Abstract

A propagation model of vector beams generated by metasurfaces based on vector diffraction theory is established theoretically and verified experimentally. Considering the Pancharatnam-Berry phase introduced by the metasurface, analytical forms of vector beams for arbitrary incident polarization and topological charge of metasurfaces are found in the Fresnel and Fraunhofer diffraction regions, respectively. The complex amplitude of the resultant vector beam can be described in terms of a confluent hypergeometric function, with an intensity profile that manifests concentric rings in the Fresnel region and a single ring in the Fraunhofer one. Fraunhofer diffraction provides a method to create vector beams with simultaneously high purity and modal power. Further experiments verify the theoretical results.

© 2016 Optical Society of America

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2016 (2)

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(5), 327–332 (2016).
[Crossref]

W. Shu, Y. Ke, Y. Liu, X. Ling, H. Luo, and X. Yin, “Radial spin Hall effect of light,” Phys. Rev. A 93(1), 013839 (2016).
[Crossref]

2015 (7)

J. A. Davis, N. Hashimoto, M. Kurihara, E. Hurtado, M. Pierce, M. M. Sánchez-López, K. Badham, and I. Moreno, “Analysis of a segmented q-plate tunable retarder for the generation of first-order vector beams,” Appl. Opt. 54(32), 9583–9590 (2015).
[Crossref] [PubMed]

K. Y. Bliokh, F. J. Rodríguez-Fortuño, F. Nori, and A. V. Zayats, “Spin-orbit interactions of light,” Nat. Photonics 9(12), 796–808 (2015).
[Crossref]

P. Chen, W. Ji, B.-Y. Wei, W. Hu, V. Chigrinov, and Y.-Q. Lu, “Generation of arbitrary vector beams with liquid crystal polarization converters and vector-photoaligned q-plates,” Appl. Phys. Lett. 107(24), 241102 (2015).
[Crossref]

G. Milione, A. Dudley, T. A. Nguyen, O. Chakraborty, E. Karimi, and A. Forbes, “Measuring the self-healing of the spatially inhomogeneous states of polarization of vector Bessel beams,” J. Opt. 17(3), 035617 (2015).
[Crossref]

V. D’Ambrosio, F. Baccari, S. Slussarenko, L. Marrucci, and F. Sciarrino, “Arbitrary, direct and deterministic manipulation of vector beams via electrically-tuned q-plates,” Sci. Report 5, 7840 (2015).
[Crossref]

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]

G. Milione, T. A. Nguyen, J. Leach, D. A. Nolan, and R. R. Alfano, “Using the nonseparability of vector beams to encode information for optical communication,” Opt. Lett. 40(21), 4887–4890 (2015).
[Crossref] [PubMed]

2014 (2)

Y. Liu, X. Ling, X. Yi, X. Zhou, H. Luo, and S. Wen, “Realization of polarization evolution on higher-order Poincaré sphere with metasurface,” Appl. Phys. Lett. 104(19), 191110 (2014).
[Crossref]

X. Ling, X. Zhou, W. Shu, H. Luo, and S. Wen, “Realization of tunable photonic spin hall effect by tailoring the Pancharatnam-Berry phase,” Sci. Rep. 4, 5557 (2014).
[Crossref] [PubMed]

2013 (3)

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

D. Maluenda, I. Juvells, R. Martínez-Herrero, and A. Carnicer, “Reconfigurable beams with arbitrary polarization and shape distributions at a given plane,” Opt. Express 21(5), 5424–5431 (2013).
[Crossref]

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

2012 (5)

E. J. Galvez, S. Khadka, W. H. Schubert, and S. Nomoto, “Poincaré-beam patterns produced by nonseparable superpositions of Laguerre-Gauss and polarization modes of light,” Appl. Opt. 51(15), 2925–2934 (2012).
[Crossref] [PubMed]

V. D’Ambrosio, E. Nagali, S. P. Walborn, L. Aolita, S. Slussarenko, L. Marrucci, and F. Sciarrino, “Complete experimental toolbox for alignment-free quantum communication,” Nat. Commun. 3, 961 (2012).
[Crossref]

F. Cardano, E. Karimi, S. Slussarenko, L. Marrucci, C. de Lisio, and E. Santamato, “Polarization pattern of vector vortex beams generated by q-plates with different topological charges,” Appl. Opt. 51(10), C1–C6 (2012).
[Crossref] [PubMed]

X. Ling, X. Zhou, H. Luo, and S. Wen, “Steering far-field spin-dependent splitting of light by inhomogeneous anisotropic media,” Phys. Rev. A 86(5), 053824 (2012).
[Crossref]

M. Kang, J. Chen, B. Gu, Y. Li, L. T. Vuong, and H.-T. Wang, “Spatial splitting of spin states in subwavelength metallic microstructures via partial conversion of spin-to-orbital angular momentum,” Phys. Rev. A 85(3), 035801 (2012).
[Crossref]

2011 (5)

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

M. Beresna, M. Gecevičius, P. G. Kazansky, and T. Gertus, “Radially polarized optical vortex converter created by femtosecond laser nanostructuring of glass,” Appl. Phys. Lett. 98(20), 201101 (2011).
[Crossref]

M. Beresna, M. Gecevičius, and P. G. Kazansky, “Polarization sensitive elements fabricated by femtosecond laser nanostructuring of glass,” Opt. Mat. Express 1(4), 783–795 (2011).
[Crossref]

A. Holleczek, A. Aiello, C. Gabriel, C. Marquardt, and G. Leuchs, “Classical and quantum properties of cylindrically polarized states of light,” Opt. Express 19(10), 9714–9736 (2011).
[Crossref] [PubMed]

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

2010 (4)

C. Hnatovsky, V. G. Shvedov, W. Krolikowski, and A. V. Rode, “Materials processing with a tightly focused femtosecond laser vortex pulse,” Opt. Lett. 35(20), 3417–3419 (2010).
[Crossref] [PubMed]

B. J. Roxworthy and K. C. Toussaint, “Optical trapping with π-phase cylindrical vector beams,” New J. Phys. 12(7), 073012 (2010).
[Crossref]

A. M. Beckley, T. G. Brown, and M. A. Alonso, “Full Poincaré beams,” Opt. Express 18(10), 10777–10785 (2010).
[Crossref] [PubMed]

E. Karimi, S. Slussarenko, B. Piccirillo, L. Marrucci, and E. Santamato, “Polarization-controlled evolution of light transverse modes and associated Pancharatnam geometric phase in orbital angular momentum,” Phys. Rev. A 81(5), 053813 (2010).
[Crossref]

2009 (2)

2008 (2)

A. Ya. Bekshaev and A. I. Karamoch, “Spatial characteristics of vortex light beams produced by diffraction gratings with embedded phase singularity,” Opt. Commun. 281(6), 1366–1374 (2008).
[Crossref]

V. V. Kotlyar and A. A. Kovalev, “Family of hypergeometric laser beams,” J. Opt. Soc. Am. A 25(1), 262–270 (2008).
[Crossref]

2007 (5)

2006 (3)

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]

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]

A. F. Abouraddy and K. C. Toussaint, “Three-dimensional polarization control in microscopy,” Phys. Rev. Lett. 96(15), 153901 (2006).
[Crossref] [PubMed]

2005 (2)

2004 (2)

V. A. Pas’ko, I. V. Basistiy, M. V. Vasnetsov, and M. S. Soskin, “Analysis of optical vortex beams with integer and fractional topological charge,” Proc. SPIE 5477, 83–88 (2004).
[Crossref]

M. V. Berry, “Optical vortices evolving from helicoidal integer and fractional phase steps,” J. Opt. A 6(4), 259–268 (2004).
[Crossref]

2003 (2)

G. Peele and K. A. Nugent, “X-ray vortex beams: a theoretical analysis,” Opt. Express 11(19), 2315–2322 (2003).
[Crossref] [PubMed]

R. Dorn, S. Quabis, and G. Leuchs, “Sharper focus for a radially polarized light beam,” Phys. Rev. Lett. 91(23), 233901 (2003).
[Crossref] [PubMed]

2002 (2)

A. Ciattoni, B. Crosignanic, and P. D. Porto, “Vectorial analytical description of propagation of a highly nonparaxial beam,” Opt. Commun. 202(1), 17–20 (2002).
[Crossref]

Z. Bomzon, G. Biener, V. Kleiner, and E. Hasman, “Radially and azimuthally polarized beams generated by space-variant dielectric subwavelength gratings,” Opt. Lett. 27(5), 285–287 (2002).
[Crossref]

2001 (1)

L. Novotny, M. R. Beversluis, K. S. Youngworth, and T. G. Brown, “Longitudinal field modes probed by single molecules,” Phys. Rev. Lett. 86(23), 5251–5254 (2001).
[Crossref] [PubMed]

1998 (1)

1996 (1)

1995 (1)

W. Kimura, G. H. Kim, R. D. Romea, L. C. Steinhauer, I. V. Pogorelsky, K. P. Kusche, R. C. Fernow, X. Wang, and Y. Liu, “Laser acceleration of relativistic electrons using the inverse Cherenkov effect,” Phys. Rev. Lett. 74(4), 546–549 (1995).
[Crossref] [PubMed]

1993 (1)

G. Indebetouw, “Optical vortices and their propagation,” J. Mod. Opt. 40(1), 73–87 (1993).
[Crossref]

1987 (1)

M. V. Berry, “The adiabatic phase and Pancharatnams phase for polarized light,” J. Mod. Opt. 34(11), 1401–1407 (1987).
[Crossref]

1974 (1)

M. J. Stephen and J. P. Straley, “Physics of liquid crystals,” Rev. Mod. Phys. 46(4), 617–704 (1974).
[Crossref]

1956 (1)

S. Pancharatnam, “Generalized theory of interference, and its applications,” Proc. Indian Acad. Sci., Sect. A 44(5), 247–262 (1956).

Abouraddy, A. F.

A. F. Abouraddy and K. C. Toussaint, “Three-dimensional polarization control in microscopy,” Phys. Rev. Lett. 96(15), 153901 (2006).
[Crossref] [PubMed]

Ahmad, M. A.

Aiello, A.

Alfano, R. R.

Almazov, A. A.

Alonso, M. A.

Aolita, L.

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

V. D’Ambrosio, E. Nagali, S. P. Walborn, L. Aolita, S. Slussarenko, L. Marrucci, and F. Sciarrino, “Complete experimental toolbox for alignment-free quantum communication,” Nat. Commun. 3, 961 (2012).
[Crossref]

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

Quabis, S.

R. Dorn, S. Quabis, and G. Leuchs, “Sharper focus for a radially polarized light beam,” Phys. Rev. Lett. 91(23), 233901 (2003).
[Crossref] [PubMed]

Re, L. D.

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

Ren, Y.

Ritsch-Marte, M.

C. Maurer, A. Jesacher, S. Fürhapter, S. Bernet, and M. Ritsch-Marte, “Tailoring of arbitrary optical vector beams,” New J. Phys. 9(3), 78 (2007).
[Crossref]

Rode, A. V.

Rodríguez-Fortuño, F. J.

K. Y. Bliokh, F. J. Rodríguez-Fortuño, F. Nori, and A. V. Zayats, “Spin-orbit interactions of light,” Nat. Photonics 9(12), 796–808 (2015).
[Crossref]

Romea, R. D.

W. Kimura, G. H. Kim, R. D. Romea, L. C. Steinhauer, I. V. Pogorelsky, K. P. Kusche, R. C. Fernow, X. Wang, and Y. Liu, “Laser acceleration of relativistic electrons using the inverse Cherenkov effect,” Phys. Rev. Lett. 74(4), 546–549 (1995).
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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(5), 327–332 (2016).
[Crossref]

Roxworthy, B. J.

B. J. Roxworthy and K. C. Toussaint, “Optical trapping with π-phase cylindrical vector beams,” New J. Phys. 12(7), 073012 (2010).
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Rozas, D.

Ryzhik, I. M.

I. S. Gradshteyn and I. M. Ryzhik, Table of Integrals, Series, and Products, 7th ed. (Academic Press, 2007).

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Saleh, B. E. A.

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

Sánchez-López, M. M.

Santamato, E.

Schadt, M.

Schubert, W. H.

Sciarrino, F.

V. D’Ambrosio, F. Baccari, S. Slussarenko, L. Marrucci, and F. Sciarrino, “Arbitrary, direct and deterministic manipulation of vector beams via electrically-tuned q-plates,” Sci. Report 5, 7840 (2015).
[Crossref]

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

V. D’Ambrosio, E. Nagali, S. P. Walborn, L. Aolita, S. Slussarenko, L. Marrucci, and F. Sciarrino, “Complete experimental toolbox for alignment-free quantum communication,” Nat. Commun. 3, 961 (2012).
[Crossref]

Shu, W.

W. Shu, Y. Ke, Y. Liu, X. Ling, H. Luo, and X. Yin, “Radial spin Hall effect of light,” Phys. Rev. A 93(1), 013839 (2016).
[Crossref]

X. Ling, X. Zhou, W. Shu, H. Luo, and S. Wen, “Realization of tunable photonic spin hall effect by tailoring the Pancharatnam-Berry phase,” Sci. Rep. 4, 5557 (2014).
[Crossref] [PubMed]

Shvedov, V. G.

Slussarenko, S.

V. D’Ambrosio, F. Baccari, S. Slussarenko, L. Marrucci, and F. Sciarrino, “Arbitrary, direct and deterministic manipulation of vector beams via electrically-tuned q-plates,” Sci. Report 5, 7840 (2015).
[Crossref]

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

V. D’Ambrosio, E. Nagali, S. P. Walborn, L. Aolita, S. Slussarenko, L. Marrucci, and F. Sciarrino, “Complete experimental toolbox for alignment-free quantum communication,” Nat. Commun. 3, 961 (2012).
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E. Karimi, S. Slussarenko, B. Piccirillo, L. Marrucci, and E. Santamato, “Polarization-controlled evolution of light transverse modes and associated Pancharatnam geometric phase in orbital angular momentum,” Phys. Rev. A 81(5), 053813 (2010).
[Crossref]

Soifer, V. A.

Soskin, M. S.

V. A. Pas’ko, I. V. Basistiy, M. V. Vasnetsov, and M. S. Soskin, “Analysis of optical vortex beams with integer and fractional topological charge,” Proc. SPIE 5477, 83–88 (2004).
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Spagnolo, N.

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

Stalder, M.

Steinhauer, L. C.

W. Kimura, G. H. Kim, R. D. Romea, L. C. Steinhauer, I. V. Pogorelsky, K. P. Kusche, R. C. Fernow, X. Wang, and Y. Liu, “Laser acceleration of relativistic electrons using the inverse Cherenkov effect,” Phys. Rev. Lett. 74(4), 546–549 (1995).
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M. J. Stephen and J. P. Straley, “Physics of liquid crystals,” Rev. Mod. Phys. 46(4), 617–704 (1974).
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M. J. Stephen and J. P. Straley, “Physics of liquid crystals,” Rev. Mod. Phys. 46(4), 617–704 (1974).
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Sztul, H. I.

G. Milione, H. I. Sztul, D. A. Nolan, and R. R. Alfano, “Higher-order Poincaré sphere, Stokes parameters, and the angular momentum of light,” Phys. Rev. Lett. 107(5), 053601 (2011).
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B. J. Roxworthy and K. C. Toussaint, “Optical trapping with π-phase cylindrical vector beams,” New J. Phys. 12(7), 073012 (2010).
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A. F. Abouraddy and K. C. Toussaint, “Three-dimensional polarization control in microscopy,” Phys. Rev. Lett. 96(15), 153901 (2006).
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Turunen, J.

Vasnetsov, M. V.

V. A. Pas’ko, I. V. Basistiy, M. V. Vasnetsov, and M. S. Soskin, “Analysis of optical vortex beams with integer and fractional topological charge,” Proc. SPIE 5477, 83–88 (2004).
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M. Kang, J. Chen, B. Gu, Y. Li, L. T. Vuong, and H.-T. Wang, “Spatial splitting of spin states in subwavelength metallic microstructures via partial conversion of spin-to-orbital angular momentum,” Phys. Rev. A 85(3), 035801 (2012).
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Walborn, S. P.

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

V. D’Ambrosio, E. Nagali, S. P. Walborn, L. Aolita, S. Slussarenko, L. Marrucci, and F. Sciarrino, “Complete experimental toolbox for alignment-free quantum communication,” Nat. Commun. 3, 961 (2012).
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Wang, H. T.

Wang, H.-T.

M. Kang, J. Chen, B. Gu, Y. Li, L. T. Vuong, and H.-T. Wang, “Spatial splitting of spin states in subwavelength metallic microstructures via partial conversion of spin-to-orbital angular momentum,” Phys. Rev. A 85(3), 035801 (2012).
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Wang, X.

W. Kimura, G. H. Kim, R. D. Romea, L. C. Steinhauer, I. V. Pogorelsky, K. P. Kusche, R. C. Fernow, X. Wang, and Y. Liu, “Laser acceleration of relativistic electrons using the inverse Cherenkov effect,” Phys. Rev. Lett. 74(4), 546–549 (1995).
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Wang, X. L.

Wei, B.-Y.

P. Chen, W. Ji, B.-Y. Wei, W. Hu, V. Chigrinov, and Y.-Q. Lu, “Generation of arbitrary vector beams with liquid crystal polarization converters and vector-photoaligned q-plates,” Appl. Phys. Lett. 107(24), 241102 (2015).
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Wen, S.

Y. Liu, X. Ling, X. Yi, X. Zhou, H. Luo, and S. Wen, “Realization of polarization evolution on higher-order Poincaré sphere with metasurface,” Appl. Phys. Lett. 104(19), 191110 (2014).
[Crossref]

X. Ling, X. Zhou, W. Shu, H. Luo, and S. Wen, “Realization of tunable photonic spin hall effect by tailoring the Pancharatnam-Berry phase,” Sci. Rep. 4, 5557 (2014).
[Crossref] [PubMed]

X. Ling, X. Zhou, H. Luo, and S. Wen, “Steering far-field spin-dependent splitting of light by inhomogeneous anisotropic media,” Phys. Rev. A 86(5), 053824 (2012).
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Wolf, E.

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Ya. Bekshaev, A.

A. Ya. Bekshaev and A. I. Karamoch, “Spatial characteristics of vortex light beams produced by diffraction gratings with embedded phase singularity,” Opt. Commun. 281(6), 1366–1374 (2008).
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Yi, X.

Y. Liu, X. Ling, X. Yi, X. Zhou, H. Luo, and S. Wen, “Realization of polarization evolution on higher-order Poincaré sphere with metasurface,” Appl. Phys. Lett. 104(19), 191110 (2014).
[Crossref]

Yin, X.

W. Shu, Y. Ke, Y. Liu, X. Ling, H. Luo, and X. Yin, “Radial spin Hall effect of light,” Phys. Rev. A 93(1), 013839 (2016).
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Youngworth, K. S.

L. Novotny, M. R. Beversluis, K. S. Youngworth, and T. G. Brown, “Longitudinal field modes probed by single molecules,” Phys. Rev. Lett. 86(23), 5251–5254 (2001).
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Zayats, A. V.

K. Y. Bliokh, F. J. Rodríguez-Fortuño, F. Nori, and A. V. Zayats, “Spin-orbit interactions of light,” Nat. Photonics 9(12), 796–808 (2015).
[Crossref]

Zhan, Q.

Zhang, S.

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

Zhao, H. F.

Zhou, X.

Y. Liu, X. Ling, X. Yi, X. Zhou, H. Luo, and S. Wen, “Realization of polarization evolution on higher-order Poincaré sphere with metasurface,” Appl. Phys. Lett. 104(19), 191110 (2014).
[Crossref]

X. Ling, X. Zhou, W. Shu, H. Luo, and S. Wen, “Realization of tunable photonic spin hall effect by tailoring the Pancharatnam-Berry phase,” Sci. Rep. 4, 5557 (2014).
[Crossref] [PubMed]

X. Ling, X. Zhou, H. Luo, and S. Wen, “Steering far-field spin-dependent splitting of light by inhomogeneous anisotropic media,” Phys. Rev. A 86(5), 053824 (2012).
[Crossref]

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Appl. Phys. Lett. (3)

M. Beresna, M. Gecevičius, P. G. Kazansky, and T. Gertus, “Radially polarized optical vortex converter created by femtosecond laser nanostructuring of glass,” Appl. Phys. Lett. 98(20), 201101 (2011).
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Y. Liu, X. Ling, X. Yi, X. Zhou, H. Luo, and S. Wen, “Realization of polarization evolution on higher-order Poincaré sphere with metasurface,” Appl. Phys. Lett. 104(19), 191110 (2014).
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P. Chen, W. Ji, B.-Y. Wei, W. Hu, V. Chigrinov, and Y.-Q. Lu, “Generation of arbitrary vector beams with liquid crystal polarization converters and vector-photoaligned q-plates,” Appl. Phys. Lett. 107(24), 241102 (2015).
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J. Opt. Soc. Am. B (1)

Nano Lett. (1)

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

Nat. Commun. (2)

V. D’Ambrosio, E. Nagali, S. P. Walborn, L. Aolita, S. Slussarenko, L. Marrucci, and F. Sciarrino, “Complete experimental toolbox for alignment-free quantum communication,” Nat. Commun. 3, 961 (2012).
[Crossref]

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

Nat. Photonics (2)

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(5), 327–332 (2016).
[Crossref]

K. Y. Bliokh, F. J. Rodríguez-Fortuño, F. Nori, and A. V. Zayats, “Spin-orbit interactions of light,” Nat. Photonics 9(12), 796–808 (2015).
[Crossref]

New J. Phys. (2)

B. J. Roxworthy and K. C. Toussaint, “Optical trapping with π-phase cylindrical vector beams,” New J. Phys. 12(7), 073012 (2010).
[Crossref]

C. Maurer, A. Jesacher, S. Fürhapter, S. Bernet, and M. Ritsch-Marte, “Tailoring of arbitrary optical vector beams,” New J. Phys. 9(3), 78 (2007).
[Crossref]

Opt. Commun. (2)

A. Ciattoni, B. Crosignanic, and P. D. Porto, “Vectorial analytical description of propagation of a highly nonparaxial beam,” Opt. Commun. 202(1), 17–20 (2002).
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A. Ya. Bekshaev and A. I. Karamoch, “Spatial characteristics of vortex light beams produced by diffraction gratings with embedded phase singularity,” Opt. Commun. 281(6), 1366–1374 (2008).
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Opt. Express (6)

Opt. Lett. (10)

C. Hnatovsky, V. G. Shvedov, W. Krolikowski, and A. V. Rode, “Materials processing with a tightly focused femtosecond laser vortex pulse,” Opt. Lett. 35(20), 3417–3419 (2010).
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G. Milione, M. P. J. Lavery, H. Huang, Y. Ren, G. Xie, T. A. Nguyen, E. Karimi, L. Marrucci, D. A. Nolan, R. R. Alfano, and A. E. Willner, “4 × 20 Gbit/s mode division multiplexing over free space using vector modes and a q-plate mode (de)multiplexer,” Opt. Lett. 40(9), 1980–1983 (2015).
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G. Milione, T. A. Nguyen, J. Leach, D. A. Nolan, and R. R. Alfano, “Using the nonseparability of vector beams to encode information for optical communication,” Opt. Lett. 40(21), 4887–4890 (2015).
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X. L. Wang, J. P. Ding, W. J. Ni, C. S. Guo, and H. T. Wang, “Generation of arbitrary vector beams with a spatial light modulator and a common path interferometric arrangement,” Opt. Lett. 32(24), 3549–3551 (2007).
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E. Karimi, B. Piccirillo, L. Marrucci, and E. Santamato, “Light propagation in a birefringent plate with topological charge,” Opt. Lett. 34(8), 1225–1227 (2009).
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G. Machavariani, Y. Lumer, I. Moshe, A. Meir, and S. Jackel, “Efficient extracavity generation of radially and azimuthally polarized beams,” Opt. Lett. 32(11), 1468–1470 (2007).
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Opt. Mat. Express (1)

M. Beresna, M. Gecevičius, and P. G. Kazansky, “Polarization sensitive elements fabricated by femtosecond laser nanostructuring of glass,” Opt. Mat. Express 1(4), 783–795 (2011).
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Phys. Rev. A (4)

E. Karimi, S. Slussarenko, B. Piccirillo, L. Marrucci, and E. Santamato, “Polarization-controlled evolution of light transverse modes and associated Pancharatnam geometric phase in orbital angular momentum,” Phys. Rev. A 81(5), 053813 (2010).
[Crossref]

X. Ling, X. Zhou, H. Luo, and S. Wen, “Steering far-field spin-dependent splitting of light by inhomogeneous anisotropic media,” Phys. Rev. A 86(5), 053824 (2012).
[Crossref]

W. Shu, Y. Ke, Y. Liu, X. Ling, H. Luo, and X. Yin, “Radial spin Hall effect of light,” Phys. Rev. A 93(1), 013839 (2016).
[Crossref]

M. Kang, J. Chen, B. Gu, Y. Li, L. T. Vuong, and H.-T. Wang, “Spatial splitting of spin states in subwavelength metallic microstructures via partial conversion of spin-to-orbital angular momentum,” Phys. Rev. A 85(3), 035801 (2012).
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Phys. Rev. Lett. (6)

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).
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R. Dorn, S. Quabis, and G. Leuchs, “Sharper focus for a radially polarized light beam,” Phys. Rev. Lett. 91(23), 233901 (2003).
[Crossref] [PubMed]

A. F. Abouraddy and K. C. Toussaint, “Three-dimensional polarization control in microscopy,” Phys. Rev. Lett. 96(15), 153901 (2006).
[Crossref] [PubMed]

L. Novotny, M. R. Beversluis, K. S. Youngworth, and T. G. Brown, “Longitudinal field modes probed by single molecules,” Phys. Rev. Lett. 86(23), 5251–5254 (2001).
[Crossref] [PubMed]

W. Kimura, G. H. Kim, R. D. Romea, L. C. Steinhauer, I. V. Pogorelsky, K. P. Kusche, R. C. Fernow, X. Wang, and Y. Liu, “Laser acceleration of relativistic electrons using the inverse Cherenkov effect,” Phys. Rev. Lett. 74(4), 546–549 (1995).
[Crossref] [PubMed]

G. Milione, H. I. Sztul, D. A. Nolan, and R. R. Alfano, “Higher-order Poincaré sphere, Stokes parameters, and the angular momentum of light,” Phys. Rev. Lett. 107(5), 053601 (2011).
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Proc. SPIE (1)

V. A. Pas’ko, I. V. Basistiy, M. V. Vasnetsov, and M. S. Soskin, “Analysis of optical vortex beams with integer and fractional topological charge,” Proc. SPIE 5477, 83–88 (2004).
[Crossref]

Prog. Opt. (1)

E. Hasman, G. Biener, A. Niv, and V. Kleiner, “Space-variant polarization manipulation,” Prog. Opt. 47215–289 (2005).
[Crossref]

Rev. Mod. Phys. (1)

M. J. Stephen and J. P. Straley, “Physics of liquid crystals,” Rev. Mod. Phys. 46(4), 617–704 (1974).
[Crossref]

Sci. Rep. (1)

X. Ling, X. Zhou, W. Shu, H. Luo, and S. Wen, “Realization of tunable photonic spin hall effect by tailoring the Pancharatnam-Berry phase,” Sci. Rep. 4, 5557 (2014).
[Crossref] [PubMed]

Sci. Report (1)

V. D’Ambrosio, F. Baccari, S. Slussarenko, L. Marrucci, and F. Sciarrino, “Arbitrary, direct and deterministic manipulation of vector beams via electrically-tuned q-plates,” Sci. Report 5, 7840 (2015).
[Crossref]

Other (4)

M. Born and E. Wolf, Principles of Optics (Cambridge University Press, 1999).
[Crossref]

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

J. W. Goodman, Introduction to Fourier Optics, 3rd ed. (Roberts and Company Publishers, 2005).

I. S. Gradshteyn and I. M. Ryzhik, Table of Integrals, Series, and Products, 7th ed. (Academic Press, 2007).

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Figures (9)

Fig. 1
Fig. 1 (a) Experimental setup to generate vector beams. A He-Ne laser (632.8 nm, 17 mW, Thorlabs HNL210L-EC) outputs a linearly polarized Gaussian beam. GLP, Glan laser polarizer; QWP, quarter-wave plate; CCD, charge coupled device (Coherent LaserCam HR). (b) Schematic illustrations of the orientation of local optical axes in three pieces of metasurfaces used in the experiments.
Fig. 2
Fig. 2 Normalized transverse intensities and local polarization distributions of vector beams generated with metasurfaces of different topological charge q. The left, middle and right columns correspond to q = 0.5, 1 and 1.5, respectively. The top and bottom rows are theoretical and experimental results, respectively.
Fig. 3
Fig. 3 The radial intensity distributions for vector beams generated with metasurfaces of different topological charge q. (a) and (b) are theoretical and experimental results measured at z = 50 cm, respectively.
Fig. 4
Fig. 4 The radial intensity distributions for vector beam measured at different propagation distances. (a) and (b) are theoretical and experimental results for the case q = 1, respectively. The intensities are normalized by the center intensity of the incident Gaussian beam.
Fig. 5
Fig. 5 The intensity distributions of a vector beam passing through a linear polarizer. The transmission axis of the polarizer is indicated by the arrow at the upper left corner. The top and bottom rows are theoretical and experimental results, respectively. Here q = 1 and z = 50 cm.
Fig. 6
Fig. 6 Stokes parameters for the case q = 1 and z = 50 cm. The top and bottom rows are respectively theoretical and experimental results, corresponding to Figs. 2(c) and 2(d).
Fig. 7
Fig. 7 Distributions of normalized intensity and polarization of vector beam for the case q = 1 in the Fraunhofer region (f = 100 cm). (a) and (b) are theoretical and experimental results, respectively. (c) and (d) are intensities on the x and y axes.
Fig. 8
Fig. 8 The intensity distributions of the resultant vector beam passing through a linear polarizer for the case q = 1 in the Fraunhofer region (f = 100 cm). Transmission axis of the polarizer is indicated by an arrow at the upper left corner. The top and bottom rows are theoretical and experimental results, respectively.
Fig. 9
Fig. 9 Stokes parameters for the case q = 1 in the Fraunhofer region (f = 100 cm). The top and bottom rows are respectively theoretical and experimental results corresponding to Fig. 7(a) and 7(b).

Equations (19)

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

E i ( x , y , 0 ) = E 0 ( x , y ) ( cos ϑ e i φ | + + sin ϑ e i φ | ) ,
T = ( cos 2 α sin 2 α sin 2 α cos 2 α ) .
α = q θ + α 0 ,
E ( x , y , 0 ) = E 0 [ sin ϑ e i ( 2 α φ ) | + + cos ϑ e i ( 2 α φ ) | ] .
E ( x , y , z ) = exp ( i k z ) i λ z d x d y E ( x , y , 0 ) exp { i k 2 z [ ( x x ) 2 + ( y y ) 2 ] } .
E ( x , y , z ) = E + | + + E | .
E ± = c ± exp [ i k ( z + r 2 2 z ) ± i φ ] i λ z 0 0 2 π ρ d ρ d ϕ E 0 exp [ i k ρ 2 2 z i k r ρ z cos ( ϕ θ ) i 2 α ] ,
E ± = c ± exp [ i k ( z + r 2 2 z ) i ( 2 α φ ) ] i λ z 2 π ( 1 ) | q | 0 exp ( ρ 2 w 0 2 + i k ρ 2 2 z ) J 2 | q | ( k r ρ z ) ρ d ρ .
0 x μ e α x 2 J ν ( β x ) d x = β ν Γ ( μ + ν + 1 2 ) 2 ν + 1 α μ + ν + 1 2 Γ ( ν + 1 ) F 1 2 ( μ + ν + 1 2 , ν + 1 , β 2 4 α ) ,
E ± = c ± A ( r , z ) e i k z + i k r 2 2 z i ( 2 α φ ) .
A ( r , z ) = 2 2 | q | Γ ( 1 / 2 + | q | ) k w 0 2 k w 0 2 + i 2 z ( i k 2 r 2 w 0 2 2 k w 0 2 z + i 4 z 2 ) | q | F 1 2 ( 1 + | q | , 1 + 2 | q | , i k 2 r 2 w 0 2 2 k w 0 2 z + i 4 z 2 ) .
E ± = c ± G ( r , z ) e i ( 2 α φ ) ( i k 2 r 2 w 0 2 2 k w 0 2 z + i 4 z 2 ) | q | 2 2 | q | π Γ ( 1 / 2 + | q | ) F 1 2 ( | q | , 1 + 2 | q | , i k 2 r 2 w 0 2 2 k w 0 2 z + i 4 z 2 ) ,
G ( r , z ) = k w 0 2 k w 0 2 + i 2 z e i k z k r 2 k w 0 2 + i 2 z .
E ( x , y , z ) = A ( r , z ) e i k z + i k r 2 2 z [ sin ϑ e i ( 2 α φ ) | + + cos ϑ e i ( 2 α φ ) | ] .
E ( x , y , z ) = 1 2 A ( r , z ) e i k z + i k r 2 2 z [ sin ϑ e i ( 2 α φ ) + cos ϑ e i ( 2 α φ ) i sin ϑ e i ( 2 α φ ) i cos ϑ e i ( 2 α φ ) ] .
E ( x , y , z ) = A ( r , z ) e i k z + i k r 2 2 z [ cos ( 2 α φ ) sin ( 2 α φ ) ] .
E ( x , y , z ) = A ( r , z ) e i k z + i k r 2 2 z i ( 2 α φ ) | .
A ( r , z ) = 2 2 | q | Γ ( 1 / 2 + | q | ) k w 0 2 2 i z ( k 2 r 2 w 0 2 4 z 2 ) | q | F 1 2 ( 1 + | q | , 1 + 2 | q | , k 2 r 2 w 0 2 4 z 2 ) .
S 1 = S 0 sin 2 ϑ cos 2 φ , S 2 = S 0 sin 2 ϑ sin 2 φ , S 3 = S 0 cos 2 ϑ .

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