang, C. Hu, P. Gao, C. Huang, H. Ren, X. Li, F. Qin, J. Yang, M. Gu, M. Hong, and X. Luo, “Catenary optics for achromatic generation of perfect optical angular momentum,” Sci. Adv. 1(9), e1500396 (2015).
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Yao, E.

J. Leach, E. Yao, and M. J. Padgett, “Observation of the vortex structure of a non-integer vortex beam,” New J. Phys. 6, 71 (2004).
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Yu, N.

N. Yu and F. Capasso, “Flat optics with designer metasurfaces,” Nat. Mater. 13(2), 139–150 (2014).
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N. Yu, P. Genevet, M. A. Kats, F. Aieta, J.-P. Tetienne, F. Capasso, and Z. Gaburro, “Light propagation with phase discontinuities: generalized laws of reflection and refraction,” Science 334(6054), 333–337 (2011).
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Zambrini, R.

J. B. Götte, S. Franke-Arnold, R. Zambrini, and S. M. Barnett, “Quantum formulation of fractional orbital angular momentum,” J. Mod. Opt. 54(12), 1723–1738 (2007).
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Zeilinger, A.

A. Mair, A. Vaziri, G. Weihs, and A. Zeilinger, “Entanglement of the orbital angular momentum states of photons,” Nature 412(6844), 313–316 (2001).
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Zhang, L.

M. Q. Mehmood, S. Mei, S. Hussain, K. Huang, S. Y. Siew, L. Zhang, T. Zhang, X. Ling, H. Liu, J. Teng, A. Danner, S. Zhang, and C.-W. Qiu, “Visible-frequency metasurface for structuring and spatially multiplexing optical vortices,” Adv. Mater. 28(13), 2533–2539 (2016).
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M. Q. Mehmood, S. Mei, S. Hussain, K. Huang, S. Y. Siew, L. Zhang, T. Zhang, X. Ling, H. Liu, J. Teng, A. Danner, S. Zhang, and C.-W. Qiu, “Visible-frequency metasurface for structuring and spatially multiplexing optical vortices,” Adv. Mater. 28(13), 2533–2539 (2016).
[Crossref] [PubMed]

G. Li, M. Kang, S. Chen, S. Zhang, E. Y. Pun, K. W. Cheah, and J. Li, “Spin-enabled plasmonic metasurfaces for manipulating orbital angular momentum of light,” Nano Lett. 13(9), 4148–4151 (2013).
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Zhang, T.

M. Q. Mehmood, S. Mei, S. Hussain, K. Huang, S. Y. Siew, L. Zhang, T. Zhang, X. Ling, H. Liu, J. Teng, A. Danner, S. Zhang, and C.-W. Qiu, “Visible-frequency metasurface for structuring and spatially multiplexing optical vortices,” Adv. Mater. 28(13), 2533–2539 (2016).
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M. Pu, X. Li, X. Ma, Y. Wang, Z. Zhao, C. Wang, C. Hu, P. Gao, C. Huang, H. Ren, X. Li, F. Qin, J. Yang, M. Gu, M. Hong, and X. Luo, “Catenary optics for achromatic generation of perfect optical angular momentum,” Sci. Adv. 1(9), e1500396 (2015).
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Adv. Mater. (1)

M. Q. Mehmood, S. Mei, S. Hussain, K. Huang, S. Y. Siew, L. Zhang, T. Zhang, X. Ling, H. Liu, J. Teng, A. Danner, S. Zhang, and C.-W. Qiu, “Visible-frequency metasurface for structuring and spatially multiplexing optical vortices,” Adv. Mater. 28(13), 2533–2539 (2016).
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Adv. Optical Mater. (1)

D. Hakobyan, H. Magallanes, G. Seniutinas, S. Juodkazis, and E. Brasselet, “Tailoring orbital angular momentum of light in the visible domain with metallic metasurfaces,” Adv. Optical Mater. 4(2), 306 (2015).

Appl. Phys. Lett. (2)

F. Bouchard, I. De Leon, S. A. Schulz, J. Upham, E. Karimi, and R. W. Boyd, “Optical spin-to-orbital momentum conversion in ultra-thin metasurfaces with arbitrary topological charges,” Appl. Phys. Lett. 105(10), 101905 (2014).
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L. Marrucci, C. Manzo, and D. Paparo, “Pancharatnam-Berry phase optical elements for wave front shaping,” Appl. Phys. Lett. 88(22), 221102 (2006).
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J. Mod. Opt. (1)

J. B. Götte, S. Franke-Arnold, R. Zambrini, and S. M. Barnett, “Quantum formulation of fractional orbital angular momentum,” J. Mod. Opt. 54(12), 1723–1738 (2007).
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E. Karimi, S. A. Schulz, I. De Leon, H. Qassim, J. Upham, and R. W. Boyd, “Generating optical orbital angular momentum at visible wavelengths using a plasmonic metasurface,” Light Sci. Appl. 3(5), e167 (2014).
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Nano Lett. (3)

M. I. Shalaev, J. Sun, A. Tsukernik, A. Pandey, K. Nikolskiy, and N. M. Litchinitser, “High-Efficiency all-dielectric metasurfaces for ultracompact beam manipulation in transmission mode,” Nano Lett. 15(9), 6261–6266 (2015).
[Crossref] [PubMed]

G. Li, M. Kang, S. Chen, S. Zhang, E. Y. Pun, K. W. Cheah, and J. Li, “Spin-enabled plasmonic metasurfaces for manipulating orbital angular momentum of light,” Nano Lett. 13(9), 4148–4151 (2013).
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J. Lin, P. Genevet, M. A. Kats, N. Antoniou, and F. Capasso, “Nanostructured holograms for broadband manipulation of vector beams,” Nano Lett. 13(9), 4269–4274 (2013).
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Nat. Commun. (4)

A. Ambrosio, L. Marrucci, F. Borbone, A. Roviello, and P. Maddalena, “Light-induced spiral mass transport in azo-polymer films under vortex-beam illumination,” Nat. Commun. 3, 989 (2012).
[Crossref] [PubMed]

V. D’Ambrosio, N. Spagnolo, L. Del Re, S. Slussarenko, Y. Li, L. C. Kwek, L. Marrucci, S. P. Walborn, L. Aolita, and F. Sciarrino, “Photonic polarization gears for ultra-sensitive angular measurements,” Nat. Commun. 4, 2432 (2013).
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M. Khorasaninejad and K. B. Crozier, “Silicon nanofin grating as a miniature chirality-distinguishing beam-splitter,” Nat. Commun. 5, 5386 (2014).
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A. Arbabi, Y. Horie, A. J. Ball, M. Bagheri, and A. Faraon, “Subwavelength-thick lenses with high numerical apertures and large efficiency based on high-contrast transmitarrays,” Nat. Commun. 6, 7069 (2015).
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Nat. Mater. (1)

N. Yu and F. Capasso, “Flat optics with designer metasurfaces,” Nat. Mater. 13(2), 139–150 (2014).
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Nat. Nanotechnol. (1)

A. Arbabi, Y. Horie, M. Bagheri, and A. Faraon, “Dielectric metasurfaces for complete control of phase and polarization with subwavelength spatial resolution and high transmission,” Nat. Nanotechnol. 10(11), 937–943 (2015).
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Nat. Photonics (2)

E. Nagali, L. Sansoni, F. Sciarrino, F. De Martini, L. Marrucci, B. Piccirillo, E. Karimi, and E. Santamato, “Optimal quantum cloning of orbital angular momentum photon qubits through Hong–Ou–Mandel coalescence,” Nat. Photonics 3(12), 720–723 (2009).
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M. J. Padgett and R. Bowman, “Tweezers with a twist,” Nat. Photonics 5(6), 343–348 (2011).
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Nature (1)

A. Mair, A. Vaziri, G. Weihs, and A. Zeilinger, “Entanglement of the orbital angular momentum states of photons,” Nature 412(6844), 313–316 (2001).
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New J. Phys. (2)

F. Bouchard, H. Mand, M. Mirhosseini, E. Karimi, and R. W. Boyd, “Achromatic orbital angular momentum generator,” New J. Phys. 16(12), 123006 (2014).
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J. Leach, E. Yao, and M. J. Padgett, “Observation of the vortex structure of a non-integer vortex beam,” New J. Phys. 6, 71 (2004).
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Opt. Commun. (4)

G. Machavariani, N. Davidson, E. Hasman, S. Blit, A. A. Ishaaya, and A. A. Friesem, “Efficient conversion of a Gaussian beam to a high purity helical beam,” Opt. Commun. 209(4-6), 265–271 (2002).
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Figures (12)

Fig. 1
Fig. 1 (a) Schematic of the working principle of a spin-orbital angular momentum converter. A left circularly polarized beam with plane wavefront is turned into a right circularly polarized helical mode. In this representation the helical mode has a topological charge equal to 2, as the wavefront is composed of two intertwined helices. (b) Angled-view SEM image of one of our devices ( q=1 ) showing the orientation of the TiO2 nanofins on the glass substrate, φ is the azimuthal angle and |r| is the distance from the center.
Fig. 2
Fig. 2 (a) and (b), Scanning electron microscope image of TiO2-based spin-orbital angular momentum converters with q=0.5 and q=1 respectively (scale bar = 650 nm). The insets show the devices observed in cross-polarization at the design wavelength of 532nm. (c), Sketch (top view) of the interferometric setup used to characterize the devices. The interference of the helical mode and the reference beam was monitored at port 1 by means of a CCD. The polarization state of the beam after each optical element is sketched. The laser polarization is linear and perpendicular to the optical table. Light becomes circularly polarized after the first quarter waveplate (QWP1). The helical mode generated by the device is circularly polarized with opposite handedness. The helical mode after the polarization filter (QWP2 followed by LP2) is linearly polarized parallel to the optical table. The reference beam in the lower arm of the interferometer becomes also linearly polarized parallel to the optical table after passing through a half waveplate (HWP) that rotates the polarization direction by 90°. (d), Transverse intensity distribution of the vortex beam generated by the device of Fig. 2 (a). This beam has a topological charge equal to 1. (e), Interference patterns obtained with tilted reference beam (pitchforks) or collinear reference beam (spirals) in the setup of Fig. 2(c). The flipped features result from opposite handedness of the beam that illuminates the device. (f), (g), Same as (d) and (e) for the device in Fig. 2(b).
Fig. 3
Fig. 3 Transverse intensity profile of a beam with topological charge 5 generated by means of our q=2.5 spin-orbital angular momentum converter. (b), The q=2.5 device imaged in cross-polarization. (c), (d), Images of the interference patterns obtained with a collinear reference beam (Fig. 2(c)) for incident left or right circular polarized light. (e), (f), (g), (h), Same as for (a), (b), (c), (d) for the topological charge 10 beam and the q=5 device. Scale for (e) is same as shown in (a).
Fig. 4
Fig. 4 (a), Transverse intensity distribution of a beam with topological charge 6.5 at 55μm from the device exit plane. (b), Interference pattern arising from the interference with a reference beam at oblique incidence. The resulting pitchfork pattern shows the singularity line surrounded by alternating single charge vortices, a characteristic feature of fractional helical modes. The direction of the singularity line in (a) and (b) is the same although in these figures they are on opposite directions due to the camera orientation during the experiment.
Fig. 5
Fig. 5 (a) Schematic of the nanofins azimuthal distribution in the inner part of metasurface device with interleaved patterns that generate collinear beams having topological charges | |=5 and | |=10 . The device has a 500 μm diameter and contains more than 700 interleaved radial rows of nanofins. (b), (c), Transverse intensity distributions of the light emerging from the metasurface for opposite handedness of the incident light. (d), (e), Simulated intensity patterns for collinear 5 and 10 topological charge beams. (f), Sketch of the setup that allows illumination of the transparent devices from the glass and air side simultaneously with circularly polarized beams of opposite handedness. In this case, there are two light beams, whose power can be made equal by suitably balancing the two arms, circularly polarized with opposite handedness that simultaneously illuminate the device from opposite sides at normal incidence. In this configuration, the helical modes propagating towards optical port 2 and 3 have also opposite wave-front handedness. This setup was also used to obtain the intensity distributions of Figs. 5(b) and 5(c).
Fig. 6
Fig. 6 (a) Perspective view of a single nanofin that makes up our devices. The fabrication process produces fins with a given height, h, which is 600 nm for all devices. (b), Top view of the TiO2 nanofin. The fins are designed with width, W, length, L and rotation angle with respect to the x-axis, α. The length and width of the nanofin sets the relative phase delay between orthogonal components of an incident electric field and the rotation provides the geometric phase. (c), Cross section through the width of a single nanofin, showing the simulated electric field components. The real part of the x-component (left) and y-component (right) of the electric field. At the design parameters of W = 90 nm, L = 250 nm, h = 600 nm, there is a π phase delay between the x- and y-components.
Fig. 7
Fig. 7 (a) The devices are produced on a circular 1-inch diameter fused silica wafer, which is then integrated into a commercial opto-mechanic component. (b), Magnified view of the 1-inch wafer in (a) showing six devices on the same substrate. The devices are placed in a rectangular array across the wafer, which allows easy selection of a device by moving it into the illuminating beam path.
Fig. 8
Fig. 8 Image of the singularity region of a q=0.5 device.
Fig. 9
Fig. 9 Images of the donut beams at three different wavelengths from a supercontinuum laser: 480 nm ((a) and (d)), 550 nm ((b) and (e)) and 633 nm ((c) and (f)). The images in the upper row are taken with the setup of Fig. 2 (c) while the images in the lower row are taken by removing the polarization filter. The scale bar of 0.4mm in Fig. 9 applies to all the panels.
Fig. 10
Fig. 10 Nanofin dephasing and conversion efficiency as a function of wavelength. Simulated dephasing between the x- and y- components of the electric field after passing through the nanofins (red line) and the resulting ideal conversion efficiency (blue line).
Fig. 11
Fig. 11 Far-field image of the 6.5 topological charge vortex beam.
Fig. 12
Fig. 12 (a), Scanning Electron Microscopy micrograph of an interlaced q=±2.5 device. (b), light distribution at 45 cm from the device exit plane. (c), simulated interference pattern of two collinear beams with topological charges + 5 and −5.

Equations (1)

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E out = 1 2 ( 1+ e iΓ )σ+ 1 2 ( 1 e iΓ ) e i2α σ

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