Abstract

We propose and numerically demonstrate a Pancharatnam-Berry optical element (PBOE) device that simultaneously sorts spin (SAM) and orbital (OAM) angular momentum. This device exploits the circular polarization selective properties of PBOEs to modulate independently the orthogonal SAM eigenstates within a geometric optical transformation that sorts OAM, enabling single measurement characterization of the full angular momentum eigenstate. This expands the available state space for OAM communication and enables characterization of the eigenmode composition of structured polarization beams. We define the two-dimensional orientation patterns of the transversely varying half-waveplate PBOEs that implement the angular momentum sorter. We show that the device discriminates the OAM and SAM eigenstates of optical beams including laser cavity modes such as Laguerre-Gaussian OAM eigenmodes, Hermite-Gaussian modes, and hybrid modes with complex structured polarization. We also demonstrate that it can determine the m parameter of higher order LGml Laguerre-Gaussian modes. The ability of this device to decode information from spatially structured optical phase has potential for applications in communication, encryption, modal characterization, and scientific measurements.

© 2016 Optical Society of America

Full Article  |  PDF Article
OSA Recommended Articles
Generalized optical angular momentum sorter and its application to high-dimensional quantum cryptography

Hugo Larocque, Jérémie Gagnon-Bischoff, Dominic Mortimer, Yingwen Zhang, Frédéric Bouchard, Jeremy Upham, Vincenzo Grillo, Robert W. Boyd, and Ebrahim Karimi
Opt. Express 25(17) 19832-19843 (2017)

Experimental realization to efficiently sort vector beams by polarization topological charge via Pancharatnam–Berry phase modulation

Shuiqin Zheng, Ying Li, Qinggang Lin, Xuanke Zeng, Guoliang Zheng, Yi Cai, Zhenkuan Chen, Shixiang Xu, and Dianyuan Fan
Photon. Res. 6(5) 385-389 (2018)

Formation of helical beams by use of Pancharatnam–Berry phase optical elements

Gabriel Biener, Avi Niv, Vladimir Kleiner, and Erez Hasman
Opt. Lett. 27(21) 1875-1877 (2002)

References

  • View by:
  • |
  • |
  • |

  1. J. Leach, M. J. Padgett, S. M. Barnett, S. Franke-Arnold, and J. Courtial, “Measuring the orbital angular momentum of a single photon,” Phys. Rev. Lett. 88(25), 257901 (2002).
    [Crossref] [PubMed]
  2. J. Wang, J. Y. Yang, I. F. Fazal, N. Ahmed, Y. Yan, H. Huang, Y. Ren, Y. Yue, S. Dolinar, M. Tur, and A. E. Willner, “Terabit free-space data transmission employing orbital angular momentum multiplexing,” Nat. Photonics 6(7), 488–496 (2012).
    [Crossref]
  3. H. Huang, G. Xie, Y. Yan, N. Ahmed, Y. Ren, Y. Yue, D. Rogawski, M. J. Willner, B. I. Erkmen, K. M. Birnbaum, S. J. Dolinar, M. P. J. Lavery, M. J. Padgett, M. Tur, and A. E. Willner, “100 Tbit/s free-space data link enabled by three-dimensional multiplexing of orbital angular momentum, polarization, and wavelength,” Opt. Lett. 39(2), 197–200 (2014).
    [Crossref] [PubMed]
  4. N. Bozinovic, Y. Yue, Y. Ren, M. Tur, P. Kristensen, H. Huang, A. E. Willner, and S. Ramachandran, “Terabit-scale orbital angular momentum mode division multiplexing in fibers,” Science 340(6140), 1545–1548 (2013).
    [Crossref] [PubMed]
  5. A. E. Willner, H. Huang, Y. Yen, Y. Ren, N. Ahmed, G. Xie, C. Bao, L. Li, Y. Cao, Z. Zhao, J. Wang, M. P. J. Lavery, M. Tur, S. Ramachandran, A. F. Molisch, N. Ashrafi, and S. Ashrafi, “Optical communications using orbital angular momentum beams,” Adv. Opt. Photonics 7(1), 66–106 (2015).
  6. G. Molina-Terriza, J. P. Torres, and L. Torner, “Management of the angular momentum of light: preparation of photons in multidimensional vector states of angular momentum,” Phys. Rev. Lett. 88(1), 013601 (2001).
    [Crossref] [PubMed]
  7. A. Vaziri, G. Weihs, and A. Zeilinger, “Experimental two-photon, three-dimensional entanglement for quantum communication,” Phys. Rev. Lett. 89(24), 240401 (2002).
    [Crossref] [PubMed]
  8. G. C. G. Berkhout, M. P. J. Lavery, J. Courtial, M. W. Beijersbergen, and M. J. Padgett, “Efficient sorting of orbital angular momentum states of light,” Phys. Rev. Lett. 105(15), 153601 (2010).
    [Crossref] [PubMed]
  9. M. P. J. Lavery, D. J. Robertson, G. C. G. Berkhout, G. D. Love, M. J. Padgett, and J. Courtial, “Refractive elements for the measurement of the orbital angular momentum of a single photon,” Opt. Express 20(3), 2110–2115 (2012).
    [Crossref] [PubMed]
  10. L. Marrucci, C. Manzo, and D. Paparo, “Pancharatnam-Berry phase optical elements for wave front shaping in the visible domain: switchable hylical modes generation,” Appl. Phys. Lett. 88(22), 221102 (2006).
    [Crossref]
  11. Z. Bomzon, G. Biener, V. Kleiner, and E. Hasman, “Space-variant Pancharatnam-Berry phase optical elements with computer-generated subwavelength gratings,” Opt. Lett. 27(13), 1141–1143 (2002).
    [Crossref] [PubMed]
  12. C. Provenzano, P. Pagliusi, and G. Cipparrone, “Highly efficient liquid crystal based diffraction grating induced by polarization holograms at the aligning surfaces,” Appl. Phys. Lett. 89(12), 121105 (2006).
    [Crossref]
  13. S. Slussarenko, B. Piccirillo, V. Chigrinov, L. Marrucci, and E. Santamato, “Liquid crystal spatial-mode converters for the orbital angular momentum of light,” J. Opt. 15(2), 025406 (2013).
    [Crossref]
  14. S. R. Nersisyan, N. V. Tabiryan, D. M. Steeves, and B. R. Kimball, “The promise of diffractive waveplates,” Opt. Photonics News 21(3), 40–45 (2010).
    [Crossref]
  15. S. R. Nersisyan, N. V. Tabiryan, D. Mawet, and E. Serabyn, “Improving vector vortex waveplates for high-contrast coronagraphy,” Opt. Express 21(7), 8205–8213 (2013).
    [Crossref] [PubMed]
  16. S. Nersisyan, N. Tabiryan, D. M. Steeves, and B. R. Kimball, “Fabrication of liquid crystal polymer axial waveplates for UV-IR wavelengths,” Opt. Express 17(14), 11926–11934 (2009).
    [Crossref] [PubMed]
  17. H. Sarkissian, S. V. Serak, N. V. Tabiryan, L. B. Glebov, V. Rotar, and B. Y. Zeldovich, “Polarization-controlled switching between diffraction orders in transverse-periodically aligned nematic liquid crystals,” Opt. Lett. 31(15), 2248–2250 (2006).
    [Crossref] [PubMed]
  18. L. Goldenberg, V. Lisinetskii, A. Ryabchun, A. Bobrovsky, and S. Schrader, “Liquid crystalline azobenzene-containing polymer as a matrix for distributed feedback lasers,” ACS Photonics 1(9), 885–893 (2014).
    [Crossref]
  19. A. Niv, G. Biener, V. Kleiner, and E. Hasman, “Manipulation of the Pancharatnam phase in vectorial vortices,” Opt. Express 14(10), 4208–4220 (2006).
    [Crossref] [PubMed]
  20. D. Lin, P. Fan, E. Hasman, and M. L. Brongersma, “Dielectric gradient metasurface optical elements,” Science 345(6194), 298–302 (2014).
    [Crossref] [PubMed]
  21. A. Niv, G. Biener, V. Kleiner, and E. Hasman, “Rotating vectorial vortices produced by space-variant subwavelength gratings,” Opt. Lett. 30(21), 2933–2935 (2005).
    [Crossref] [PubMed]
  22. 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]
  23. F. Aieta, P. Genevet, M. A. Kats, N. Yu, R. Blanchard, Z. Gaburro, and F. Capasso, “Aberration-free ultrathin flat lenses and axicons at telecom wavelengths based on plasmonic metasurfaces,” Nano Lett. 12(9), 4932–4936 (2012).
    [Crossref] [PubMed]
  24. M. Malik, M. Mirhosseini, M. P. J. Lavery, J. Leach, M. J. Padgett, and R. W. Boyd, “Direct measurement of a 27-dimensional orbital-angular-momentum state vector,” Nat. Commun. 5, 3115 (2014).
    [Crossref] [PubMed]
  25. J. Cederquist and A. M. Tai, “Computer-generated holograms for geometric transformations,” Appl. Opt. 23(18), 3099–3104 (1984).
    [Crossref] [PubMed]
  26. P. Pagliusi, C. Provenzano, A. Mazzulla, L. Giorgini, and G. Cipparrone, “Spectrograph based on a single diffractive element for real-time measurement of circular dichroism,” Appl. Spectrosc. 62(5), 465–468 (2008).
    [Crossref] [PubMed]
  27. O. Bryngdahl, “Geometrical transformations in optics,” J. Opt. Soc. Am. 64(8), 1092–1099 (1974).
    [Crossref]
  28. T. C. Poon and T. Kim, Engineering Optics with MATLAB (World Scientific Publishing Co., 2006), Ch. 3.
  29. M. N. O’Sullivan, M. Mirhosseini, M. Malik, and R. W. Boyd, “Near-perfect sorting of orbital angular momentum and angular position states of light,” Opt. Express 20(22), 24444–24449 (2012).
    [Crossref] [PubMed]
  30. M. Mirhosseini, M. Malik, Z. Shi, and R. W. Boyd, “Efficient separation of the orbital angular momentum eigenstates of light,” Nat. Commun. 4, 2781 (2013).
    [Crossref] [PubMed]
  31. 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]
  32. S. Ramachadran and P. Kristensen, “Optical vortices in fiber,” Nanophotonics 2(5–6), 455–474 (2013).
  33. B. E. A. Saleh and M. C. Teich, Fundamentals of Photonics Second Edition (John Wiley and Sons, 2007), Ch. 3.
  34. M. J. Padgett and J. Courtial, “Poincaré-sphere equivalent for light beams containing orbital angular momentum,” Opt. Lett. 24(7), 430–432 (1999).
    [Crossref] [PubMed]
  35. 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]
  36. L. Novotny and B. Hecht, Principles of Nano-Optics (Cambridge University Press, 2006), Ch. 3.
  37. S. Golowich, N. Bozinovic, P. Kristensen, and S. Ramachandran, “Complex mode amplitude measurement for a six-mode optical fiber,” Opt. Express 21(4), 4931–4944 (2013).
    [Crossref] [PubMed]
  38. D. L. Andrews, Structured Light and Its Applications: An Introduction to Phase-Structured Beams and Nanoscale Optical Forces (Academic Press, 2008).
  39. N. Lawrence, J. Trevino, and L. D. Negro, “Control of optical orbital angular momentum by Vogel spiral arrays of metallic nanoparticles,” Opt. Lett. 37(24), 5076–5078 (2012).
    [Crossref] [PubMed]
  40. F. K. Fatemi and G. Beadie, “Rapid complex mode decomposition of vector beams by common path interferometry,” Opt. Express 21(26), 32291–32305 (2013).
    [Crossref] [PubMed]

2015 (2)

A. E. Willner, H. Huang, Y. Yen, Y. Ren, N. Ahmed, G. Xie, C. Bao, L. Li, Y. Cao, Z. Zhao, J. Wang, M. P. J. Lavery, M. Tur, S. Ramachandran, A. F. Molisch, N. Ashrafi, and S. Ashrafi, “Optical communications using orbital angular momentum beams,” Adv. Opt. Photonics 7(1), 66–106 (2015).

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]

2014 (4)

L. Goldenberg, V. Lisinetskii, A. Ryabchun, A. Bobrovsky, and S. Schrader, “Liquid crystalline azobenzene-containing polymer as a matrix for distributed feedback lasers,” ACS Photonics 1(9), 885–893 (2014).
[Crossref]

M. Malik, M. Mirhosseini, M. P. J. Lavery, J. Leach, M. J. Padgett, and R. W. Boyd, “Direct measurement of a 27-dimensional orbital-angular-momentum state vector,” Nat. Commun. 5, 3115 (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]

H. Huang, G. Xie, Y. Yan, N. Ahmed, Y. Ren, Y. Yue, D. Rogawski, M. J. Willner, B. I. Erkmen, K. M. Birnbaum, S. J. Dolinar, M. P. J. Lavery, M. J. Padgett, M. Tur, and A. E. Willner, “100 Tbit/s free-space data link enabled by three-dimensional multiplexing of orbital angular momentum, polarization, and wavelength,” Opt. Lett. 39(2), 197–200 (2014).
[Crossref] [PubMed]

2013 (7)

S. Golowich, N. Bozinovic, P. Kristensen, and S. Ramachandran, “Complex mode amplitude measurement for a six-mode optical fiber,” Opt. Express 21(4), 4931–4944 (2013).
[Crossref] [PubMed]

S. R. Nersisyan, N. V. Tabiryan, D. Mawet, and E. Serabyn, “Improving vector vortex waveplates for high-contrast coronagraphy,” Opt. Express 21(7), 8205–8213 (2013).
[Crossref] [PubMed]

F. K. Fatemi and G. Beadie, “Rapid complex mode decomposition of vector beams by common path interferometry,” Opt. Express 21(26), 32291–32305 (2013).
[Crossref] [PubMed]

S. Ramachadran and P. Kristensen, “Optical vortices in fiber,” Nanophotonics 2(5–6), 455–474 (2013).

M. Mirhosseini, M. Malik, Z. Shi, and R. W. Boyd, “Efficient separation of the orbital angular momentum eigenstates of light,” Nat. Commun. 4, 2781 (2013).
[Crossref] [PubMed]

S. Slussarenko, B. Piccirillo, V. Chigrinov, L. Marrucci, and E. Santamato, “Liquid crystal spatial-mode converters for the orbital angular momentum of light,” J. Opt. 15(2), 025406 (2013).
[Crossref]

N. Bozinovic, Y. Yue, Y. Ren, M. Tur, P. Kristensen, H. Huang, A. E. Willner, and S. Ramachandran, “Terabit-scale orbital angular momentum mode division multiplexing in fibers,” Science 340(6140), 1545–1548 (2013).
[Crossref] [PubMed]

2012 (5)

J. Wang, J. Y. Yang, I. F. Fazal, N. Ahmed, Y. Yan, H. Huang, Y. Ren, Y. Yue, S. Dolinar, M. Tur, and A. E. Willner, “Terabit free-space data transmission employing orbital angular momentum multiplexing,” Nat. Photonics 6(7), 488–496 (2012).
[Crossref]

F. Aieta, P. Genevet, M. A. Kats, N. Yu, R. Blanchard, Z. Gaburro, and F. Capasso, “Aberration-free ultrathin flat lenses and axicons at telecom wavelengths based on plasmonic metasurfaces,” Nano Lett. 12(9), 4932–4936 (2012).
[Crossref] [PubMed]

M. P. J. Lavery, D. J. Robertson, G. C. G. Berkhout, G. D. Love, M. J. Padgett, and J. Courtial, “Refractive elements for the measurement of the orbital angular momentum of a single photon,” Opt. Express 20(3), 2110–2115 (2012).
[Crossref] [PubMed]

M. N. O’Sullivan, M. Mirhosseini, M. Malik, and R. W. Boyd, “Near-perfect sorting of orbital angular momentum and angular position states of light,” Opt. Express 20(22), 24444–24449 (2012).
[Crossref] [PubMed]

N. Lawrence, J. Trevino, and L. D. Negro, “Control of optical orbital angular momentum by Vogel spiral arrays of metallic nanoparticles,” Opt. Lett. 37(24), 5076–5078 (2012).
[Crossref] [PubMed]

2011 (1)

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]

2010 (2)

S. R. Nersisyan, N. V. Tabiryan, D. M. Steeves, and B. R. Kimball, “The promise of diffractive waveplates,” Opt. Photonics News 21(3), 40–45 (2010).
[Crossref]

G. C. G. Berkhout, M. P. J. Lavery, J. Courtial, M. W. Beijersbergen, and M. J. Padgett, “Efficient sorting of orbital angular momentum states of light,” Phys. Rev. Lett. 105(15), 153601 (2010).
[Crossref] [PubMed]

2009 (1)

2008 (1)

2006 (5)

A. Niv, G. Biener, V. Kleiner, and E. Hasman, “Manipulation of the Pancharatnam phase in vectorial vortices,” Opt. Express 14(10), 4208–4220 (2006).
[Crossref] [PubMed]

H. Sarkissian, S. V. Serak, N. V. Tabiryan, L. B. Glebov, V. Rotar, and B. Y. Zeldovich, “Polarization-controlled switching between diffraction orders in transverse-periodically aligned nematic liquid crystals,” Opt. Lett. 31(15), 2248–2250 (2006).
[Crossref] [PubMed]

L. Marrucci, C. Manzo, and D. Paparo, “Pancharatnam-Berry phase optical elements for wave front shaping in the visible domain: switchable hylical modes generation,” Appl. Phys. Lett. 88(22), 221102 (2006).
[Crossref]

C. Provenzano, P. Pagliusi, and G. Cipparrone, “Highly efficient liquid crystal based diffraction grating induced by polarization holograms at the aligning surfaces,” Appl. Phys. Lett. 89(12), 121105 (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 (1)

2002 (3)

Z. Bomzon, G. Biener, V. Kleiner, and E. Hasman, “Space-variant Pancharatnam-Berry phase optical elements with computer-generated subwavelength gratings,” Opt. Lett. 27(13), 1141–1143 (2002).
[Crossref] [PubMed]

J. Leach, M. J. Padgett, S. M. Barnett, S. Franke-Arnold, and J. Courtial, “Measuring the orbital angular momentum of a single photon,” Phys. Rev. Lett. 88(25), 257901 (2002).
[Crossref] [PubMed]

A. Vaziri, G. Weihs, and A. Zeilinger, “Experimental two-photon, three-dimensional entanglement for quantum communication,” Phys. Rev. Lett. 89(24), 240401 (2002).
[Crossref] [PubMed]

2001 (1)

G. Molina-Terriza, J. P. Torres, and L. Torner, “Management of the angular momentum of light: preparation of photons in multidimensional vector states of angular momentum,” Phys. Rev. Lett. 88(1), 013601 (2001).
[Crossref] [PubMed]

1999 (1)

1984 (1)

1974 (1)

Ahmed, N.

A. E. Willner, H. Huang, Y. Yen, Y. Ren, N. Ahmed, G. Xie, C. Bao, L. Li, Y. Cao, Z. Zhao, J. Wang, M. P. J. Lavery, M. Tur, S. Ramachandran, A. F. Molisch, N. Ashrafi, and S. Ashrafi, “Optical communications using orbital angular momentum beams,” Adv. Opt. Photonics 7(1), 66–106 (2015).

H. Huang, G. Xie, Y. Yan, N. Ahmed, Y. Ren, Y. Yue, D. Rogawski, M. J. Willner, B. I. Erkmen, K. M. Birnbaum, S. J. Dolinar, M. P. J. Lavery, M. J. Padgett, M. Tur, and A. E. Willner, “100 Tbit/s free-space data link enabled by three-dimensional multiplexing of orbital angular momentum, polarization, and wavelength,” Opt. Lett. 39(2), 197–200 (2014).
[Crossref] [PubMed]

J. Wang, J. Y. Yang, I. F. Fazal, N. Ahmed, Y. Yan, H. Huang, Y. Ren, Y. Yue, S. Dolinar, M. Tur, and A. E. Willner, “Terabit free-space data transmission employing orbital angular momentum multiplexing,” Nat. Photonics 6(7), 488–496 (2012).
[Crossref]

Aieta, F.

F. Aieta, P. Genevet, M. A. Kats, N. Yu, R. Blanchard, Z. Gaburro, and F. Capasso, “Aberration-free ultrathin flat lenses and axicons at telecom wavelengths based on plasmonic metasurfaces,” Nano Lett. 12(9), 4932–4936 (2012).
[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).
[Crossref] [PubMed]

Alfano, R. R.

Ashrafi, N.

A. E. Willner, H. Huang, Y. Yen, Y. Ren, N. Ahmed, G. Xie, C. Bao, L. Li, Y. Cao, Z. Zhao, J. Wang, M. P. J. Lavery, M. Tur, S. Ramachandran, A. F. Molisch, N. Ashrafi, and S. Ashrafi, “Optical communications using orbital angular momentum beams,” Adv. Opt. Photonics 7(1), 66–106 (2015).

Ashrafi, S.

A. E. Willner, H. Huang, Y. Yen, Y. Ren, N. Ahmed, G. Xie, C. Bao, L. Li, Y. Cao, Z. Zhao, J. Wang, M. P. J. Lavery, M. Tur, S. Ramachandran, A. F. Molisch, N. Ashrafi, and S. Ashrafi, “Optical communications using orbital angular momentum beams,” Adv. Opt. Photonics 7(1), 66–106 (2015).

Bao, C.

A. E. Willner, H. Huang, Y. Yen, Y. Ren, N. Ahmed, G. Xie, C. Bao, L. Li, Y. Cao, Z. Zhao, J. Wang, M. P. J. Lavery, M. Tur, S. Ramachandran, A. F. Molisch, N. Ashrafi, and S. Ashrafi, “Optical communications using orbital angular momentum beams,” Adv. Opt. Photonics 7(1), 66–106 (2015).

Barnett, S. M.

J. Leach, M. J. Padgett, S. M. Barnett, S. Franke-Arnold, and J. Courtial, “Measuring the orbital angular momentum of a single photon,” Phys. Rev. Lett. 88(25), 257901 (2002).
[Crossref] [PubMed]

Beadie, G.

Beijersbergen, M. W.

G. C. G. Berkhout, M. P. J. Lavery, J. Courtial, M. W. Beijersbergen, and M. J. Padgett, “Efficient sorting of orbital angular momentum states of light,” Phys. Rev. Lett. 105(15), 153601 (2010).
[Crossref] [PubMed]

Berkhout, G. C. G.

M. P. J. Lavery, D. J. Robertson, G. C. G. Berkhout, G. D. Love, M. J. Padgett, and J. Courtial, “Refractive elements for the measurement of the orbital angular momentum of a single photon,” Opt. Express 20(3), 2110–2115 (2012).
[Crossref] [PubMed]

G. C. G. Berkhout, M. P. J. Lavery, J. Courtial, M. W. Beijersbergen, and M. J. Padgett, “Efficient sorting of orbital angular momentum states of light,” Phys. Rev. Lett. 105(15), 153601 (2010).
[Crossref] [PubMed]

Biener, G.

Birnbaum, K. M.

Blanchard, R.

F. Aieta, P. Genevet, M. A. Kats, N. Yu, R. Blanchard, Z. Gaburro, and F. Capasso, “Aberration-free ultrathin flat lenses and axicons at telecom wavelengths based on plasmonic metasurfaces,” Nano Lett. 12(9), 4932–4936 (2012).
[Crossref] [PubMed]

Bobrovsky, A.

L. Goldenberg, V. Lisinetskii, A. Ryabchun, A. Bobrovsky, and S. Schrader, “Liquid crystalline azobenzene-containing polymer as a matrix for distributed feedback lasers,” ACS Photonics 1(9), 885–893 (2014).
[Crossref]

Bomzon, Z.

Boyd, R. W.

M. Malik, M. Mirhosseini, M. P. J. Lavery, J. Leach, M. J. Padgett, and R. W. Boyd, “Direct measurement of a 27-dimensional orbital-angular-momentum state vector,” Nat. Commun. 5, 3115 (2014).
[Crossref] [PubMed]

M. Mirhosseini, M. Malik, Z. Shi, and R. W. Boyd, “Efficient separation of the orbital angular momentum eigenstates of light,” Nat. Commun. 4, 2781 (2013).
[Crossref] [PubMed]

M. N. O’Sullivan, M. Mirhosseini, M. Malik, and R. W. Boyd, “Near-perfect sorting of orbital angular momentum and angular position states of light,” Opt. Express 20(22), 24444–24449 (2012).
[Crossref] [PubMed]

Bozinovic, N.

S. Golowich, N. Bozinovic, P. Kristensen, and S. Ramachandran, “Complex mode amplitude measurement for a six-mode optical fiber,” Opt. Express 21(4), 4931–4944 (2013).
[Crossref] [PubMed]

N. Bozinovic, Y. Yue, Y. Ren, M. Tur, P. Kristensen, H. Huang, A. E. Willner, and S. Ramachandran, “Terabit-scale orbital angular momentum mode division multiplexing in fibers,” Science 340(6140), 1545–1548 (2013).
[Crossref] [PubMed]

Brongersma, M. L.

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

Bryngdahl, O.

Cao, Y.

A. E. Willner, H. Huang, Y. Yen, Y. Ren, N. Ahmed, G. Xie, C. Bao, L. Li, Y. Cao, Z. Zhao, J. Wang, M. P. J. Lavery, M. Tur, S. Ramachandran, A. F. Molisch, N. Ashrafi, and S. Ashrafi, “Optical communications using orbital angular momentum beams,” Adv. Opt. Photonics 7(1), 66–106 (2015).

Capasso, F.

F. Aieta, P. Genevet, M. A. Kats, N. Yu, R. Blanchard, Z. Gaburro, and F. Capasso, “Aberration-free ultrathin flat lenses and axicons at telecom wavelengths based on plasmonic metasurfaces,” Nano Lett. 12(9), 4932–4936 (2012).
[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).
[Crossref] [PubMed]

Cederquist, J.

Chigrinov, V.

S. Slussarenko, B. Piccirillo, V. Chigrinov, L. Marrucci, and E. Santamato, “Liquid crystal spatial-mode converters for the orbital angular momentum of light,” J. Opt. 15(2), 025406 (2013).
[Crossref]

Cipparrone, G.

P. Pagliusi, C. Provenzano, A. Mazzulla, L. Giorgini, and G. Cipparrone, “Spectrograph based on a single diffractive element for real-time measurement of circular dichroism,” Appl. Spectrosc. 62(5), 465–468 (2008).
[Crossref] [PubMed]

C. Provenzano, P. Pagliusi, and G. Cipparrone, “Highly efficient liquid crystal based diffraction grating induced by polarization holograms at the aligning surfaces,” Appl. Phys. Lett. 89(12), 121105 (2006).
[Crossref]

Courtial, J.

M. P. J. Lavery, D. J. Robertson, G. C. G. Berkhout, G. D. Love, M. J. Padgett, and J. Courtial, “Refractive elements for the measurement of the orbital angular momentum of a single photon,” Opt. Express 20(3), 2110–2115 (2012).
[Crossref] [PubMed]

G. C. G. Berkhout, M. P. J. Lavery, J. Courtial, M. W. Beijersbergen, and M. J. Padgett, “Efficient sorting of orbital angular momentum states of light,” Phys. Rev. Lett. 105(15), 153601 (2010).
[Crossref] [PubMed]

J. Leach, M. J. Padgett, S. M. Barnett, S. Franke-Arnold, and J. Courtial, “Measuring the orbital angular momentum of a single photon,” Phys. Rev. Lett. 88(25), 257901 (2002).
[Crossref] [PubMed]

M. J. Padgett and J. Courtial, “Poincaré-sphere equivalent for light beams containing orbital angular momentum,” Opt. Lett. 24(7), 430–432 (1999).
[Crossref] [PubMed]

Dolinar, S.

J. Wang, J. Y. Yang, I. F. Fazal, N. Ahmed, Y. Yan, H. Huang, Y. Ren, Y. Yue, S. Dolinar, M. Tur, and A. E. Willner, “Terabit free-space data transmission employing orbital angular momentum multiplexing,” Nat. Photonics 6(7), 488–496 (2012).
[Crossref]

Dolinar, S. J.

Erkmen, B. I.

Fan, P.

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

Fatemi, F. K.

Fazal, I. F.

J. Wang, J. Y. Yang, I. F. Fazal, N. Ahmed, Y. Yan, H. Huang, Y. Ren, Y. Yue, S. Dolinar, M. Tur, and A. E. Willner, “Terabit free-space data transmission employing orbital angular momentum multiplexing,” Nat. Photonics 6(7), 488–496 (2012).
[Crossref]

Franke-Arnold, S.

J. Leach, M. J. Padgett, S. M. Barnett, S. Franke-Arnold, and J. Courtial, “Measuring the orbital angular momentum of a single photon,” Phys. Rev. Lett. 88(25), 257901 (2002).
[Crossref] [PubMed]

Gaburro, Z.

F. Aieta, P. Genevet, M. A. Kats, N. Yu, R. Blanchard, Z. Gaburro, and F. Capasso, “Aberration-free ultrathin flat lenses and axicons at telecom wavelengths based on plasmonic metasurfaces,” Nano Lett. 12(9), 4932–4936 (2012).
[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).
[Crossref] [PubMed]

Genevet, P.

F. Aieta, P. Genevet, M. A. Kats, N. Yu, R. Blanchard, Z. Gaburro, and F. Capasso, “Aberration-free ultrathin flat lenses and axicons at telecom wavelengths based on plasmonic metasurfaces,” Nano Lett. 12(9), 4932–4936 (2012).
[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).
[Crossref] [PubMed]

Giorgini, L.

Glebov, L. B.

Goldenberg, L.

L. Goldenberg, V. Lisinetskii, A. Ryabchun, A. Bobrovsky, and S. Schrader, “Liquid crystalline azobenzene-containing polymer as a matrix for distributed feedback lasers,” ACS Photonics 1(9), 885–893 (2014).
[Crossref]

Golowich, S.

Hasman, E.

Huang, H.

A. E. Willner, H. Huang, Y. Yen, Y. Ren, N. Ahmed, G. Xie, C. Bao, L. Li, Y. Cao, Z. Zhao, J. Wang, M. P. J. Lavery, M. Tur, S. Ramachandran, A. F. Molisch, N. Ashrafi, and S. Ashrafi, “Optical communications using orbital angular momentum beams,” Adv. Opt. Photonics 7(1), 66–106 (2015).

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. Xie, Y. Yan, N. Ahmed, Y. Ren, Y. Yue, D. Rogawski, M. J. Willner, B. I. Erkmen, K. M. Birnbaum, S. J. Dolinar, M. P. J. Lavery, M. J. Padgett, M. Tur, and A. E. Willner, “100 Tbit/s free-space data link enabled by three-dimensional multiplexing of orbital angular momentum, polarization, and wavelength,” Opt. Lett. 39(2), 197–200 (2014).
[Crossref] [PubMed]

N. Bozinovic, Y. Yue, Y. Ren, M. Tur, P. Kristensen, H. Huang, A. E. Willner, and S. Ramachandran, “Terabit-scale orbital angular momentum mode division multiplexing in fibers,” Science 340(6140), 1545–1548 (2013).
[Crossref] [PubMed]

J. Wang, J. Y. Yang, I. F. Fazal, N. Ahmed, Y. Yan, H. Huang, Y. Ren, Y. Yue, S. Dolinar, M. Tur, and A. E. Willner, “Terabit free-space data transmission employing orbital angular momentum multiplexing,” Nat. Photonics 6(7), 488–496 (2012).
[Crossref]

Karimi, E.

Kats, M. A.

F. Aieta, P. Genevet, M. A. Kats, N. Yu, R. Blanchard, Z. Gaburro, and F. Capasso, “Aberration-free ultrathin flat lenses and axicons at telecom wavelengths based on plasmonic metasurfaces,” Nano Lett. 12(9), 4932–4936 (2012).
[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).
[Crossref] [PubMed]

Kimball, B. R.

S. R. Nersisyan, N. V. Tabiryan, D. M. Steeves, and B. R. Kimball, “The promise of diffractive waveplates,” Opt. Photonics News 21(3), 40–45 (2010).
[Crossref]

S. Nersisyan, N. Tabiryan, D. M. Steeves, and B. R. Kimball, “Fabrication of liquid crystal polymer axial waveplates for UV-IR wavelengths,” Opt. Express 17(14), 11926–11934 (2009).
[Crossref] [PubMed]

Kleiner, V.

Kristensen, P.

N. Bozinovic, Y. Yue, Y. Ren, M. Tur, P. Kristensen, H. Huang, A. E. Willner, and S. Ramachandran, “Terabit-scale orbital angular momentum mode division multiplexing in fibers,” Science 340(6140), 1545–1548 (2013).
[Crossref] [PubMed]

S. Ramachadran and P. Kristensen, “Optical vortices in fiber,” Nanophotonics 2(5–6), 455–474 (2013).

S. Golowich, N. Bozinovic, P. Kristensen, and S. Ramachandran, “Complex mode amplitude measurement for a six-mode optical fiber,” Opt. Express 21(4), 4931–4944 (2013).
[Crossref] [PubMed]

Lavery, M. P. J.

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]

A. E. Willner, H. Huang, Y. Yen, Y. Ren, N. Ahmed, G. Xie, C. Bao, L. Li, Y. Cao, Z. Zhao, J. Wang, M. P. J. Lavery, M. Tur, S. Ramachandran, A. F. Molisch, N. Ashrafi, and S. Ashrafi, “Optical communications using orbital angular momentum beams,” Adv. Opt. Photonics 7(1), 66–106 (2015).

H. Huang, G. Xie, Y. Yan, N. Ahmed, Y. Ren, Y. Yue, D. Rogawski, M. J. Willner, B. I. Erkmen, K. M. Birnbaum, S. J. Dolinar, M. P. J. Lavery, M. J. Padgett, M. Tur, and A. E. Willner, “100 Tbit/s free-space data link enabled by three-dimensional multiplexing of orbital angular momentum, polarization, and wavelength,” Opt. Lett. 39(2), 197–200 (2014).
[Crossref] [PubMed]

M. Malik, M. Mirhosseini, M. P. J. Lavery, J. Leach, M. J. Padgett, and R. W. Boyd, “Direct measurement of a 27-dimensional orbital-angular-momentum state vector,” Nat. Commun. 5, 3115 (2014).
[Crossref] [PubMed]

M. P. J. Lavery, D. J. Robertson, G. C. G. Berkhout, G. D. Love, M. J. Padgett, and J. Courtial, “Refractive elements for the measurement of the orbital angular momentum of a single photon,” Opt. Express 20(3), 2110–2115 (2012).
[Crossref] [PubMed]

G. C. G. Berkhout, M. P. J. Lavery, J. Courtial, M. W. Beijersbergen, and M. J. Padgett, “Efficient sorting of orbital angular momentum states of light,” Phys. Rev. Lett. 105(15), 153601 (2010).
[Crossref] [PubMed]

Lawrence, N.

Leach, J.

M. Malik, M. Mirhosseini, M. P. J. Lavery, J. Leach, M. J. Padgett, and R. W. Boyd, “Direct measurement of a 27-dimensional orbital-angular-momentum state vector,” Nat. Commun. 5, 3115 (2014).
[Crossref] [PubMed]

J. Leach, M. J. Padgett, S. M. Barnett, S. Franke-Arnold, and J. Courtial, “Measuring the orbital angular momentum of a single photon,” Phys. Rev. Lett. 88(25), 257901 (2002).
[Crossref] [PubMed]

Li, L.

A. E. Willner, H. Huang, Y. Yen, Y. Ren, N. Ahmed, G. Xie, C. Bao, L. Li, Y. Cao, Z. Zhao, J. Wang, M. P. J. Lavery, M. Tur, S. Ramachandran, A. F. Molisch, N. Ashrafi, and S. Ashrafi, “Optical communications using orbital angular momentum beams,” Adv. Opt. Photonics 7(1), 66–106 (2015).

Lin, D.

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

Lisinetskii, V.

L. Goldenberg, V. Lisinetskii, A. Ryabchun, A. Bobrovsky, and S. Schrader, “Liquid crystalline azobenzene-containing polymer as a matrix for distributed feedback lasers,” ACS Photonics 1(9), 885–893 (2014).
[Crossref]

Love, G. D.

Malik, M.

M. Malik, M. Mirhosseini, M. P. J. Lavery, J. Leach, M. J. Padgett, and R. W. Boyd, “Direct measurement of a 27-dimensional orbital-angular-momentum state vector,” Nat. Commun. 5, 3115 (2014).
[Crossref] [PubMed]

M. Mirhosseini, M. Malik, Z. Shi, and R. W. Boyd, “Efficient separation of the orbital angular momentum eigenstates of light,” Nat. Commun. 4, 2781 (2013).
[Crossref] [PubMed]

M. N. O’Sullivan, M. Mirhosseini, M. Malik, and R. W. Boyd, “Near-perfect sorting of orbital angular momentum and angular position states of light,” Opt. Express 20(22), 24444–24449 (2012).
[Crossref] [PubMed]

Manzo, C.

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]

L. Marrucci, C. Manzo, and D. Paparo, “Pancharatnam-Berry phase optical elements for wave front shaping in the visible domain: switchable hylical modes generation,” Appl. Phys. Lett. 88(22), 221102 (2006).
[Crossref]

Marrucci, L.

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]

S. Slussarenko, B. Piccirillo, V. Chigrinov, L. Marrucci, and E. Santamato, “Liquid crystal spatial-mode converters for the orbital angular momentum of light,” J. Opt. 15(2), 025406 (2013).
[Crossref]

L. Marrucci, C. Manzo, and D. Paparo, “Pancharatnam-Berry phase optical elements for wave front shaping in the visible domain: switchable hylical modes generation,” Appl. Phys. Lett. 88(22), 221102 (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]

Mawet, D.

Mazzulla, A.

Milione, G.

Mirhosseini, M.

M. Malik, M. Mirhosseini, M. P. J. Lavery, J. Leach, M. J. Padgett, and R. W. Boyd, “Direct measurement of a 27-dimensional orbital-angular-momentum state vector,” Nat. Commun. 5, 3115 (2014).
[Crossref] [PubMed]

M. Mirhosseini, M. Malik, Z. Shi, and R. W. Boyd, “Efficient separation of the orbital angular momentum eigenstates of light,” Nat. Commun. 4, 2781 (2013).
[Crossref] [PubMed]

M. N. O’Sullivan, M. Mirhosseini, M. Malik, and R. W. Boyd, “Near-perfect sorting of orbital angular momentum and angular position states of light,” Opt. Express 20(22), 24444–24449 (2012).
[Crossref] [PubMed]

Molina-Terriza, G.

G. Molina-Terriza, J. P. Torres, and L. Torner, “Management of the angular momentum of light: preparation of photons in multidimensional vector states of angular momentum,” Phys. Rev. Lett. 88(1), 013601 (2001).
[Crossref] [PubMed]

Molisch, A. F.

A. E. Willner, H. Huang, Y. Yen, Y. Ren, N. Ahmed, G. Xie, C. Bao, L. Li, Y. Cao, Z. Zhao, J. Wang, M. P. J. Lavery, M. Tur, S. Ramachandran, A. F. Molisch, N. Ashrafi, and S. Ashrafi, “Optical communications using orbital angular momentum beams,” Adv. Opt. Photonics 7(1), 66–106 (2015).

Negro, L. D.

Nersisyan, S.

Nersisyan, S. R.

S. R. Nersisyan, N. V. Tabiryan, D. Mawet, and E. Serabyn, “Improving vector vortex waveplates for high-contrast coronagraphy,” Opt. Express 21(7), 8205–8213 (2013).
[Crossref] [PubMed]

S. R. Nersisyan, N. V. Tabiryan, D. M. Steeves, and B. R. Kimball, “The promise of diffractive waveplates,” Opt. Photonics News 21(3), 40–45 (2010).
[Crossref]

Nguyen, T. A.

Niv, A.

Nolan, D. A.

O’Sullivan, M. N.

Padgett, M. J.

M. Malik, M. Mirhosseini, M. P. J. Lavery, J. Leach, M. J. Padgett, and R. W. Boyd, “Direct measurement of a 27-dimensional orbital-angular-momentum state vector,” Nat. Commun. 5, 3115 (2014).
[Crossref] [PubMed]

H. Huang, G. Xie, Y. Yan, N. Ahmed, Y. Ren, Y. Yue, D. Rogawski, M. J. Willner, B. I. Erkmen, K. M. Birnbaum, S. J. Dolinar, M. P. J. Lavery, M. J. Padgett, M. Tur, and A. E. Willner, “100 Tbit/s free-space data link enabled by three-dimensional multiplexing of orbital angular momentum, polarization, and wavelength,” Opt. Lett. 39(2), 197–200 (2014).
[Crossref] [PubMed]

M. P. J. Lavery, D. J. Robertson, G. C. G. Berkhout, G. D. Love, M. J. Padgett, and J. Courtial, “Refractive elements for the measurement of the orbital angular momentum of a single photon,” Opt. Express 20(3), 2110–2115 (2012).
[Crossref] [PubMed]

G. C. G. Berkhout, M. P. J. Lavery, J. Courtial, M. W. Beijersbergen, and M. J. Padgett, “Efficient sorting of orbital angular momentum states of light,” Phys. Rev. Lett. 105(15), 153601 (2010).
[Crossref] [PubMed]

J. Leach, M. J. Padgett, S. M. Barnett, S. Franke-Arnold, and J. Courtial, “Measuring the orbital angular momentum of a single photon,” Phys. Rev. Lett. 88(25), 257901 (2002).
[Crossref] [PubMed]

M. J. Padgett and J. Courtial, “Poincaré-sphere equivalent for light beams containing orbital angular momentum,” Opt. Lett. 24(7), 430–432 (1999).
[Crossref] [PubMed]

Pagliusi, P.

P. Pagliusi, C. Provenzano, A. Mazzulla, L. Giorgini, and G. Cipparrone, “Spectrograph based on a single diffractive element for real-time measurement of circular dichroism,” Appl. Spectrosc. 62(5), 465–468 (2008).
[Crossref] [PubMed]

C. Provenzano, P. Pagliusi, and G. Cipparrone, “Highly efficient liquid crystal based diffraction grating induced by polarization holograms at the aligning surfaces,” Appl. Phys. Lett. 89(12), 121105 (2006).
[Crossref]

Paparo, D.

L. Marrucci, C. Manzo, and D. Paparo, “Pancharatnam-Berry phase optical elements for wave front shaping in the visible domain: switchable hylical modes generation,” Appl. Phys. Lett. 88(22), 221102 (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]

Piccirillo, B.

S. Slussarenko, B. Piccirillo, V. Chigrinov, L. Marrucci, and E. Santamato, “Liquid crystal spatial-mode converters for the orbital angular momentum of light,” J. Opt. 15(2), 025406 (2013).
[Crossref]

Provenzano, C.

P. Pagliusi, C. Provenzano, A. Mazzulla, L. Giorgini, and G. Cipparrone, “Spectrograph based on a single diffractive element for real-time measurement of circular dichroism,” Appl. Spectrosc. 62(5), 465–468 (2008).
[Crossref] [PubMed]

C. Provenzano, P. Pagliusi, and G. Cipparrone, “Highly efficient liquid crystal based diffraction grating induced by polarization holograms at the aligning surfaces,” Appl. Phys. Lett. 89(12), 121105 (2006).
[Crossref]

Ramachadran, S.

S. Ramachadran and P. Kristensen, “Optical vortices in fiber,” Nanophotonics 2(5–6), 455–474 (2013).

Ramachandran, S.

A. E. Willner, H. Huang, Y. Yen, Y. Ren, N. Ahmed, G. Xie, C. Bao, L. Li, Y. Cao, Z. Zhao, J. Wang, M. P. J. Lavery, M. Tur, S. Ramachandran, A. F. Molisch, N. Ashrafi, and S. Ashrafi, “Optical communications using orbital angular momentum beams,” Adv. Opt. Photonics 7(1), 66–106 (2015).

N. Bozinovic, Y. Yue, Y. Ren, M. Tur, P. Kristensen, H. Huang, A. E. Willner, and S. Ramachandran, “Terabit-scale orbital angular momentum mode division multiplexing in fibers,” Science 340(6140), 1545–1548 (2013).
[Crossref] [PubMed]

S. Golowich, N. Bozinovic, P. Kristensen, and S. Ramachandran, “Complex mode amplitude measurement for a six-mode optical fiber,” Opt. Express 21(4), 4931–4944 (2013).
[Crossref] [PubMed]

Ren, Y.

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]

A. E. Willner, H. Huang, Y. Yen, Y. Ren, N. Ahmed, G. Xie, C. Bao, L. Li, Y. Cao, Z. Zhao, J. Wang, M. P. J. Lavery, M. Tur, S. Ramachandran, A. F. Molisch, N. Ashrafi, and S. Ashrafi, “Optical communications using orbital angular momentum beams,” Adv. Opt. Photonics 7(1), 66–106 (2015).

H. Huang, G. Xie, Y. Yan, N. Ahmed, Y. Ren, Y. Yue, D. Rogawski, M. J. Willner, B. I. Erkmen, K. M. Birnbaum, S. J. Dolinar, M. P. J. Lavery, M. J. Padgett, M. Tur, and A. E. Willner, “100 Tbit/s free-space data link enabled by three-dimensional multiplexing of orbital angular momentum, polarization, and wavelength,” Opt. Lett. 39(2), 197–200 (2014).
[Crossref] [PubMed]

N. Bozinovic, Y. Yue, Y. Ren, M. Tur, P. Kristensen, H. Huang, A. E. Willner, and S. Ramachandran, “Terabit-scale orbital angular momentum mode division multiplexing in fibers,” Science 340(6140), 1545–1548 (2013).
[Crossref] [PubMed]

J. Wang, J. Y. Yang, I. F. Fazal, N. Ahmed, Y. Yan, H. Huang, Y. Ren, Y. Yue, S. Dolinar, M. Tur, and A. E. Willner, “Terabit free-space data transmission employing orbital angular momentum multiplexing,” Nat. Photonics 6(7), 488–496 (2012).
[Crossref]

Robertson, D. J.

Rogawski, D.

Rotar, V.

Ryabchun, A.

L. Goldenberg, V. Lisinetskii, A. Ryabchun, A. Bobrovsky, and S. Schrader, “Liquid crystalline azobenzene-containing polymer as a matrix for distributed feedback lasers,” ACS Photonics 1(9), 885–893 (2014).
[Crossref]

Santamato, E.

S. Slussarenko, B. Piccirillo, V. Chigrinov, L. Marrucci, and E. Santamato, “Liquid crystal spatial-mode converters for the orbital angular momentum of light,” J. Opt. 15(2), 025406 (2013).
[Crossref]

Sarkissian, H.

Schrader, S.

L. Goldenberg, V. Lisinetskii, A. Ryabchun, A. Bobrovsky, and S. Schrader, “Liquid crystalline azobenzene-containing polymer as a matrix for distributed feedback lasers,” ACS Photonics 1(9), 885–893 (2014).
[Crossref]

Serabyn, E.

Serak, S. V.

Shi, Z.

M. Mirhosseini, M. Malik, Z. Shi, and R. W. Boyd, “Efficient separation of the orbital angular momentum eigenstates of light,” Nat. Commun. 4, 2781 (2013).
[Crossref] [PubMed]

Slussarenko, S.

S. Slussarenko, B. Piccirillo, V. Chigrinov, L. Marrucci, and E. Santamato, “Liquid crystal spatial-mode converters for the orbital angular momentum of light,” J. Opt. 15(2), 025406 (2013).
[Crossref]

Steeves, D. M.

S. R. Nersisyan, N. V. Tabiryan, D. M. Steeves, and B. R. Kimball, “The promise of diffractive waveplates,” Opt. Photonics News 21(3), 40–45 (2010).
[Crossref]

S. Nersisyan, N. Tabiryan, D. M. Steeves, and B. R. Kimball, “Fabrication of liquid crystal polymer axial waveplates for UV-IR wavelengths,” Opt. Express 17(14), 11926–11934 (2009).
[Crossref] [PubMed]

Tabiryan, N.

Tabiryan, N. V.

Tai, A. M.

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).
[Crossref] [PubMed]

Torner, L.

G. Molina-Terriza, J. P. Torres, and L. Torner, “Management of the angular momentum of light: preparation of photons in multidimensional vector states of angular momentum,” Phys. Rev. Lett. 88(1), 013601 (2001).
[Crossref] [PubMed]

Torres, J. P.

G. Molina-Terriza, J. P. Torres, and L. Torner, “Management of the angular momentum of light: preparation of photons in multidimensional vector states of angular momentum,” Phys. Rev. Lett. 88(1), 013601 (2001).
[Crossref] [PubMed]

Trevino, J.

Tur, M.

A. E. Willner, H. Huang, Y. Yen, Y. Ren, N. Ahmed, G. Xie, C. Bao, L. Li, Y. Cao, Z. Zhao, J. Wang, M. P. J. Lavery, M. Tur, S. Ramachandran, A. F. Molisch, N. Ashrafi, and S. Ashrafi, “Optical communications using orbital angular momentum beams,” Adv. Opt. Photonics 7(1), 66–106 (2015).

H. Huang, G. Xie, Y. Yan, N. Ahmed, Y. Ren, Y. Yue, D. Rogawski, M. J. Willner, B. I. Erkmen, K. M. Birnbaum, S. J. Dolinar, M. P. J. Lavery, M. J. Padgett, M. Tur, and A. E. Willner, “100 Tbit/s free-space data link enabled by three-dimensional multiplexing of orbital angular momentum, polarization, and wavelength,” Opt. Lett. 39(2), 197–200 (2014).
[Crossref] [PubMed]

N. Bozinovic, Y. Yue, Y. Ren, M. Tur, P. Kristensen, H. Huang, A. E. Willner, and S. Ramachandran, “Terabit-scale orbital angular momentum mode division multiplexing in fibers,” Science 340(6140), 1545–1548 (2013).
[Crossref] [PubMed]

J. Wang, J. Y. Yang, I. F. Fazal, N. Ahmed, Y. Yan, H. Huang, Y. Ren, Y. Yue, S. Dolinar, M. Tur, and A. E. Willner, “Terabit free-space data transmission employing orbital angular momentum multiplexing,” Nat. Photonics 6(7), 488–496 (2012).
[Crossref]

Vaziri, A.

A. Vaziri, G. Weihs, and A. Zeilinger, “Experimental two-photon, three-dimensional entanglement for quantum communication,” Phys. Rev. Lett. 89(24), 240401 (2002).
[Crossref] [PubMed]

Wang, J.

A. E. Willner, H. Huang, Y. Yen, Y. Ren, N. Ahmed, G. Xie, C. Bao, L. Li, Y. Cao, Z. Zhao, J. Wang, M. P. J. Lavery, M. Tur, S. Ramachandran, A. F. Molisch, N. Ashrafi, and S. Ashrafi, “Optical communications using orbital angular momentum beams,” Adv. Opt. Photonics 7(1), 66–106 (2015).

J. Wang, J. Y. Yang, I. F. Fazal, N. Ahmed, Y. Yan, H. Huang, Y. Ren, Y. Yue, S. Dolinar, M. Tur, and A. E. Willner, “Terabit free-space data transmission employing orbital angular momentum multiplexing,” Nat. Photonics 6(7), 488–496 (2012).
[Crossref]

Weihs, G.

A. Vaziri, G. Weihs, and A. Zeilinger, “Experimental two-photon, three-dimensional entanglement for quantum communication,” Phys. Rev. Lett. 89(24), 240401 (2002).
[Crossref] [PubMed]

Willner, A. E.

A. E. Willner, H. Huang, Y. Yen, Y. Ren, N. Ahmed, G. Xie, C. Bao, L. Li, Y. Cao, Z. Zhao, J. Wang, M. P. J. Lavery, M. Tur, S. Ramachandran, A. F. Molisch, N. Ashrafi, and S. Ashrafi, “Optical communications using orbital angular momentum beams,” Adv. Opt. Photonics 7(1), 66–106 (2015).

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. Xie, Y. Yan, N. Ahmed, Y. Ren, Y. Yue, D. Rogawski, M. J. Willner, B. I. Erkmen, K. M. Birnbaum, S. J. Dolinar, M. P. J. Lavery, M. J. Padgett, M. Tur, and A. E. Willner, “100 Tbit/s free-space data link enabled by three-dimensional multiplexing of orbital angular momentum, polarization, and wavelength,” Opt. Lett. 39(2), 197–200 (2014).
[Crossref] [PubMed]

N. Bozinovic, Y. Yue, Y. Ren, M. Tur, P. Kristensen, H. Huang, A. E. Willner, and S. Ramachandran, “Terabit-scale orbital angular momentum mode division multiplexing in fibers,” Science 340(6140), 1545–1548 (2013).
[Crossref] [PubMed]

J. Wang, J. Y. Yang, I. F. Fazal, N. Ahmed, Y. Yan, H. Huang, Y. Ren, Y. Yue, S. Dolinar, M. Tur, and A. E. Willner, “Terabit free-space data transmission employing orbital angular momentum multiplexing,” Nat. Photonics 6(7), 488–496 (2012).
[Crossref]

Willner, M. J.

Xie, G.

Yan, Y.

Yang, J. Y.

J. Wang, J. Y. Yang, I. F. Fazal, N. Ahmed, Y. Yan, H. Huang, Y. Ren, Y. Yue, S. Dolinar, M. Tur, and A. E. Willner, “Terabit free-space data transmission employing orbital angular momentum multiplexing,” Nat. Photonics 6(7), 488–496 (2012).
[Crossref]

Yen, Y.

A. E. Willner, H. Huang, Y. Yen, Y. Ren, N. Ahmed, G. Xie, C. Bao, L. Li, Y. Cao, Z. Zhao, J. Wang, M. P. J. Lavery, M. Tur, S. Ramachandran, A. F. Molisch, N. Ashrafi, and S. Ashrafi, “Optical communications using orbital angular momentum beams,” Adv. Opt. Photonics 7(1), 66–106 (2015).

Yu, N.

F. Aieta, P. Genevet, M. A. Kats, N. Yu, R. Blanchard, Z. Gaburro, and F. Capasso, “Aberration-free ultrathin flat lenses and axicons at telecom wavelengths based on plasmonic metasurfaces,” Nano Lett. 12(9), 4932–4936 (2012).
[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).
[Crossref] [PubMed]

Yue, Y.

H. Huang, G. Xie, Y. Yan, N. Ahmed, Y. Ren, Y. Yue, D. Rogawski, M. J. Willner, B. I. Erkmen, K. M. Birnbaum, S. J. Dolinar, M. P. J. Lavery, M. J. Padgett, M. Tur, and A. E. Willner, “100 Tbit/s free-space data link enabled by three-dimensional multiplexing of orbital angular momentum, polarization, and wavelength,” Opt. Lett. 39(2), 197–200 (2014).
[Crossref] [PubMed]

N. Bozinovic, Y. Yue, Y. Ren, M. Tur, P. Kristensen, H. Huang, A. E. Willner, and S. Ramachandran, “Terabit-scale orbital angular momentum mode division multiplexing in fibers,” Science 340(6140), 1545–1548 (2013).
[Crossref] [PubMed]

J. Wang, J. Y. Yang, I. F. Fazal, N. Ahmed, Y. Yan, H. Huang, Y. Ren, Y. Yue, S. Dolinar, M. Tur, and A. E. Willner, “Terabit free-space data transmission employing orbital angular momentum multiplexing,” Nat. Photonics 6(7), 488–496 (2012).
[Crossref]

Zeilinger, A.

A. Vaziri, G. Weihs, and A. Zeilinger, “Experimental two-photon, three-dimensional entanglement for quantum communication,” Phys. Rev. Lett. 89(24), 240401 (2002).
[Crossref] [PubMed]

Zeldovich, B. Y.

Zhao, Z.

A. E. Willner, H. Huang, Y. Yen, Y. Ren, N. Ahmed, G. Xie, C. Bao, L. Li, Y. Cao, Z. Zhao, J. Wang, M. P. J. Lavery, M. Tur, S. Ramachandran, A. F. Molisch, N. Ashrafi, and S. Ashrafi, “Optical communications using orbital angular momentum beams,” Adv. Opt. Photonics 7(1), 66–106 (2015).

ACS Photonics (1)

L. Goldenberg, V. Lisinetskii, A. Ryabchun, A. Bobrovsky, and S. Schrader, “Liquid crystalline azobenzene-containing polymer as a matrix for distributed feedback lasers,” ACS Photonics 1(9), 885–893 (2014).
[Crossref]

Adv. Opt. Photonics (1)

A. E. Willner, H. Huang, Y. Yen, Y. Ren, N. Ahmed, G. Xie, C. Bao, L. Li, Y. Cao, Z. Zhao, J. Wang, M. P. J. Lavery, M. Tur, S. Ramachandran, A. F. Molisch, N. Ashrafi, and S. Ashrafi, “Optical communications using orbital angular momentum beams,” Adv. Opt. Photonics 7(1), 66–106 (2015).

Appl. Opt. (1)

Appl. Phys. Lett. (2)

L. Marrucci, C. Manzo, and D. Paparo, “Pancharatnam-Berry phase optical elements for wave front shaping in the visible domain: switchable hylical modes generation,” Appl. Phys. Lett. 88(22), 221102 (2006).
[Crossref]

C. Provenzano, P. Pagliusi, and G. Cipparrone, “Highly efficient liquid crystal based diffraction grating induced by polarization holograms at the aligning surfaces,” Appl. Phys. Lett. 89(12), 121105 (2006).
[Crossref]

Appl. Spectrosc. (1)

J. Opt. (1)

S. Slussarenko, B. Piccirillo, V. Chigrinov, L. Marrucci, and E. Santamato, “Liquid crystal spatial-mode converters for the orbital angular momentum of light,” J. Opt. 15(2), 025406 (2013).
[Crossref]

J. Opt. Soc. Am. (1)

Nano Lett. (1)

F. Aieta, P. Genevet, M. A. Kats, N. Yu, R. Blanchard, Z. Gaburro, and F. Capasso, “Aberration-free ultrathin flat lenses and axicons at telecom wavelengths based on plasmonic metasurfaces,” Nano Lett. 12(9), 4932–4936 (2012).
[Crossref] [PubMed]

Nanophotonics (1)

S. Ramachadran and P. Kristensen, “Optical vortices in fiber,” Nanophotonics 2(5–6), 455–474 (2013).

Nat. Commun. (2)

M. Mirhosseini, M. Malik, Z. Shi, and R. W. Boyd, “Efficient separation of the orbital angular momentum eigenstates of light,” Nat. Commun. 4, 2781 (2013).
[Crossref] [PubMed]

M. Malik, M. Mirhosseini, M. P. J. Lavery, J. Leach, M. J. Padgett, and R. W. Boyd, “Direct measurement of a 27-dimensional orbital-angular-momentum state vector,” Nat. Commun. 5, 3115 (2014).
[Crossref] [PubMed]

Nat. Photonics (1)

J. Wang, J. Y. Yang, I. F. Fazal, N. Ahmed, Y. Yan, H. Huang, Y. Ren, Y. Yue, S. Dolinar, M. Tur, and A. E. Willner, “Terabit free-space data transmission employing orbital angular momentum multiplexing,” Nat. Photonics 6(7), 488–496 (2012).
[Crossref]

Opt. Express (7)

Opt. Lett. (7)

N. Lawrence, J. Trevino, and L. D. Negro, “Control of optical orbital angular momentum by Vogel spiral arrays of metallic nanoparticles,” Opt. Lett. 37(24), 5076–5078 (2012).
[Crossref] [PubMed]

M. J. Padgett and J. Courtial, “Poincaré-sphere equivalent for light beams containing orbital angular momentum,” Opt. Lett. 24(7), 430–432 (1999).
[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]

A. Niv, G. Biener, V. Kleiner, and E. Hasman, “Rotating vectorial vortices produced by space-variant subwavelength gratings,” Opt. Lett. 30(21), 2933–2935 (2005).
[Crossref] [PubMed]

H. Sarkissian, S. V. Serak, N. V. Tabiryan, L. B. Glebov, V. Rotar, and B. Y. Zeldovich, “Polarization-controlled switching between diffraction orders in transverse-periodically aligned nematic liquid crystals,” Opt. Lett. 31(15), 2248–2250 (2006).
[Crossref] [PubMed]

Z. Bomzon, G. Biener, V. Kleiner, and E. Hasman, “Space-variant Pancharatnam-Berry phase optical elements with computer-generated subwavelength gratings,” Opt. Lett. 27(13), 1141–1143 (2002).
[Crossref] [PubMed]

H. Huang, G. Xie, Y. Yan, N. Ahmed, Y. Ren, Y. Yue, D. Rogawski, M. J. Willner, B. I. Erkmen, K. M. Birnbaum, S. J. Dolinar, M. P. J. Lavery, M. J. Padgett, M. Tur, and A. E. Willner, “100 Tbit/s free-space data link enabled by three-dimensional multiplexing of orbital angular momentum, polarization, and wavelength,” Opt. Lett. 39(2), 197–200 (2014).
[Crossref] [PubMed]

Opt. Photonics News (1)

S. R. Nersisyan, N. V. Tabiryan, D. M. Steeves, and B. R. Kimball, “The promise of diffractive waveplates,” Opt. Photonics News 21(3), 40–45 (2010).
[Crossref]

Phys. Rev. Lett. (5)

J. Leach, M. J. Padgett, S. M. Barnett, S. Franke-Arnold, and J. Courtial, “Measuring the orbital angular momentum of a single photon,” Phys. Rev. Lett. 88(25), 257901 (2002).
[Crossref] [PubMed]

G. Molina-Terriza, J. P. Torres, and L. Torner, “Management of the angular momentum of light: preparation of photons in multidimensional vector states of angular momentum,” Phys. Rev. Lett. 88(1), 013601 (2001).
[Crossref] [PubMed]

A. Vaziri, G. Weihs, and A. Zeilinger, “Experimental two-photon, three-dimensional entanglement for quantum communication,” Phys. Rev. Lett. 89(24), 240401 (2002).
[Crossref] [PubMed]

G. C. G. Berkhout, M. P. J. Lavery, J. Courtial, M. W. Beijersbergen, and M. J. Padgett, “Efficient sorting of orbital angular momentum states of light,” Phys. Rev. Lett. 105(15), 153601 (2010).
[Crossref] [PubMed]

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]

Science (3)

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]

N. Bozinovic, Y. Yue, Y. Ren, M. Tur, P. Kristensen, H. Huang, A. E. Willner, and S. Ramachandran, “Terabit-scale orbital angular momentum mode division multiplexing in fibers,” Science 340(6140), 1545–1548 (2013).
[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]

Other (4)

T. C. Poon and T. Kim, Engineering Optics with MATLAB (World Scientific Publishing Co., 2006), Ch. 3.

B. E. A. Saleh and M. C. Teich, Fundamentals of Photonics Second Edition (John Wiley and Sons, 2007), Ch. 3.

L. Novotny and B. Hecht, Principles of Nano-Optics (Cambridge University Press, 2006), Ch. 3.

D. L. Andrews, Structured Light and Its Applications: An Introduction to Phase-Structured Beams and Nanoscale Optical Forces (Academic Press, 2008).

Cited By

OSA participates in Crossref's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (8)

Fig. 1
Fig. 1 The angle α(x,y) of an implementation of the (a) transformation α 1 (x,y) and (b) phase correction α 2 (x,y) PBOEs. Two-dimensional slow-axis orientation map of the (c) transformation and (d) phase correction PBOEs.
Fig. 2
Fig. 2 (a) The OAM and SAM sorter, a 4-f imaging system with a transformation PBOE in the Object plane, and phase correction PBOE in the Fourier plane. The sorted angular momentum eigenstates appear in the Image plane. (b) Optical intensity of a linearly polarized input Gaussian beam modulated by a topological phase factor exp(j2lϕ) than propagated 500mm to the transformation PBOE with OAM 2 , λ = 1550nm. (c) Intensity distribution at the Transform plane. The |L SAM component is imaged onto the –x side of the Transform plane while the |R SAM component is imaged onto the + x side, allowing the phase correction PBOE to independently modulate the two SAM states. (d) Intensity at the Image plane. |L SAM is focused to a point onto the + x side and |R SAM onto the -x. The focused spots are displaced in the y-direction according to the OAM eigenstate. Sorter parameters are a = 1.3mm, b = 1, Λ = 1.8mm, and f = 500mm. All intensity profiles are normalized to their own maximum intensity.
Fig. 3
Fig. 3 (a) A superposition of the sorted OAM eigenstates from a Gaussian beam modulated by a phase factor exp(jlϕ) for l = 12, 9, 6, 3, 0, −3, −6, −9, −12 for both left-circular and right-circular polarization. The intensity of each sorter output is normalized to its own maximum. (b) y-position of each sorted OAM and SAM eigenstate. (c) Cross-section along the y-direction of the sorter output for l = 0 – 4.
Fig. 4
Fig. 4 Intensity profile of the (a) L G 0 +1 and (b) L G 0 1 Laguerre-Gaussian modes, and the (c) H G 01 =L G 0 +1 +L G 0 1 Hermite-Gaussian mode. Sorter output for the L G 0 +1 mode (a1) left-circularly polarized, (a2) right-circularly polarized, and (a3) linearlly polarized. (b1), (b2), and (b3) the same for L G 0 1 . (c1), (c2), and (c3) the same for H G 01 . All intensity profiles are normalized to their own maximum.
Fig. 5
Fig. 5 (a) Poincaré-sphere. (b) Fraction of total power in the |L (blue) and |R (red) spots in the PBOE angular momentum sorter output. (c) Equivalent Poincaré-sphere for the L G 0 ±1 modes. (d) Fraction of total power in the L G 0 +1 (blue) and L G 0 1 (red) spots in the PBOE angular momentum sorter output.
Fig. 6
Fig. 6 The intensity profile and structured transverse polarization direction of the (a) TM01, (b) TE01, (d) HE21o, and (e) HE21e vector beams. Sorter results for (c) the TM01 and TE01, and (f) the HE21o and HE21e beams. All intensity profiles are normalized to their own maximum.
Fig. 7
Fig. 7 Intensity profile for L G 0 +1 (a), L G 1 +1 (b), and L G 2 +1 (c). (d) Intensity cross-sections of the sorter output along the + 1 OAM y-offset for L G 0 +1 (blue), L G 1 +1 (red), and L G 2 +1 (green). The inset shows the two-dimensional intensity profiles of these results. Each intensity profile and cross-section is normalized to the maximum value of the intensity profile. The sorter parameterΛwas decreased to 444μm to increase separation between SAM states.
Fig. 8
Fig. 8 (a1-d1) Structured intensity and polarization patterns of the hybrid modes composed of different superpositions of the L G 0 ±1 , L G 0 ±3 , L G 0 ±5 , L G 1 ±1 , L G 1 ±3 , and L G 1 ±5 cavity modes. (a2-d2) The sorter output for each of the coresponding hybrid modes. The exact cavity mode components of the modes for each SAM state are annotated on the figure. The l = ± 1 components contribute twice the power to the total field as each of the others. All intensity profiles are normalized to their own maximum.

Equations (7)

Equations on this page are rendered with MathJax. Learn more.

M(x,y)=[ cos2α(x,y) sin2α(x,y) sin2α(x,y) cos2α(x,y) ].
α 1 (x,y)= πa λf ( y tan 1 ( y x )xln( x 2 + y 2 b )+x ),
α 2 (x,y)= π Λ x+ πab λf { ( 1 )exp( x a ) cos( y a ); x0 ( +1 ) exp( + x a )cos( y a ); x<0 ,
L G m l ( x,y;z=0 )= ( | x 2 + y 2 | W o ) l L m l ( 2( x 2 + y 2 ) W 0 2 )exp( ( x 2 + y 2 ) W 0 2 jlφ ),
H G pq (x,y)= W o p+q p x p y q G 0 (x,y),
[ U x U y ]=[ L G m l L G m l exp( j( θ+ π 2 ) ) ],
[ U x U y ]=[ L G m +|l| cos( θ 2 )L G m |l| sin( θ 2 ) jL G m +|l| cos( θ 2 )jL G m |l| sin( θ 2 ) ],

Metrics