Abstract

Optical elements coupling the spin and orbital angular momentum (SAM/OAM) of light have found a range of applications in classical and quantum optics. The J-plate, with J referring to the photon’s total angular momentum (TAM), is a metasurface device that imparts two arbitrary OAM states on an arbitrary orthogonal basis of spin states. We demonstrate that when these J-plates are cascaded in series, they can generate several single quantum number beams and versatile superpositions thereof. Moreover, in contrast to previous spin-orbit-converters, the output polarization states of cascaded J-plates are not constrained to be the conjugate of the input states. Cascaded J-plates are also demonstrated to produce vector vortex beams and complex structured light, providing new ways to control TAM states of light.

© 2019 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

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    [Crossref] [PubMed]
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    [Crossref] [PubMed]
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    [Crossref]
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    [Crossref] [PubMed]
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    [Crossref] [PubMed]
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    [Crossref]
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    [Crossref]
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    [Crossref]

2018 (2)

K. Huang, H. Liu, S. Restuccia, M. Q. Mehmood, S.-T. Mei, D. Giovannini, A. Danner, M. J. Padgett, J.-H. Teng, and C.-W. Qiu, “Spiniform phase-encoded metagratings entangling arbitrary rational-order orbital angular momentum,” Light. Sci. & Appl. 7, 17156 (2018).
[Crossref]

Z. J. Shi, M. Khorasaninejad, Y. W. Huang, C. Roques-Carmes, A. Y. Zhu, W. T. Chen, V. Sanjeev, Z. W. Ding, M. Tamagnone, K. Chaudhary, R. C. Devlin, C. W. Qiu, and F. Capasso, “Single-layer metasurface with controllable multiwavelength functions,” Nano Lett. 18, 2420–2427 (2018).
[Crossref] [PubMed]

2017 (6)

M. Khorasaninejad and F. Capasso, “Metalenses: Versatile multifunctional photonic components,” Science. 358, eaam8100 (2017).
[Crossref] [PubMed]

R. C. Devlin, A. Ambrosio, D. Wintz, S. L. Oscurato, A. Y. Zhu, M. Khorasaninejad, J. Oh, P. Maddalena, and F. Capasso, “Spin-to-orbital angular momentum conversion in dielectric metasurfaces,” Opt. Express 25, 377–393 (2017).
[Crossref] [PubMed]

J. P. B. Mueller, N. A. Rubin, R. C. Devlin, B. Groever, and F. Capasso, “Metasurface polarization optics: Independent phase control of arbitrary orthogonal states of polarization,” Phys. Rev. Lett. 118, 113901 (2017).
[Crossref]

R. C. Devlin, A. Ambrosio, N. A. Rubin, J. P. B. Mueller, and F. Capasso, “Arbitrary spin-to-orbital angular momentum conversion of light,” Science. 358, 896–900 (2017).
[Crossref] [PubMed]

Y. Li, X. Li, L. Chen, M. Pu, J. Jin, M. Hong, and X. Luo, “Orbital angular momentum multiplexing and demultiplexing by a single metasurface,” Adv. Opt. Mater. 5, 1600502 (2017).
[Crossref]

G. Spektor, D. Kilbane, A. Mahro, B. Frank, S. Ristok, L. Gal, P. Kahl, D. Podbiel, S. Mathias, H. Giessen, F.-J. Meyer zu Heringdorf, M. Orenstein, and M. Aeschlimann, “Revealing the subfemtosecond dynamics of orbital angular momentum in nanoplasmonic vortices,” Science. 355, 1187–1191 (2017).
[Crossref] [PubMed]

2016 (4)

H. Ren, X. Li, Q. Zhang, and M. Gu, “On-chip noninterference angular momentum multiplexing of broadband light,” Science 352, 805–809 (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. United States Am. 113, 10473–10478 (2016).
[Crossref]

D. Naidoo, F. S. Roux, A. Dudley, I. Litvin, B. Piccirillo, L. Marrucci, and A. Forbes, “Controlled generation of higher-order poincaré sphere beams from a laser,” Nat. Photonics 10, 327–332 (2016).
[Crossref]

P. Miao, Z. Zhang, J. Sun, W. Walasik, S. Longhi, N. M. Litchinitser, and L. Feng, “Orbital angular momentum microlaser,” Science 353, 464–467 (2016).
[Crossref] [PubMed]

2015 (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, 937 (2015).
[Crossref] [PubMed]

2014 (2)

A. Nicolas, L. Veissier, L. Giner, E. Giacobino, D. Maxein, and J. Laurat, “A quantum memory for orbital angular momentum photonic qubits,” Nat. Photonics 8, 234 (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, e167 (2014).
[Crossref]

2012 (3)

J. Wang, J.-Y. Yang, I. M. Fazal, N. Ahmed, Y. Yan, H. Huang, Y. Ren, Y. Yue, S. Dolinar, M. Tur, S. Dolinar, M. Tur, and A. E. Willner, “Terabit free-space data transmission employing orbital angular momentum multiplexing,” Nat. Photonics 6, 488 (2012).
[Crossref]

R. Fickler, R. Lapkiewicz, W. N. Plick, M. Krenn, C. Schaeff, S. Ramelow, and A. Zeilinger, “Quantum entanglement of high angular momenta,” Science. 338, 640–643 (2012).
[Crossref] [PubMed]

E. J. Galvez, S. Khadka, W. H. Schubert, and S. Nomoto, “Poincare-beam patterns produced by nonseparable superpositions of laguerre-gauss and polarization modes of light,” Appl. Opt. 51, 2925–2934 (2012).
[Crossref] [PubMed]

2011 (4)

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

N. Shitrit, I. Bretner, Y. Gorodetski, V. Kleiner, and E. Hasman, “Optical spin hall effects in plasmonic chains,” Nano Lett. 11, 2038–2042 (2011).
[Crossref] [PubMed]

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

A. Kumar, P. Vaity, and R. P. Singh, “Crafting the core asymmetry to lift the degeneracy of optical vortices,” Opt. Express 19, 6182–6190 (2011).
[Crossref] [PubMed]

2009 (1)

E. Nagali, F. Sciarrino, F. De Martini, L. Marrucci, B. Piccirillo, E. Karimi, and E. Santamato, “Quantum information transfer from spin to orbital angular momentum of photons,” Phys. Rev. Lett. 103, 013601 (2009).
[Crossref] [PubMed]

2006 (1)

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

2004 (1)

2002 (2)

M. Babiker, C. Bennett, D. Andrews, and L. D. Romero, “Orbital angular momentum exchange in the interaction of twisted light with molecules,” Phys. Rev. Lett. 89, 143601 (2002).
[Crossref] [PubMed]

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

1994 (3)

S. W. Hell and J. Wichmann, “Breaking the diffraction resolution limit by stimulated emission: stimulated-emission-depletion fluorescence microscopy,” Opt. Lett. 19, 780–782 (1994).
[Crossref] [PubMed]

S. Van Enk and G. Nienhuis, “Commutation rules and eigenvalues of spin and orbital angular momentum of radiation fields,” J. Mod. Opt. 41, 963–977 (1994).
[Crossref]

M. Beijersbergen, R. Coerwinkel, M. Kristensen, and J. Woerdman, “Helical-wavefront laser beams produced with a spiral phaseplate,” Opt. Commun. 112, 321–327 (1994).
[Crossref]

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, 8185–8189 (1992).
[Crossref] [PubMed]

1989 (1)

P. Coullet, L. Gil, and F. Rocca, “Optical vortices,” Opt. Commun. 73, 403–408 (1989).
[Crossref]

1988 (1)

C. Tamm, “Frequency locking of two transverse optical modes of a laser,” Phys. Rev. A 38, 5960 (1988).
[Crossref]

1966 (1)

1936 (1)

R. A. Beth, “Mechanical detection and measurement of the angular momentum of light,” Phys. Rev. 50, 115 (1936).
[Crossref]

1909 (1)

J. H. Poynting, “The wave motion of a revolving shaft, and a suggestion as to the angular momentum in a beam of circularly polarised light,” Proc. R. Soc. Lond., A Contain. Pap. Math. Phys. Character 82, 560–567 (1909).
[Crossref]

Aeschlimann, M.

G. Spektor, D. Kilbane, A. Mahro, B. Frank, S. Ristok, L. Gal, P. Kahl, D. Podbiel, S. Mathias, H. Giessen, F.-J. Meyer zu Heringdorf, M. Orenstein, and M. Aeschlimann, “Revealing the subfemtosecond dynamics of orbital angular momentum in nanoplasmonic vortices,” Science. 355, 1187–1191 (2017).
[Crossref] [PubMed]

Ahmed, N.

J. Wang, J.-Y. Yang, I. M. Fazal, N. Ahmed, Y. Yan, H. Huang, Y. Ren, Y. Yue, S. Dolinar, M. Tur, S. Dolinar, M. Tur, and A. E. Willner, “Terabit free-space data transmission employing orbital angular momentum multiplexing,” Nat. Photonics 6, 488 (2012).
[Crossref]

Alfano, R.

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

Allen, L.

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, 8185–8189 (1992).
[Crossref] [PubMed]

Ambrosio, A.

Andrews, D.

M. Babiker, C. Bennett, D. Andrews, and L. D. Romero, “Orbital angular momentum exchange in the interaction of twisted light with molecules,” Phys. Rev. Lett. 89, 143601 (2002).
[Crossref] [PubMed]

Arbabi, A.

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, 937 (2015).
[Crossref] [PubMed]

Babiker, M.

M. Babiker, C. Bennett, D. Andrews, and L. D. Romero, “Orbital angular momentum exchange in the interaction of twisted light with molecules,” Phys. Rev. Lett. 89, 143601 (2002).
[Crossref] [PubMed]

Bagheri, M.

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, 937 (2015).
[Crossref] [PubMed]

Barnett, S. M.

Beijersbergen, M.

M. Beijersbergen, R. Coerwinkel, M. Kristensen, and J. Woerdman, “Helical-wavefront laser beams produced with a spiral phaseplate,” Opt. Commun. 112, 321–327 (1994).
[Crossref]

Beijersbergen, M. W.

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, 8185–8189 (1992).
[Crossref] [PubMed]

Bennett, C.

M. Babiker, C. Bennett, D. Andrews, and L. D. Romero, “Orbital angular momentum exchange in the interaction of twisted light with molecules,” Phys. Rev. Lett. 89, 143601 (2002).
[Crossref] [PubMed]

Beth, R. A.

R. A. Beth, “Mechanical detection and measurement of the angular momentum of light,” Phys. Rev. 50, 115 (1936).
[Crossref]

Biener, G.

Bowman, R.

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

Boyd, R. W.

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, e167 (2014).
[Crossref]

Bretner, I.

N. Shitrit, I. Bretner, Y. Gorodetski, V. Kleiner, and E. Hasman, “Optical spin hall effects in plasmonic chains,” Nano Lett. 11, 2038–2042 (2011).
[Crossref] [PubMed]

Capasso, F.

Z. J. Shi, M. Khorasaninejad, Y. W. Huang, C. Roques-Carmes, A. Y. Zhu, W. T. Chen, V. Sanjeev, Z. W. Ding, M. Tamagnone, K. Chaudhary, R. C. Devlin, C. W. Qiu, and F. Capasso, “Single-layer metasurface with controllable multiwavelength functions,” Nano Lett. 18, 2420–2427 (2018).
[Crossref] [PubMed]

J. P. B. Mueller, N. A. Rubin, R. C. Devlin, B. Groever, and F. Capasso, “Metasurface polarization optics: Independent phase control of arbitrary orthogonal states of polarization,” Phys. Rev. Lett. 118, 113901 (2017).
[Crossref]

R. C. Devlin, A. Ambrosio, N. A. Rubin, J. P. B. Mueller, and F. Capasso, “Arbitrary spin-to-orbital angular momentum conversion of light,” Science. 358, 896–900 (2017).
[Crossref] [PubMed]

M. Khorasaninejad and F. Capasso, “Metalenses: Versatile multifunctional photonic components,” Science. 358, eaam8100 (2017).
[Crossref] [PubMed]

R. C. Devlin, A. Ambrosio, D. Wintz, S. L. Oscurato, A. Y. Zhu, M. Khorasaninejad, J. Oh, P. Maddalena, and F. Capasso, “Spin-to-orbital angular momentum conversion in dielectric metasurfaces,” Opt. Express 25, 377–393 (2017).
[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. United States Am. 113, 10473–10478 (2016).
[Crossref]

Chaudhary, K.

Z. J. Shi, M. Khorasaninejad, Y. W. Huang, C. Roques-Carmes, A. Y. Zhu, W. T. Chen, V. Sanjeev, Z. W. Ding, M. Tamagnone, K. Chaudhary, R. C. Devlin, C. W. Qiu, and F. Capasso, “Single-layer metasurface with controllable multiwavelength functions,” Nano Lett. 18, 2420–2427 (2018).
[Crossref] [PubMed]

Chen, L.

Y. Li, X. Li, L. Chen, M. Pu, J. Jin, M. Hong, and X. Luo, “Orbital angular momentum multiplexing and demultiplexing by a single metasurface,” Adv. Opt. Mater. 5, 1600502 (2017).
[Crossref]

Chen, W. T.

Z. J. Shi, M. Khorasaninejad, Y. W. Huang, C. Roques-Carmes, A. Y. Zhu, W. T. Chen, V. Sanjeev, Z. W. Ding, M. Tamagnone, K. Chaudhary, R. C. Devlin, C. W. Qiu, and F. Capasso, “Single-layer metasurface with controllable multiwavelength functions,” Nano Lett. 18, 2420–2427 (2018).
[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. United States Am. 113, 10473–10478 (2016).
[Crossref]

Coerwinkel, R.

M. Beijersbergen, R. Coerwinkel, M. Kristensen, and J. Woerdman, “Helical-wavefront laser beams produced with a spiral phaseplate,” Opt. Commun. 112, 321–327 (1994).
[Crossref]

Coullet, P.

P. Coullet, L. Gil, and F. Rocca, “Optical vortices,” Opt. Commun. 73, 403–408 (1989).
[Crossref]

Courtial, J.

Danner, A.

K. Huang, H. Liu, S. Restuccia, M. Q. Mehmood, S.-T. Mei, D. Giovannini, A. Danner, M. J. Padgett, J.-H. Teng, and C.-W. Qiu, “Spiniform phase-encoded metagratings entangling arbitrary rational-order orbital angular momentum,” Light. Sci. & Appl. 7, 17156 (2018).
[Crossref]

De Leon, I.

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Qiu, C. W.

Z. J. Shi, M. Khorasaninejad, Y. W. Huang, C. Roques-Carmes, A. Y. Zhu, W. T. Chen, V. Sanjeev, Z. W. Ding, M. Tamagnone, K. Chaudhary, R. C. Devlin, C. W. Qiu, and F. Capasso, “Single-layer metasurface with controllable multiwavelength functions,” Nano Lett. 18, 2420–2427 (2018).
[Crossref] [PubMed]

Qiu, C.-W.

K. Huang, H. Liu, S. Restuccia, M. Q. Mehmood, S.-T. Mei, D. Giovannini, A. Danner, M. J. Padgett, J.-H. Teng, and C.-W. Qiu, “Spiniform phase-encoded metagratings entangling arbitrary rational-order orbital angular momentum,” Light. Sci. & Appl. 7, 17156 (2018).
[Crossref]

Ramelow, S.

R. Fickler, R. Lapkiewicz, W. N. Plick, M. Krenn, C. Schaeff, S. Ramelow, and A. Zeilinger, “Quantum entanglement of high angular momenta,” Science. 338, 640–643 (2012).
[Crossref] [PubMed]

Ren, H.

H. Ren, X. Li, Q. Zhang, and M. Gu, “On-chip noninterference angular momentum multiplexing of broadband light,” Science 352, 805–809 (2016).
[Crossref] [PubMed]

Ren, Y.

J. Wang, J.-Y. Yang, I. M. Fazal, N. Ahmed, Y. Yan, H. Huang, Y. Ren, Y. Yue, S. Dolinar, M. Tur, S. Dolinar, M. Tur, and A. E. Willner, “Terabit free-space data transmission employing orbital angular momentum multiplexing,” Nat. Photonics 6, 488 (2012).
[Crossref]

Restuccia, S.

K. Huang, H. Liu, S. Restuccia, M. Q. Mehmood, S.-T. Mei, D. Giovannini, A. Danner, M. J. Padgett, J.-H. Teng, and C.-W. Qiu, “Spiniform phase-encoded metagratings entangling arbitrary rational-order orbital angular momentum,” Light. Sci. & Appl. 7, 17156 (2018).
[Crossref]

Ristok, S.

G. Spektor, D. Kilbane, A. Mahro, B. Frank, S. Ristok, L. Gal, P. Kahl, D. Podbiel, S. Mathias, H. Giessen, F.-J. Meyer zu Heringdorf, M. Orenstein, and M. Aeschlimann, “Revealing the subfemtosecond dynamics of orbital angular momentum in nanoplasmonic vortices,” Science. 355, 1187–1191 (2017).
[Crossref] [PubMed]

Rocca, F.

P. Coullet, L. Gil, and F. Rocca, “Optical vortices,” Opt. Commun. 73, 403–408 (1989).
[Crossref]

Romero, L. D.

M. Babiker, C. Bennett, D. Andrews, and L. D. Romero, “Orbital angular momentum exchange in the interaction of twisted light with molecules,” Phys. Rev. Lett. 89, 143601 (2002).
[Crossref] [PubMed]

Roques-Carmes, C.

Z. J. Shi, M. Khorasaninejad, Y. W. Huang, C. Roques-Carmes, A. Y. Zhu, W. T. Chen, V. Sanjeev, Z. W. Ding, M. Tamagnone, K. Chaudhary, R. C. Devlin, C. W. Qiu, and F. Capasso, “Single-layer metasurface with controllable multiwavelength functions,” Nano Lett. 18, 2420–2427 (2018).
[Crossref] [PubMed]

Roux, F. S.

D. Naidoo, F. S. Roux, A. Dudley, I. Litvin, B. Piccirillo, L. Marrucci, and A. Forbes, “Controlled generation of higher-order poincaré sphere beams from a laser,” Nat. Photonics 10, 327–332 (2016).
[Crossref]

Rubin, N. A.

J. P. B. Mueller, N. A. Rubin, R. C. Devlin, B. Groever, and F. Capasso, “Metasurface polarization optics: Independent phase control of arbitrary orthogonal states of polarization,” Phys. Rev. Lett. 118, 113901 (2017).
[Crossref]

R. C. Devlin, A. Ambrosio, N. A. Rubin, J. P. B. Mueller, and F. Capasso, “Arbitrary spin-to-orbital angular momentum conversion of light,” Science. 358, 896–900 (2017).
[Crossref] [PubMed]

Sanjeev, V.

Z. J. Shi, M. Khorasaninejad, Y. W. Huang, C. Roques-Carmes, A. Y. Zhu, W. T. Chen, V. Sanjeev, Z. W. Ding, M. Tamagnone, K. Chaudhary, R. C. Devlin, C. W. Qiu, and F. Capasso, “Single-layer metasurface with controllable multiwavelength functions,” Nano Lett. 18, 2420–2427 (2018).
[Crossref] [PubMed]

Santamato, E.

E. Nagali, F. Sciarrino, F. De Martini, L. Marrucci, B. Piccirillo, E. Karimi, and E. Santamato, “Quantum information transfer from spin to orbital angular momentum of photons,” Phys. Rev. Lett. 103, 013601 (2009).
[Crossref] [PubMed]

Schaeff, C.

R. Fickler, R. Lapkiewicz, W. N. Plick, M. Krenn, C. Schaeff, S. Ramelow, and A. Zeilinger, “Quantum entanglement of high angular momenta,” Science. 338, 640–643 (2012).
[Crossref] [PubMed]

Schubert, W. H.

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, e167 (2014).
[Crossref]

Sciarrino, F.

E. Nagali, F. Sciarrino, F. De Martini, L. Marrucci, B. Piccirillo, E. Karimi, and E. Santamato, “Quantum information transfer from spin to orbital angular momentum of photons,” Phys. Rev. Lett. 103, 013601 (2009).
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Z. J. Shi, M. Khorasaninejad, Y. W. Huang, C. Roques-Carmes, A. Y. Zhu, W. T. Chen, V. Sanjeev, Z. W. Ding, M. Tamagnone, K. Chaudhary, R. C. Devlin, C. W. Qiu, and F. Capasso, “Single-layer metasurface with controllable multiwavelength functions,” Nano Lett. 18, 2420–2427 (2018).
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N. Shitrit, I. Bretner, Y. Gorodetski, V. Kleiner, and E. Hasman, “Optical spin hall effects in plasmonic chains,” Nano Lett. 11, 2038–2042 (2011).
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Singh, R. P.

Spektor, G.

G. Spektor, D. Kilbane, A. Mahro, B. Frank, S. Ristok, L. Gal, P. Kahl, D. Podbiel, S. Mathias, H. Giessen, F.-J. Meyer zu Heringdorf, M. Orenstein, and M. Aeschlimann, “Revealing the subfemtosecond dynamics of orbital angular momentum in nanoplasmonic vortices,” Science. 355, 1187–1191 (2017).
[Crossref] [PubMed]

Spreeuw, R. J. C.

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, 8185–8189 (1992).
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P. Miao, Z. Zhang, J. Sun, W. Walasik, S. Longhi, N. M. Litchinitser, and L. Feng, “Orbital angular momentum microlaser,” Science 353, 464–467 (2016).
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Sztul, H.

G. Milione, H. Sztul, D. Nolan, and R. Alfano, “Higher-order poincaré sphere, stokes parameters, and the angular momentum of light,” Phys. Rev. Lett. 107, 053601 (2011).
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Z. J. Shi, M. Khorasaninejad, Y. W. Huang, C. Roques-Carmes, A. Y. Zhu, W. T. Chen, V. Sanjeev, Z. W. Ding, M. Tamagnone, K. Chaudhary, R. C. Devlin, C. W. Qiu, and F. Capasso, “Single-layer metasurface with controllable multiwavelength functions,” Nano Lett. 18, 2420–2427 (2018).
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C. Tamm, “Frequency locking of two transverse optical modes of a laser,” Phys. Rev. A 38, 5960 (1988).
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K. Huang, H. Liu, S. Restuccia, M. Q. Mehmood, S.-T. Mei, D. Giovannini, A. Danner, M. J. Padgett, J.-H. Teng, and C.-W. Qiu, “Spiniform phase-encoded metagratings entangling arbitrary rational-order orbital angular momentum,” Light. Sci. & Appl. 7, 17156 (2018).
[Crossref]

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J. Wang, J.-Y. Yang, I. M. Fazal, N. Ahmed, Y. Yan, H. Huang, Y. Ren, Y. Yue, S. Dolinar, M. Tur, S. Dolinar, M. Tur, and A. E. Willner, “Terabit free-space data transmission employing orbital angular momentum multiplexing,” Nat. Photonics 6, 488 (2012).
[Crossref]

J. Wang, J.-Y. Yang, I. M. Fazal, N. Ahmed, Y. Yan, H. Huang, Y. Ren, Y. Yue, S. Dolinar, M. Tur, S. Dolinar, M. Tur, and A. E. Willner, “Terabit free-space data transmission employing orbital angular momentum multiplexing,” Nat. Photonics 6, 488 (2012).
[Crossref]

Upham, J.

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, e167 (2014).
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Veissier, L.

A. Nicolas, L. Veissier, L. Giner, E. Giacobino, D. Maxein, and J. Laurat, “A quantum memory for orbital angular momentum photonic qubits,” Nat. Photonics 8, 234 (2014).
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P. Miao, Z. Zhang, J. Sun, W. Walasik, S. Longhi, N. M. Litchinitser, and L. Feng, “Orbital angular momentum microlaser,” Science 353, 464–467 (2016).
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Wang, J.

J. Wang, J.-Y. Yang, I. M. Fazal, N. Ahmed, Y. Yan, H. Huang, Y. Ren, Y. Yue, S. Dolinar, M. Tur, S. Dolinar, M. Tur, and A. E. Willner, “Terabit free-space data transmission employing orbital angular momentum multiplexing,” Nat. Photonics 6, 488 (2012).
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Wichmann, J.

Willner, A. E.

J. Wang, J.-Y. Yang, I. M. Fazal, N. Ahmed, Y. Yan, H. Huang, Y. Ren, Y. Yue, S. Dolinar, M. Tur, S. Dolinar, M. Tur, and A. E. Willner, “Terabit free-space data transmission employing orbital angular momentum multiplexing,” Nat. Photonics 6, 488 (2012).
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M. Beijersbergen, R. Coerwinkel, M. Kristensen, and J. Woerdman, “Helical-wavefront laser beams produced with a spiral phaseplate,” Opt. Commun. 112, 321–327 (1994).
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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, 8185–8189 (1992).
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J. Wang, J.-Y. Yang, I. M. Fazal, N. Ahmed, Y. Yan, H. Huang, Y. Ren, Y. Yue, S. Dolinar, M. Tur, S. Dolinar, M. Tur, and A. E. Willner, “Terabit free-space data transmission employing orbital angular momentum multiplexing,” Nat. Photonics 6, 488 (2012).
[Crossref]

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J. Wang, J.-Y. Yang, I. M. Fazal, N. Ahmed, Y. Yan, H. Huang, Y. Ren, Y. Yue, S. Dolinar, M. Tur, S. Dolinar, M. Tur, and A. E. Willner, “Terabit free-space data transmission employing orbital angular momentum multiplexing,” Nat. Photonics 6, 488 (2012).
[Crossref]

Yue, Y.

J. Wang, J.-Y. Yang, I. M. Fazal, N. Ahmed, Y. Yan, H. Huang, Y. Ren, Y. Yue, S. Dolinar, M. Tur, S. Dolinar, M. Tur, and A. E. Willner, “Terabit free-space data transmission employing orbital angular momentum multiplexing,” Nat. Photonics 6, 488 (2012).
[Crossref]

Zeilinger, A.

R. Fickler, R. Lapkiewicz, W. N. Plick, M. Krenn, C. Schaeff, S. Ramelow, and A. Zeilinger, “Quantum entanglement of high angular momenta,” Science. 338, 640–643 (2012).
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H. Ren, X. Li, Q. Zhang, and M. Gu, “On-chip noninterference angular momentum multiplexing of broadband light,” Science 352, 805–809 (2016).
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P. Miao, Z. Zhang, J. Sun, W. Walasik, S. Longhi, N. M. Litchinitser, and L. Feng, “Orbital angular momentum microlaser,” Science 353, 464–467 (2016).
[Crossref] [PubMed]

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Z. J. Shi, M. Khorasaninejad, Y. W. Huang, C. Roques-Carmes, A. Y. Zhu, W. T. Chen, V. Sanjeev, Z. W. Ding, M. Tamagnone, K. Chaudhary, R. C. Devlin, C. W. Qiu, and F. Capasso, “Single-layer metasurface with controllable multiwavelength functions,” Nano Lett. 18, 2420–2427 (2018).
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[Crossref]

K. Huang, H. Liu, S. Restuccia, M. Q. Mehmood, S.-T. Mei, D. Giovannini, A. Danner, M. J. Padgett, J.-H. Teng, and C.-W. Qiu, “Spiniform phase-encoded metagratings entangling arbitrary rational-order orbital angular momentum,” Light. Sci. & Appl. 7, 17156 (2018).
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Z. J. Shi, M. Khorasaninejad, Y. W. Huang, C. Roques-Carmes, A. Y. Zhu, W. T. Chen, V. Sanjeev, Z. W. Ding, M. Tamagnone, K. Chaudhary, R. C. Devlin, C. W. Qiu, and F. Capasso, “Single-layer metasurface with controllable multiwavelength functions,” Nano Lett. 18, 2420–2427 (2018).
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H. Ren, X. Li, Q. Zhang, and M. Gu, “On-chip noninterference angular momentum multiplexing of broadband light,” Science 352, 805–809 (2016).
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[Crossref] [PubMed]

G. Spektor, D. Kilbane, A. Mahro, B. Frank, S. Ristok, L. Gal, P. Kahl, D. Podbiel, S. Mathias, H. Giessen, F.-J. Meyer zu Heringdorf, M. Orenstein, and M. Aeschlimann, “Revealing the subfemtosecond dynamics of orbital angular momentum in nanoplasmonic vortices,” Science. 355, 1187–1191 (2017).
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Figures (7)

Fig. 1
Fig. 1 Conceptual schematic of three types of spin-orbit converters: Q-plate, J-plate, and cascaded J-plates. (a) Q-plates operate on a circular polarization basis (|R〉 or |L〉) and theoutput OAM states corresponding to these circular polarizations are constrained to hold conjugate (equal and opposite) topological charges (|〉 and |−〉). (b) J-plates operate on arbitrary orthogonal polarization basis (|λ+〉 or λ〉) and the two possible output orbital states |m〉 and |n〉 can be independent. But the output spin states, or polarizations, on which these vortex beams are imparted must be the same states as the input spin states with flipped handedness (opposite sense of rotation). (c) Cascaded J-plates overcome the restriction mentioned above. The output spin states can be another arbitrary orthogonal polarization basis (|κ+〉 and (|κ〉) independent of the input polarization basis (|λ+〉 and |λ〉). Here, two kets are used in succession to describe spin and orbital states.
Fig. 2
Fig. 2 (a) Schematic: Cascaded J-plates enable the generation of versatile total angular momentum (TAM) states of light. Braket notation is used for describing how the J-plates (J1 and J2) and analyzer (|Ψa〉〈Ψa|) operate on the incident state (|Ψi〉). Versatile TAM states (|Ψa〉〈Ψa| J2J1 |Ψi〉) can be generated by selection of incident state, analyzer state, and the order of J-plates. (b) The higher order Poincaré sphere (HOPS) is a convenient representation to understand the action of the J-plate on incident light. Two HOPSs represent the functionality of the J-plates J1 (top) and J2 (bottom). Red dots i–iv mark the eigen-polarization states and designed TAM states that J1 and J2 can generate: |x〉 |m〉 and |y〉 |n〉 for J1 (top) and |R〉 |p〉 and |L〉 |q〉 for J2 (bottom). (c) Phase profiles to be imparted on the eigen-polarization states i–iv of each J-plate. The phase is from two terms, an azimuthal phase factor of exp(iℓϕ) and a grating phase along x-axis exp (ikx sin ζ) for tilt output. The parameters , and ζ are OAM quantum number and tilt angle of the output beam, respectively. (d) SEM images of J1 and J2 samples.
Fig. 3
Fig. 3 (a) These tables document the possible non-separable TAM combinations that can be generated by the J-plate cascade, in this case with the light encountering J1 before J2. Measured intensity profiles (left) and interferograms (right) with a reference beam are shown. The incident polarization state |Ψi〉 (|x〉 or |y〉) and final analyzer state |Ψa〉〈Ψa| (|R〉〈R| or |L〉〈L|) producing the beams are shown at the top and left of the table, respectively. This table is a key to determine the output beam with knowledge of the input polarization and analyzer configuration. (b) An identical table corresponding to the case where J2 precedes J1, that is, J1J2i〉. The corresponding incident states are |L〉 or |R〉 and analyzer states are |x〉〈x| or |y〉〈y| in this case.
Fig. 4
Fig. 4 Beam profiles and interferograms produced when the input is varied and the final analyzer is kept fixed. If |Ψa〉 = |R〉, from Eq. (12), |Ψo〉 = C (α |R〉 |4〉 − |R〉 |5〉) with α and β parameterizing the input polarization. (a) The cascaded HOPS representing possible TAM states of J2J1 while the analyzer state is fixed as |R〉. The cascaded HOPS contains one sphere for all possible incident polarizations |Ψi〉 (light red sphere, left) and another one depicting all possible analyzer polarizations |Ψa〉 (yellow sphere, right). The dots on the left HOPS mark the results corresponding to b–e, with red denoting eigenstates and blue denoting non-eigenstates. (b–e) Measured intensity (b), calculated intensity (c), measured interferogram (d), and calculated phase profile (e) of the output states. The states in (b–e) i–vi are marked as dots on the cascaded HOPS in (a). The white dashed circles in (d–e) label the positions of off-axis singularities in the interferogram and phase profiles.
Fig. 5
Fig. 5 Beam profiles and interferograms produced when the input is fixed and the final analyzer is varied. If |Ψi〉 = |x〉, from Eq. (12), |Ψo〉 = C |γR + ηL〉 (γ |4〉 − η |6〉) where γ and η parameterize the analyzer polarization state. (a) The cascaded HOPS representing possible TAM states of J2J1 while the incident polarization is fixed as |x〉. Here the possible TAM states are shown on the analyzer sphere. (b–e) Measured intensity (b), calculated intensity (c), measured interferogram (d), and calculated phase (e) of the output states. The states in (b–e) i–vi are marked as circles on the cascaded HOPS in (a). The white dashed circles in (d–e) label the position of the off-axis singularity.
Fig. 6
Fig. 6 Beam profiles and interferograms produced when the analyzer polarization is varied and input is fixed at a polarization that is not an eigen-polarization state of J1. If |Ψi〉 = |45°〉, from Eq. (12), the output state is |Ψo〉 = C |γR + ηL〉 (γ |4〉 − |5〉 − η |6〉 − |7〉) where γ and η parameterize the polarization state of the analyzer. (a) The cascaded HOPS representing possible TAM states of J2J1 while the incident polarization is fixed as |45°〉. (b–e) Measured intensity (b), calculated intensity (c), measured interferogram (d), and calculated phase (e) of the output states. The states in (b–e) i–vi are marked as circles on the cascaded HOPS in (a). The white dots in (b–e) label the position of off-axis singularities.
Fig. 7
Fig. 7 The measured (top row) and calculated (bottom row) intensity profile of 4 TAM states and the polarization ellipse diagrams. (a) Superposition of |R〉 |4〉 and |L〉 |6〉 produced by J2J1 |x〉 |0〉. (b) Superposition of |R〉 |5〉 and |L〉 |7〉 produced by J2J1 |y〉 |0〉. (c) Superposition of |x〉 |4〉 and |y〉 |5〉 produced by J1J2 |L〉 |0〉. (d) Superposition of |x〉 |6〉 and |y〉 |7〉 produced by J1J2 |R〉 |0〉.

Equations (15)

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J | λ + | = | ( λ + ) * | + m
J | λ | = | ( λ ) * | + n .
| λ + = [ cos χ e i δ sin χ ] ; | λ = [ sin χ e i δ cos χ ] ; | ( λ + ) * = [ cos χ e i δ sin χ ] ; | ( λ ) * = [ sin χ e i δ cos χ ] ,
J 1 | x | = | x | + m ,
J 1 | y | = | y | + n ,
J 2 | L | = | R | + p ,
J 2 | R | = | L | + q ,
J 1 ( ϕ ) = | x x | e i m ϕ + | y y | e i n ϕ = [ e i m ϕ 0 0 e i n ϕ ] ,
J 2 ( ϕ ) = | L R | e i p ϕ + | R L | e i q ϕ = 1 2 [ ( e i p ϕ + e i q ϕ ) i ( e i p ϕ e i q ϕ ) i ( e i p ϕ e i q ϕ ) ( e i p ϕ + e i q ϕ ) ] .
J ( x , y ) = [ e i ϕ + ( x , y ) ( λ 1 + ) * e i ϕ ( x , y ) ( λ 1 ) * e i ϕ + ( x , y ) ( λ 2 + ) * e i ϕ ( x , y ) ( λ 2 ) * ] [ ( λ 1 + ) ( λ 1 ) ( λ 2 + ) ( λ 2 ) ] 1 = R [ θ ( x , y ) ] [ e i ϕ l ( x , y ) 0 0 e i ϕ s ( x , y ) ] R [ θ ( x , y ) ]
J 1 J 2 | α x + β y = | L R | x e i ( m + p ) ϕ + | R L | x e i ( m + q ) ϕ + | L R | y e i ( n + p ) ϕ + | R L | y e i ( n + p ) ϕ .
| Ψ o = | Ψ a Ψ a | J 2 J 1 | Ψ i = | γ R + η L γ R + η L | J 2 J 1 | α x + β y = C [ γ ( α | m + p i β | n + p ) η ( α | m + q + i β | n + q ) ] | γ R + η L ,
Φ n Θ = 1 | 1 2 | .
P = [ P x P y P 45 P 135 P L P R ] = [ 1 1 0 0 1 1 0 0 1 0 1 0 1 0 1 0 1 0 0 1 1 0 0 1 ] [ S 0 S 1 S 2 S 3 ] = A S ,
S = ( A T A ) 1 A T P

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