Abstract

Vector beams contain complex polarization structures and they are inherently non-separable in the polarization and spatial degrees of freedom. The spatially variant polarizations of vector beams have enabled many important applications in a variety of fields ranging from classical to quantum physics. In this study, we designed and realized a setup based on Mach-Zehnder interferometer for achieving the vector beams at arbitrary points of higher-order Poincaré sphere, through manipulating two eigenstates in the Mach-Zehnder interferometer system with the combined spiral phase plate. We demonstrated the generation of different kinds of higher-order Poincaré beams, including the beams at points on a latitude or longitude of higher-order Poincaré sphere, Bell states for |l| = 1 and |l| = 2, radially polarized beams of very high order with l = 16, etc. Vector beams of high quality and good accuracy are experimentally achieved, and the flexibility, feasibility and high efficiency of the setup are demonstrated by the practical performance.

© 2020 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

Full Article  |  PDF Article
OSA Recommended Articles
Anisotropic polarization modulation for the production of arbitrary Poincaré beams

Shiyao Fu, Chunqing Gao, Tonglu Wang, Yanwang Zhai, and Ci Yin
J. Opt. Soc. Am. B 35(1) 1-7 (2018)

Generation of arbitrary vector vortex beams on hybrid-order Poincaré sphere

Zhenxing Liu, Yuanyuan Liu, Yougang Ke, Yachao Liu, Weixing Shu, Hailu Luo, and Shuangchun Wen
Photon. Res. 5(1) 15-21 (2017)

Generation of arbitrary vector fields based on a pair of orthogonal elliptically polarized base vectors

Danfeng Xu, Bing Gu, Guanghao Rui, Qiwen Zhan, and Yiping Cui
Opt. Express 24(4) 4177-4186 (2016)

References

  • View by:
  • |
  • |
  • |

  1. Q. Zhan, “Cylindrical vector beams: from mathematical concepts to applications,” Adv. Opt. Photonics 1(1), 1–57 (2009).
    [Crossref]
  2. C. Rosales-Guzmán, B. Ndagano, and A. Forbes, “A review of complex vector light fields and their applications,” J. Opt. 20(12), 123001 (2018).
    [Crossref]
  3. J. Chen, C. Wan, and Q. Zhan, “Vectorial optical fields: recent advances and future prospects,” Sci. Bull. 63(1), 54–74 (2018).
    [Crossref]
  4. K. S. Youngworth and T. G. Brown, “Focusing of high numerical aperture cylindrical-vector beams,” Opt. Express 7(2), 77–87 (2000).
    [Crossref]
  5. R. Dorn, S. Quabis, and G. Leuchs, “Sharper focus for a radially polarized light beam,” Phys. Rev. Lett. 91(23), 233901 (2003).
    [Crossref]
  6. W. Chen and Q. Zhan, “Three-dimensional focus shaping with cylindrical vector beams,” Opt. Commun. 265(2), 411–417 (2006).
    [Crossref]
  7. E. Otte, K. Tekce, and C. Denz, “Tailored intensity landscapes by tight focusing of singular vector beams,” Opt. Express 25(17), 20194–20201 (2017).
    [Crossref]
  8. H.-F. Xu, R. Zhang, Z.-Q. Sheng, and J. Qu, “Focus shaping of partially coherent radially polarized vortex beam with tunable topological charge,” Opt. Express 27(17), 23959–23969 (2019).
    [Crossref]
  9. Y. Kozawa and S. Sato, “Optical trapping of micrometer-sized dielectric particles by cylindrical vector beams,” Opt. Express 18(10), 10828–10833 (2010).
    [Crossref]
  10. B. J. Roxworthy and K. C. Toussaint, “Optical trapping with π-phase cylindrical vector beams,” New J. Phys. 12(7), 073012 (2010).
    [Crossref]
  11. O. M. Maragò, P. H. Jones, P. G. Gucciardi, G. Volpe, and A. C. Ferrari, “Optical trapping and manipulation of nanostructures,” Nat. Nanotechnol. 8(11), 807–819 (2013).
    [Crossref]
  12. P. Török and P. Munro, “The use of Gauss-Laguerre vector beams in STED microscopy,” Opt. Express 12(15), 3605–3617 (2004).
    [Crossref]
  13. S. Segawa, Y. Kozawa, and S. Sato, “Resolution enhancement of confocal microscopy by subtraction method with vector beams,” Opt. Lett. 39(11), 3118–3121 (2014).
    [Crossref]
  14. S. Berg-Johansen, F. Töppel, B. Stiller, P. Banzer, M. Ornigotti, E. Giacobino, G. Leuchs, A. Aiello, and C. Marquardt, “Classically entangled optical beams for high-speed kinematic sensing,” Optica 2(10), 864–868 (2015).
    [Crossref]
  15. M. Neugebauer, P. Woźniak, A. Bag, G. Leuchs, and P. Banzer, “Polarization-controlled directional scattering for nanoscopic position sensing,” Nat. Commun. 7(1), 11286 (2016).
    [Crossref]
  16. V. G. Niziev and A. V. Nesterov, “Influence of beam polarization on laser cutting efficiency,” J. Phys. D: Appl. Phys. 32(13), 1455–1461 (1999).
    [Crossref]
  17. 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]
  18. 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]
  19. J. T. Barreiro, T.-C. Wei, and P. G. Kwiat, “Beating the channel capacity limit for linear photonic superdense coding,” Nat. Phys. 4(4), 282–286 (2008).
    [Crossref]
  20. X.-L. Wang, X.-D. Cai, Z.-E. Su, M.-C. Chen, D. Wu, L. Li, N.-L. Liu, C.-Y. Lu, and J.-W. Pan, “Quantum teleportation of multiple degrees of freedom of a single photon,” Nature 518(7540), 516–519 (2015).
    [Crossref]
  21. P. Li, B. Wang, and X. Zhang, “High-dimensional encoding based on classical nonseparability,” Opt. Express 24(13), 15143–15159 (2016).
    [Crossref]
  22. A. Sit, F. Bouchard, R. Fickler, J. Gagnon-Bischoff, H. Larocque, K. Heshami, D. Elser, C. Peuntinger, K. Günthner, B. Heim, C. Marquardt, G. Leuchs, R. W. Boyd, and E. Karimi, “High-dimensional intracity quantum cryptography with structured photons,” Optica 4(9), 1006–1010 (2017).
    [Crossref]
  23. 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]
  24. X. Yi, Y. Liu, X. Ling, X. Zhou, Y. Ke, H. Luo, S. Wen, and D. Fan, “Hybrid-order Poincaré sphere,” Phys. Rev. A 91(2), 023801 (2015).
    [Crossref]
  25. 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]
  26. S. Chen, X. Zhou, Y. Liu, X. Ling, H. Luo, and S. Wen, “Generation of arbitrary cylindrical vector beams on the higher order Poincaré sphere,” Opt. Lett. 39(18), 5274–5276 (2014).
    [Crossref]
  27. S. Fu, C. Gao, Y. Shi, K. Dai, L. Zhong, and S. Zhang, “Generating polarization vortices by using helical beams and a Twyman Green interferometer,” Opt. Lett. 40(8), 1775–1778 (2015).
    [Crossref]
  28. V. G. Niziev, R. S. Chang, and A. V. Nesterov, “Generation of inhomogeneously polarized laser beams by use of a Sagnac interferometer,” Appl. Opt. 45(33), 8393–8399 (2006).
    [Crossref]
  29. S. Liu, S. Qi, Y. Zhang, P. Li, D. Wu, L. Han, and J. Zhao, “Highly efficient generation of arbitrary vector beams with tunable polarization, phase, and amplitude,” Photonics Res. 6(4), 228–233 (2018).
    [Crossref]
  30. S. Fu, S. Zhang, T. Wang, and C. Gao, “Rectilinear lattices of polarization vortices with various spatial polarization distributions,” Opt. Express 24(16), 18486–18491 (2016).
    [Crossref]
  31. S. Fu, Y. Zhai, T. Wang, C. Yin, and C. Gao, “Tailoring arbitrary hybrid Poincaré beams through a single hologram,” Appl. Phys. Lett. 111(21), 211101 (2017).
    [Crossref]
  32. S. Fu, C. Gao, T. Wang, Y. Zhai, and C. Yin, “Anisotropic polarization modulation for the production of arbitrary Poincaré beams,” J. Opt. Soc. Am. B 35(1), 1–7 (2018).
    [Crossref]
  33. 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]
  34. 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]
  35. 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]
  36. L. Gong, Y. Ren, W. Liu, M. Wang, M. Zhong, Z. Wang, and Y. Li, “Generation of cylindrically polarized vector vortex beams with digital micromirror device,” J. Appl. Phys. 116(18), 183105 (2014).
    [Crossref]
  37. F. Yue, D. Wen, C. Zhang, B. D. Gerardot, W. Wang, S. Zhang, and X. Chen, “Multichannel Polarization-Controllable Superpositions of Orbital Angular Momentum States,” Adv. Mater. 29(15), 1603838 (2017).
    [Crossref]
  38. Y. Zhang, R. Zhang, X. Li, L. Ma, C. Liu, C. He, and C. Cheng, “Radially polarized plasmonic vector vortex generated by a metasurface spiral in gold film,” Opt. Express 25(25), 32150–32160 (2017).
    [Crossref]
  39. 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).
    [Crossref]
  40. Y. Liang, S. Yan, B. Yao, M. Lei, J. Min, and X. Yu, “Generation of cylindrical vector beams based on common-path interferometer with a vortex phase plate,” Opt. Eng. 55(4), 046117 (2016).
    [Crossref]
  41. V. V. Kotlyar, S. N. Khonina, A. A. Kovalev, V. A. Soifer, H. Elfstrom, and J. Turunen, “Diffraction of a plane, finite-radius wave by a spiral phase plate,” Opt. Lett. 31(11), 1597–1599 (2006).
    [Crossref]
  42. V. D’Ambrosio, G. Carvacho, F. Graffitti, C. Vitelli, B. Piccirillo, L. Marrucci, and F. Sciarrino, “Entangled vector vortex beams,” Phys. Rev. A 94(3), 030304 (2016).
    [Crossref]
  43. Y. Shen, X. Wang, Z. Xie, C. Min, X. Fu, Q. Liu, M. Gong, and X. Yuan, “Optical vortices 30 years on: OAM manipulation from topological charge to multiple singularities,” Light: Sci. Appl. 8(1), 90 (2019).
    [Crossref]
  44. B. Ndagano, B. Perez-Garcia, F. S. Roux, M. McLaren, C. Rosales-Guzman, Y. Zhang, O. Mouane, R. I. Hernandez-Aranda, T. Konrad, and A. Forbes, “Characterizing quantum channels with non-separable states of classical light,” Nat. Phys. 13(4), 397–402 (2017).
    [Crossref]
  45. R. Fickler, G. Campbell, B. Buchler, P. K. Lam, and A. Zeilinger, “Quantum entanglement of angular momentum states with quantum numbers up to 10,010,” Proc. Natl. Acad. Sci. 113(48), 13642–13647 (2016).
    [Crossref]
  46. Z. Qiao, G. Xie, Y. Wu, P. Yuan, J. Ma, L. Qian, and D. Fan, “Generating High-Charge Optical Vortices Directly from Laser Up to 288th Order,” Laser Photonics Rev. 12(8), 1800019 (2018).
    [Crossref]
  47. O. Emile and J. Emile, “Naked eye picometer resolution in a Michelson interferometer using conjugated twisted beams,” Opt. Lett. 42(2), 354–357 (2017).
    [Crossref]

2019 (2)

H.-F. Xu, R. Zhang, Z.-Q. Sheng, and J. Qu, “Focus shaping of partially coherent radially polarized vortex beam with tunable topological charge,” Opt. Express 27(17), 23959–23969 (2019).
[Crossref]

Y. Shen, X. Wang, Z. Xie, C. Min, X. Fu, Q. Liu, M. Gong, and X. Yuan, “Optical vortices 30 years on: OAM manipulation from topological charge to multiple singularities,” Light: Sci. Appl. 8(1), 90 (2019).
[Crossref]

2018 (5)

Z. Qiao, G. Xie, Y. Wu, P. Yuan, J. Ma, L. Qian, and D. Fan, “Generating High-Charge Optical Vortices Directly from Laser Up to 288th Order,” Laser Photonics Rev. 12(8), 1800019 (2018).
[Crossref]

C. Rosales-Guzmán, B. Ndagano, and A. Forbes, “A review of complex vector light fields and their applications,” J. Opt. 20(12), 123001 (2018).
[Crossref]

J. Chen, C. Wan, and Q. Zhan, “Vectorial optical fields: recent advances and future prospects,” Sci. Bull. 63(1), 54–74 (2018).
[Crossref]

S. Liu, S. Qi, Y. Zhang, P. Li, D. Wu, L. Han, and J. Zhao, “Highly efficient generation of arbitrary vector beams with tunable polarization, phase, and amplitude,” Photonics Res. 6(4), 228–233 (2018).
[Crossref]

S. Fu, C. Gao, T. Wang, Y. Zhai, and C. Yin, “Anisotropic polarization modulation for the production of arbitrary Poincaré beams,” J. Opt. Soc. Am. B 35(1), 1–7 (2018).
[Crossref]

2017 (7)

S. Fu, Y. Zhai, T. Wang, C. Yin, and C. Gao, “Tailoring arbitrary hybrid Poincaré beams through a single hologram,” Appl. Phys. Lett. 111(21), 211101 (2017).
[Crossref]

A. Sit, F. Bouchard, R. Fickler, J. Gagnon-Bischoff, H. Larocque, K. Heshami, D. Elser, C. Peuntinger, K. Günthner, B. Heim, C. Marquardt, G. Leuchs, R. W. Boyd, and E. Karimi, “High-dimensional intracity quantum cryptography with structured photons,” Optica 4(9), 1006–1010 (2017).
[Crossref]

E. Otte, K. Tekce, and C. Denz, “Tailored intensity landscapes by tight focusing of singular vector beams,” Opt. Express 25(17), 20194–20201 (2017).
[Crossref]

O. Emile and J. Emile, “Naked eye picometer resolution in a Michelson interferometer using conjugated twisted beams,” Opt. Lett. 42(2), 354–357 (2017).
[Crossref]

B. Ndagano, B. Perez-Garcia, F. S. Roux, M. McLaren, C. Rosales-Guzman, Y. Zhang, O. Mouane, R. I. Hernandez-Aranda, T. Konrad, and A. Forbes, “Characterizing quantum channels with non-separable states of classical light,” Nat. Phys. 13(4), 397–402 (2017).
[Crossref]

F. Yue, D. Wen, C. Zhang, B. D. Gerardot, W. Wang, S. Zhang, and X. Chen, “Multichannel Polarization-Controllable Superpositions of Orbital Angular Momentum States,” Adv. Mater. 29(15), 1603838 (2017).
[Crossref]

Y. Zhang, R. Zhang, X. Li, L. Ma, C. Liu, C. He, and C. Cheng, “Radially polarized plasmonic vector vortex generated by a metasurface spiral in gold film,” Opt. Express 25(25), 32150–32160 (2017).
[Crossref]

2016 (6)

Y. Liang, S. Yan, B. Yao, M. Lei, J. Min, and X. Yu, “Generation of cylindrical vector beams based on common-path interferometer with a vortex phase plate,” Opt. Eng. 55(4), 046117 (2016).
[Crossref]

R. Fickler, G. Campbell, B. Buchler, P. K. Lam, and A. Zeilinger, “Quantum entanglement of angular momentum states with quantum numbers up to 10,010,” Proc. Natl. Acad. Sci. 113(48), 13642–13647 (2016).
[Crossref]

V. D’Ambrosio, G. Carvacho, F. Graffitti, C. Vitelli, B. Piccirillo, L. Marrucci, and F. Sciarrino, “Entangled vector vortex beams,” Phys. Rev. A 94(3), 030304 (2016).
[Crossref]

M. Neugebauer, P. Woźniak, A. Bag, G. Leuchs, and P. Banzer, “Polarization-controlled directional scattering for nanoscopic position sensing,” Nat. Commun. 7(1), 11286 (2016).
[Crossref]

P. Li, B. Wang, and X. Zhang, “High-dimensional encoding based on classical nonseparability,” Opt. Express 24(13), 15143–15159 (2016).
[Crossref]

S. Fu, S. Zhang, T. Wang, and C. Gao, “Rectilinear lattices of polarization vortices with various spatial polarization distributions,” Opt. Express 24(16), 18486–18491 (2016).
[Crossref]

2015 (6)

2014 (3)

2013 (1)

O. M. Maragò, P. H. Jones, P. G. Gucciardi, G. Volpe, and A. C. Ferrari, “Optical trapping and manipulation of nanostructures,” Nat. Nanotechnol. 8(11), 807–819 (2013).
[Crossref]

2011 (3)

2010 (2)

Y. Kozawa and S. Sato, “Optical trapping of micrometer-sized dielectric particles by cylindrical vector beams,” Opt. Express 18(10), 10828–10833 (2010).
[Crossref]

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

2009 (1)

Q. Zhan, “Cylindrical vector beams: from mathematical concepts to applications,” Adv. Opt. Photonics 1(1), 1–57 (2009).
[Crossref]

2008 (1)

J. T. Barreiro, T.-C. Wei, and P. G. Kwiat, “Beating the channel capacity limit for linear photonic superdense coding,” Nat. Phys. 4(4), 282–286 (2008).
[Crossref]

2007 (1)

2006 (4)

V. V. Kotlyar, S. N. Khonina, A. A. Kovalev, V. A. Soifer, H. Elfstrom, and J. Turunen, “Diffraction of a plane, finite-radius wave by a spiral phase plate,” Opt. Lett. 31(11), 1597–1599 (2006).
[Crossref]

W. Chen and Q. Zhan, “Three-dimensional focus shaping with cylindrical vector beams,” Opt. Commun. 265(2), 411–417 (2006).
[Crossref]

V. G. Niziev, R. S. Chang, and A. V. Nesterov, “Generation of inhomogeneously polarized laser beams by use of a Sagnac interferometer,” Appl. Opt. 45(33), 8393–8399 (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]

2004 (1)

2003 (1)

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

2002 (1)

2000 (1)

1999 (1)

V. G. Niziev and A. V. Nesterov, “Influence of beam polarization on laser cutting efficiency,” J. Phys. D: Appl. Phys. 32(13), 1455–1461 (1999).
[Crossref]

Aiello, A.

Alfano, R. R.

Bag, A.

M. Neugebauer, P. Woźniak, A. Bag, G. Leuchs, and P. Banzer, “Polarization-controlled directional scattering for nanoscopic position sensing,” Nat. Commun. 7(1), 11286 (2016).
[Crossref]

Banzer, P.

M. Neugebauer, P. Woźniak, A. Bag, G. Leuchs, and P. Banzer, “Polarization-controlled directional scattering for nanoscopic position sensing,” Nat. Commun. 7(1), 11286 (2016).
[Crossref]

S. Berg-Johansen, F. Töppel, B. Stiller, P. Banzer, M. Ornigotti, E. Giacobino, G. Leuchs, A. Aiello, and C. Marquardt, “Classically entangled optical beams for high-speed kinematic sensing,” Optica 2(10), 864–868 (2015).
[Crossref]

Barreiro, J. T.

J. T. Barreiro, T.-C. Wei, and P. G. Kwiat, “Beating the channel capacity limit for linear photonic superdense coding,” Nat. Phys. 4(4), 282–286 (2008).
[Crossref]

Berg-Johansen, S.

Biener, G.

Bomzon, Z.

Bouchard, F.

Boyd, R. W.

Brown, T. G.

Buchler, B.

R. Fickler, G. Campbell, B. Buchler, P. K. Lam, and A. Zeilinger, “Quantum entanglement of angular momentum states with quantum numbers up to 10,010,” Proc. Natl. Acad. Sci. 113(48), 13642–13647 (2016).
[Crossref]

Cai, X.-D.

X.-L. Wang, X.-D. Cai, Z.-E. Su, M.-C. Chen, D. Wu, L. Li, N.-L. Liu, C.-Y. Lu, and J.-W. Pan, “Quantum teleportation of multiple degrees of freedom of a single photon,” Nature 518(7540), 516–519 (2015).
[Crossref]

Campbell, G.

R. Fickler, G. Campbell, B. Buchler, P. K. Lam, and A. Zeilinger, “Quantum entanglement of angular momentum states with quantum numbers up to 10,010,” Proc. Natl. Acad. Sci. 113(48), 13642–13647 (2016).
[Crossref]

Carvacho, G.

V. D’Ambrosio, G. Carvacho, F. Graffitti, C. Vitelli, B. Piccirillo, L. Marrucci, and F. Sciarrino, “Entangled vector vortex beams,” Phys. Rev. A 94(3), 030304 (2016).
[Crossref]

Chang, R. S.

Chen, J.

J. Chen, C. Wan, and Q. Zhan, “Vectorial optical fields: recent advances and future prospects,” Sci. Bull. 63(1), 54–74 (2018).
[Crossref]

Chen, M.-C.

X.-L. Wang, X.-D. Cai, Z.-E. Su, M.-C. Chen, D. Wu, L. Li, N.-L. Liu, C.-Y. Lu, and J.-W. Pan, “Quantum teleportation of multiple degrees of freedom of a single photon,” Nature 518(7540), 516–519 (2015).
[Crossref]

Chen, S.

Chen, W.

W. Chen and Q. Zhan, “Three-dimensional focus shaping with cylindrical vector beams,” Opt. Commun. 265(2), 411–417 (2006).
[Crossref]

Chen, X.

F. Yue, D. Wen, C. Zhang, B. D. Gerardot, W. Wang, S. Zhang, and X. Chen, “Multichannel Polarization-Controllable Superpositions of Orbital Angular Momentum States,” Adv. Mater. 29(15), 1603838 (2017).
[Crossref]

Cheng, C.

Chigrinov, V.

D’Ambrosio, V.

V. D’Ambrosio, G. Carvacho, F. Graffitti, C. Vitelli, B. Piccirillo, L. Marrucci, and F. Sciarrino, “Entangled vector vortex beams,” Phys. Rev. A 94(3), 030304 (2016).
[Crossref]

Dai, K.

Denz, C.

Dorn, R.

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

Du, T.

Elfstrom, H.

Elser, D.

Emile, J.

Emile, O.

Fan, D.

Z. Qiao, G. Xie, Y. Wu, P. Yuan, J. Ma, L. Qian, and D. Fan, “Generating High-Charge Optical Vortices Directly from Laser Up to 288th Order,” Laser Photonics Rev. 12(8), 1800019 (2018).
[Crossref]

X. Yi, Y. Liu, X. Ling, X. Zhou, Y. Ke, H. Luo, S. Wen, and D. Fan, “Hybrid-order Poincaré sphere,” Phys. Rev. A 91(2), 023801 (2015).
[Crossref]

Ferrari, A. C.

O. M. Maragò, P. H. Jones, P. G. Gucciardi, G. Volpe, and A. C. Ferrari, “Optical trapping and manipulation of nanostructures,” Nat. Nanotechnol. 8(11), 807–819 (2013).
[Crossref]

Fickler, R.

A. Sit, F. Bouchard, R. Fickler, J. Gagnon-Bischoff, H. Larocque, K. Heshami, D. Elser, C. Peuntinger, K. Günthner, B. Heim, C. Marquardt, G. Leuchs, R. W. Boyd, and E. Karimi, “High-dimensional intracity quantum cryptography with structured photons,” Optica 4(9), 1006–1010 (2017).
[Crossref]

R. Fickler, G. Campbell, B. Buchler, P. K. Lam, and A. Zeilinger, “Quantum entanglement of angular momentum states with quantum numbers up to 10,010,” Proc. Natl. Acad. Sci. 113(48), 13642–13647 (2016).
[Crossref]

Forbes, A.

C. Rosales-Guzmán, B. Ndagano, and A. Forbes, “A review of complex vector light fields and their applications,” J. Opt. 20(12), 123001 (2018).
[Crossref]

B. Ndagano, B. Perez-Garcia, F. S. Roux, M. McLaren, C. Rosales-Guzman, Y. Zhang, O. Mouane, R. I. Hernandez-Aranda, T. Konrad, and A. Forbes, “Characterizing quantum channels with non-separable states of classical light,” Nat. Phys. 13(4), 397–402 (2017).
[Crossref]

Fu, S.

Fu, X.

Y. Shen, X. Wang, Z. Xie, C. Min, X. Fu, Q. Liu, M. Gong, and X. Yuan, “Optical vortices 30 years on: OAM manipulation from topological charge to multiple singularities,” Light: Sci. Appl. 8(1), 90 (2019).
[Crossref]

Gabriel, C.

Gagnon-Bischoff, J.

Gao, C.

Gerardot, B. D.

F. Yue, D. Wen, C. Zhang, B. D. Gerardot, W. Wang, S. Zhang, and X. Chen, “Multichannel Polarization-Controllable Superpositions of Orbital Angular Momentum States,” Adv. Mater. 29(15), 1603838 (2017).
[Crossref]

Giacobino, E.

Gong, L.

L. Gong, Y. Ren, W. Liu, M. Wang, M. Zhong, Z. Wang, and Y. Li, “Generation of cylindrically polarized vector vortex beams with digital micromirror device,” J. Appl. Phys. 116(18), 183105 (2014).
[Crossref]

Gong, M.

Y. Shen, X. Wang, Z. Xie, C. Min, X. Fu, Q. Liu, M. Gong, and X. Yuan, “Optical vortices 30 years on: OAM manipulation from topological charge to multiple singularities,” Light: Sci. Appl. 8(1), 90 (2019).
[Crossref]

Graffitti, F.

V. D’Ambrosio, G. Carvacho, F. Graffitti, C. Vitelli, B. Piccirillo, L. Marrucci, and F. Sciarrino, “Entangled vector vortex beams,” Phys. Rev. A 94(3), 030304 (2016).
[Crossref]

Gucciardi, P. G.

O. M. Maragò, P. H. Jones, P. G. Gucciardi, G. Volpe, and A. C. Ferrari, “Optical trapping and manipulation of nanostructures,” Nat. Nanotechnol. 8(11), 807–819 (2013).
[Crossref]

Günthner, K.

Han, L.

S. Liu, S. Qi, Y. Zhang, P. Li, D. Wu, L. Han, and J. Zhao, “Highly efficient generation of arbitrary vector beams with tunable polarization, phase, and amplitude,” Photonics Res. 6(4), 228–233 (2018).
[Crossref]

Hasman, E.

He, C.

Heim, B.

Hernandez-Aranda, R. I.

B. Ndagano, B. Perez-Garcia, F. S. Roux, M. McLaren, C. Rosales-Guzman, Y. Zhang, O. Mouane, R. I. Hernandez-Aranda, T. Konrad, and A. Forbes, “Characterizing quantum channels with non-separable states of classical light,” Nat. Phys. 13(4), 397–402 (2017).
[Crossref]

Heshami, K.

Holleczek, A.

Huang, H.

Jackel, S.

Jones, P. H.

O. M. Maragò, P. H. Jones, P. G. Gucciardi, G. Volpe, and A. C. Ferrari, “Optical trapping and manipulation of nanostructures,” Nat. Nanotechnol. 8(11), 807–819 (2013).
[Crossref]

Karimi, E.

Ke, Y.

X. Yi, Y. Liu, X. Ling, X. Zhou, Y. Ke, H. Luo, S. Wen, and D. Fan, “Hybrid-order Poincaré sphere,” Phys. Rev. A 91(2), 023801 (2015).
[Crossref]

Khonina, S. N.

Kleiner, V.

Konrad, T.

B. Ndagano, B. Perez-Garcia, F. S. Roux, M. McLaren, C. Rosales-Guzman, Y. Zhang, O. Mouane, R. I. Hernandez-Aranda, T. Konrad, and A. Forbes, “Characterizing quantum channels with non-separable states of classical light,” Nat. Phys. 13(4), 397–402 (2017).
[Crossref]

Kotlyar, V. V.

Kovalev, A. A.

Kozawa, Y.

Kwiat, P. G.

J. T. Barreiro, T.-C. Wei, and P. G. Kwiat, “Beating the channel capacity limit for linear photonic superdense coding,” Nat. Phys. 4(4), 282–286 (2008).
[Crossref]

Lam, P. K.

R. Fickler, G. Campbell, B. Buchler, P. K. Lam, and A. Zeilinger, “Quantum entanglement of angular momentum states with quantum numbers up to 10,010,” Proc. Natl. Acad. Sci. 113(48), 13642–13647 (2016).
[Crossref]

Larocque, H.

Lavery, M. P. J.

Leach, J.

Lei, M.

Y. Liang, S. Yan, B. Yao, M. Lei, J. Min, and X. Yu, “Generation of cylindrical vector beams based on common-path interferometer with a vortex phase plate,” Opt. Eng. 55(4), 046117 (2016).
[Crossref]

Leuchs, G.

Li, L.

X.-L. Wang, X.-D. Cai, Z.-E. Su, M.-C. Chen, D. Wu, L. Li, N.-L. Liu, C.-Y. Lu, and J.-W. Pan, “Quantum teleportation of multiple degrees of freedom of a single photon,” Nature 518(7540), 516–519 (2015).
[Crossref]

Li, P.

S. Liu, S. Qi, Y. Zhang, P. Li, D. Wu, L. Han, and J. Zhao, “Highly efficient generation of arbitrary vector beams with tunable polarization, phase, and amplitude,” Photonics Res. 6(4), 228–233 (2018).
[Crossref]

P. Li, B. Wang, and X. Zhang, “High-dimensional encoding based on classical nonseparability,” Opt. Express 24(13), 15143–15159 (2016).
[Crossref]

Li, X.

Li, Y.

L. Gong, Y. Ren, W. Liu, M. Wang, M. Zhong, Z. Wang, and Y. Li, “Generation of cylindrically polarized vector vortex beams with digital micromirror device,” J. Appl. Phys. 116(18), 183105 (2014).
[Crossref]

Liang, Y.

Y. Liang, S. Yan, B. Yao, M. Lei, J. Min, and X. Yu, “Generation of cylindrical vector beams based on common-path interferometer with a vortex phase plate,” Opt. Eng. 55(4), 046117 (2016).
[Crossref]

Ling, X.

X. Yi, Y. Liu, X. Ling, X. Zhou, Y. Ke, H. Luo, S. Wen, and D. Fan, “Hybrid-order Poincaré sphere,” Phys. Rev. A 91(2), 023801 (2015).
[Crossref]

S. Chen, X. Zhou, Y. Liu, X. Ling, H. Luo, and S. Wen, “Generation of arbitrary cylindrical vector beams on the higher order Poincaré sphere,” Opt. Lett. 39(18), 5274–5276 (2014).
[Crossref]

Liu, C.

Liu, N.-L.

X.-L. Wang, X.-D. Cai, Z.-E. Su, M.-C. Chen, D. Wu, L. Li, N.-L. Liu, C.-Y. Lu, and J.-W. Pan, “Quantum teleportation of multiple degrees of freedom of a single photon,” Nature 518(7540), 516–519 (2015).
[Crossref]

Liu, Q.

Y. Shen, X. Wang, Z. Xie, C. Min, X. Fu, Q. Liu, M. Gong, and X. Yuan, “Optical vortices 30 years on: OAM manipulation from topological charge to multiple singularities,” Light: Sci. Appl. 8(1), 90 (2019).
[Crossref]

Liu, S.

S. Liu, S. Qi, Y. Zhang, P. Li, D. Wu, L. Han, and J. Zhao, “Highly efficient generation of arbitrary vector beams with tunable polarization, phase, and amplitude,” Photonics Res. 6(4), 228–233 (2018).
[Crossref]

Liu, W.

L. Gong, Y. Ren, W. Liu, M. Wang, M. Zhong, Z. Wang, and Y. Li, “Generation of cylindrically polarized vector vortex beams with digital micromirror device,” J. Appl. Phys. 116(18), 183105 (2014).
[Crossref]

Liu, Y.

X. Yi, Y. Liu, X. Ling, X. Zhou, Y. Ke, H. Luo, S. Wen, and D. Fan, “Hybrid-order Poincaré sphere,” Phys. Rev. A 91(2), 023801 (2015).
[Crossref]

S. Chen, X. Zhou, Y. Liu, X. Ling, H. Luo, and S. Wen, “Generation of arbitrary cylindrical vector beams on the higher order Poincaré sphere,” Opt. Lett. 39(18), 5274–5276 (2014).
[Crossref]

Lu, C.-Y.

X.-L. Wang, X.-D. Cai, Z.-E. Su, M.-C. Chen, D. Wu, L. Li, N.-L. Liu, C.-Y. Lu, and J.-W. Pan, “Quantum teleportation of multiple degrees of freedom of a single photon,” Nature 518(7540), 516–519 (2015).
[Crossref]

Lumer, Y.

Luo, H.

X. Yi, Y. Liu, X. Ling, X. Zhou, Y. Ke, H. Luo, S. Wen, and D. Fan, “Hybrid-order Poincaré sphere,” Phys. Rev. A 91(2), 023801 (2015).
[Crossref]

S. Chen, X. Zhou, Y. Liu, X. Ling, H. Luo, and S. Wen, “Generation of arbitrary cylindrical vector beams on the higher order Poincaré sphere,” Opt. Lett. 39(18), 5274–5276 (2014).
[Crossref]

Ma, J.

Z. Qiao, G. Xie, Y. Wu, P. Yuan, J. Ma, L. Qian, and D. Fan, “Generating High-Charge Optical Vortices Directly from Laser Up to 288th Order,” Laser Photonics Rev. 12(8), 1800019 (2018).
[Crossref]

Ma, L.

Machavariani, G.

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]

Maragò, O. M.

O. M. Maragò, P. H. Jones, P. G. Gucciardi, G. Volpe, and A. C. Ferrari, “Optical trapping and manipulation of nanostructures,” Nat. Nanotechnol. 8(11), 807–819 (2013).
[Crossref]

Marquardt, C.

Marrucci, L.

McLaren, M.

B. Ndagano, B. Perez-Garcia, F. S. Roux, M. McLaren, C. Rosales-Guzman, Y. Zhang, O. Mouane, R. I. Hernandez-Aranda, T. Konrad, and A. Forbes, “Characterizing quantum channels with non-separable states of classical light,” Nat. Phys. 13(4), 397–402 (2017).
[Crossref]

Meir, A.

Milione, G.

Min, C.

Y. Shen, X. Wang, Z. Xie, C. Min, X. Fu, Q. Liu, M. Gong, and X. Yuan, “Optical vortices 30 years on: OAM manipulation from topological charge to multiple singularities,” Light: Sci. Appl. 8(1), 90 (2019).
[Crossref]

Min, J.

Y. Liang, S. Yan, B. Yao, M. Lei, J. Min, and X. Yu, “Generation of cylindrical vector beams based on common-path interferometer with a vortex phase plate,” Opt. Eng. 55(4), 046117 (2016).
[Crossref]

Moshe, I.

Mouane, O.

B. Ndagano, B. Perez-Garcia, F. S. Roux, M. McLaren, C. Rosales-Guzman, Y. Zhang, O. Mouane, R. I. Hernandez-Aranda, T. Konrad, and A. Forbes, “Characterizing quantum channels with non-separable states of classical light,” Nat. Phys. 13(4), 397–402 (2017).
[Crossref]

Munro, P.

Murauski, A.

Ndagano, B.

C. Rosales-Guzmán, B. Ndagano, and A. Forbes, “A review of complex vector light fields and their applications,” J. Opt. 20(12), 123001 (2018).
[Crossref]

B. Ndagano, B. Perez-Garcia, F. S. Roux, M. McLaren, C. Rosales-Guzman, Y. Zhang, O. Mouane, R. I. Hernandez-Aranda, T. Konrad, and A. Forbes, “Characterizing quantum channels with non-separable states of classical light,” Nat. Phys. 13(4), 397–402 (2017).
[Crossref]

Nesterov, A. V.

V. G. Niziev, R. S. Chang, and A. V. Nesterov, “Generation of inhomogeneously polarized laser beams by use of a Sagnac interferometer,” Appl. Opt. 45(33), 8393–8399 (2006).
[Crossref]

V. G. Niziev and A. V. Nesterov, “Influence of beam polarization on laser cutting efficiency,” J. Phys. D: Appl. Phys. 32(13), 1455–1461 (1999).
[Crossref]

Neugebauer, M.

M. Neugebauer, P. Woźniak, A. Bag, G. Leuchs, and P. Banzer, “Polarization-controlled directional scattering for nanoscopic position sensing,” Nat. Commun. 7(1), 11286 (2016).
[Crossref]

Nguyen, T. A.

Niziev, V. G.

V. G. Niziev, R. S. Chang, and A. V. Nesterov, “Generation of inhomogeneously polarized laser beams by use of a Sagnac interferometer,” Appl. Opt. 45(33), 8393–8399 (2006).
[Crossref]

V. G. Niziev and A. V. Nesterov, “Influence of beam polarization on laser cutting efficiency,” J. Phys. D: Appl. Phys. 32(13), 1455–1461 (1999).
[Crossref]

Nolan, D. A.

Ornigotti, M.

Otte, E.

Pan, J.-W.

X.-L. Wang, X.-D. Cai, Z.-E. Su, M.-C. Chen, D. Wu, L. Li, N.-L. Liu, C.-Y. Lu, and J.-W. Pan, “Quantum teleportation of multiple degrees of freedom of a single photon,” Nature 518(7540), 516–519 (2015).
[Crossref]

Paparo, D.

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]

Perez-Garcia, B.

B. Ndagano, B. Perez-Garcia, F. S. Roux, M. McLaren, C. Rosales-Guzman, Y. Zhang, O. Mouane, R. I. Hernandez-Aranda, T. Konrad, and A. Forbes, “Characterizing quantum channels with non-separable states of classical light,” Nat. Phys. 13(4), 397–402 (2017).
[Crossref]

Peuntinger, C.

Piccirillo, B.

V. D’Ambrosio, G. Carvacho, F. Graffitti, C. Vitelli, B. Piccirillo, L. Marrucci, and F. Sciarrino, “Entangled vector vortex beams,” Phys. Rev. A 94(3), 030304 (2016).
[Crossref]

Qi, S.

S. Liu, S. Qi, Y. Zhang, P. Li, D. Wu, L. Han, and J. Zhao, “Highly efficient generation of arbitrary vector beams with tunable polarization, phase, and amplitude,” Photonics Res. 6(4), 228–233 (2018).
[Crossref]

Qian, L.

Z. Qiao, G. Xie, Y. Wu, P. Yuan, J. Ma, L. Qian, and D. Fan, “Generating High-Charge Optical Vortices Directly from Laser Up to 288th Order,” Laser Photonics Rev. 12(8), 1800019 (2018).
[Crossref]

Qiao, Z.

Z. Qiao, G. Xie, Y. Wu, P. Yuan, J. Ma, L. Qian, and D. Fan, “Generating High-Charge Optical Vortices Directly from Laser Up to 288th Order,” Laser Photonics Rev. 12(8), 1800019 (2018).
[Crossref]

Qu, J.

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]

Ren, Y.

Rosales-Guzman, C.

B. Ndagano, B. Perez-Garcia, F. S. Roux, M. McLaren, C. Rosales-Guzman, Y. Zhang, O. Mouane, R. I. Hernandez-Aranda, T. Konrad, and A. Forbes, “Characterizing quantum channels with non-separable states of classical light,” Nat. Phys. 13(4), 397–402 (2017).
[Crossref]

Rosales-Guzmán, C.

C. Rosales-Guzmán, B. Ndagano, and A. Forbes, “A review of complex vector light fields and their applications,” J. Opt. 20(12), 123001 (2018).
[Crossref]

Roux, F. S.

B. Ndagano, B. Perez-Garcia, F. S. Roux, M. McLaren, C. Rosales-Guzman, Y. Zhang, O. Mouane, R. I. Hernandez-Aranda, T. Konrad, and A. Forbes, “Characterizing quantum channels with non-separable states of classical light,” Nat. Phys. 13(4), 397–402 (2017).
[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).
[Crossref]

Santamato, E.

Sato, S.

Sciarrino, F.

V. D’Ambrosio, G. Carvacho, F. Graffitti, C. Vitelli, B. Piccirillo, L. Marrucci, and F. Sciarrino, “Entangled vector vortex beams,” Phys. Rev. A 94(3), 030304 (2016).
[Crossref]

Segawa, S.

Shen, Y.

Y. Shen, X. Wang, Z. Xie, C. Min, X. Fu, Q. Liu, M. Gong, and X. Yuan, “Optical vortices 30 years on: OAM manipulation from topological charge to multiple singularities,” Light: Sci. Appl. 8(1), 90 (2019).
[Crossref]

Sheng, Z.-Q.

Shi, Y.

Sit, A.

Slussarenko, S.

Soifer, V. A.

Stiller, B.

Su, Z.-E.

X.-L. Wang, X.-D. Cai, Z.-E. Su, M.-C. Chen, D. Wu, L. Li, N.-L. Liu, C.-Y. Lu, and J.-W. Pan, “Quantum teleportation of multiple degrees of freedom of a single photon,” Nature 518(7540), 516–519 (2015).
[Crossref]

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).
[Crossref]

Tekce, K.

Töppel, F.

Török, P.

Toussaint, K. C.

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

Turunen, J.

Vitelli, C.

V. D’Ambrosio, G. Carvacho, F. Graffitti, C. Vitelli, B. Piccirillo, L. Marrucci, and F. Sciarrino, “Entangled vector vortex beams,” Phys. Rev. A 94(3), 030304 (2016).
[Crossref]

Volpe, G.

O. M. Maragò, P. H. Jones, P. G. Gucciardi, G. Volpe, and A. C. Ferrari, “Optical trapping and manipulation of nanostructures,” Nat. Nanotechnol. 8(11), 807–819 (2013).
[Crossref]

Wan, C.

J. Chen, C. Wan, and Q. Zhan, “Vectorial optical fields: recent advances and future prospects,” Sci. Bull. 63(1), 54–74 (2018).
[Crossref]

Wang, B.

Wang, M.

L. Gong, Y. Ren, W. Liu, M. Wang, M. Zhong, Z. Wang, and Y. Li, “Generation of cylindrically polarized vector vortex beams with digital micromirror device,” J. Appl. Phys. 116(18), 183105 (2014).
[Crossref]

Wang, T.

Wang, W.

F. Yue, D. Wen, C. Zhang, B. D. Gerardot, W. Wang, S. Zhang, and X. Chen, “Multichannel Polarization-Controllable Superpositions of Orbital Angular Momentum States,” Adv. Mater. 29(15), 1603838 (2017).
[Crossref]

Wang, X.

Y. Shen, X. Wang, Z. Xie, C. Min, X. Fu, Q. Liu, M. Gong, and X. Yuan, “Optical vortices 30 years on: OAM manipulation from topological charge to multiple singularities,” Light: Sci. Appl. 8(1), 90 (2019).
[Crossref]

Wang, X.-L.

X.-L. Wang, X.-D. Cai, Z.-E. Su, M.-C. Chen, D. Wu, L. Li, N.-L. Liu, C.-Y. Lu, and J.-W. Pan, “Quantum teleportation of multiple degrees of freedom of a single photon,” Nature 518(7540), 516–519 (2015).
[Crossref]

Wang, Z.

L. Gong, Y. Ren, W. Liu, M. Wang, M. Zhong, Z. Wang, and Y. Li, “Generation of cylindrically polarized vector vortex beams with digital micromirror device,” J. Appl. Phys. 116(18), 183105 (2014).
[Crossref]

Wei, T.-C.

J. T. Barreiro, T.-C. Wei, and P. G. Kwiat, “Beating the channel capacity limit for linear photonic superdense coding,” Nat. Phys. 4(4), 282–286 (2008).
[Crossref]

Wen, D.

F. Yue, D. Wen, C. Zhang, B. D. Gerardot, W. Wang, S. Zhang, and X. Chen, “Multichannel Polarization-Controllable Superpositions of Orbital Angular Momentum States,” Adv. Mater. 29(15), 1603838 (2017).
[Crossref]

Wen, S.

X. Yi, Y. Liu, X. Ling, X. Zhou, Y. Ke, H. Luo, S. Wen, and D. Fan, “Hybrid-order Poincaré sphere,” Phys. Rev. A 91(2), 023801 (2015).
[Crossref]

S. Chen, X. Zhou, Y. Liu, X. Ling, H. Luo, and S. Wen, “Generation of arbitrary cylindrical vector beams on the higher order Poincaré sphere,” Opt. Lett. 39(18), 5274–5276 (2014).
[Crossref]

Willner, A. E.

Wozniak, P.

M. Neugebauer, P. Woźniak, A. Bag, G. Leuchs, and P. Banzer, “Polarization-controlled directional scattering for nanoscopic position sensing,” Nat. Commun. 7(1), 11286 (2016).
[Crossref]

Wu, D.

S. Liu, S. Qi, Y. Zhang, P. Li, D. Wu, L. Han, and J. Zhao, “Highly efficient generation of arbitrary vector beams with tunable polarization, phase, and amplitude,” Photonics Res. 6(4), 228–233 (2018).
[Crossref]

X.-L. Wang, X.-D. Cai, Z.-E. Su, M.-C. Chen, D. Wu, L. Li, N.-L. Liu, C.-Y. Lu, and J.-W. Pan, “Quantum teleportation of multiple degrees of freedom of a single photon,” Nature 518(7540), 516–519 (2015).
[Crossref]

Wu, Y.

Z. Qiao, G. Xie, Y. Wu, P. Yuan, J. Ma, L. Qian, and D. Fan, “Generating High-Charge Optical Vortices Directly from Laser Up to 288th Order,” Laser Photonics Rev. 12(8), 1800019 (2018).
[Crossref]

Xie, G.

Xie, Z.

Y. Shen, X. Wang, Z. Xie, C. Min, X. Fu, Q. Liu, M. Gong, and X. Yuan, “Optical vortices 30 years on: OAM manipulation from topological charge to multiple singularities,” Light: Sci. Appl. 8(1), 90 (2019).
[Crossref]

Xu, H.-F.

Yan, S.

Y. Liang, S. Yan, B. Yao, M. Lei, J. Min, and X. Yu, “Generation of cylindrical vector beams based on common-path interferometer with a vortex phase plate,” Opt. Eng. 55(4), 046117 (2016).
[Crossref]

Yao, B.

Y. Liang, S. Yan, B. Yao, M. Lei, J. Min, and X. Yu, “Generation of cylindrical vector beams based on common-path interferometer with a vortex phase plate,” Opt. Eng. 55(4), 046117 (2016).
[Crossref]

Yi, X.

X. Yi, Y. Liu, X. Ling, X. Zhou, Y. Ke, H. Luo, S. Wen, and D. Fan, “Hybrid-order Poincaré sphere,” Phys. Rev. A 91(2), 023801 (2015).
[Crossref]

Yin, C.

S. Fu, C. Gao, T. Wang, Y. Zhai, and C. Yin, “Anisotropic polarization modulation for the production of arbitrary Poincaré beams,” J. Opt. Soc. Am. B 35(1), 1–7 (2018).
[Crossref]

S. Fu, Y. Zhai, T. Wang, C. Yin, and C. Gao, “Tailoring arbitrary hybrid Poincaré beams through a single hologram,” Appl. Phys. Lett. 111(21), 211101 (2017).
[Crossref]

Youngworth, K. S.

Yu, X.

Y. Liang, S. Yan, B. Yao, M. Lei, J. Min, and X. Yu, “Generation of cylindrical vector beams based on common-path interferometer with a vortex phase plate,” Opt. Eng. 55(4), 046117 (2016).
[Crossref]

Yuan, P.

Z. Qiao, G. Xie, Y. Wu, P. Yuan, J. Ma, L. Qian, and D. Fan, “Generating High-Charge Optical Vortices Directly from Laser Up to 288th Order,” Laser Photonics Rev. 12(8), 1800019 (2018).
[Crossref]

Yuan, X.

Y. Shen, X. Wang, Z. Xie, C. Min, X. Fu, Q. Liu, M. Gong, and X. Yuan, “Optical vortices 30 years on: OAM manipulation from topological charge to multiple singularities,” Light: Sci. Appl. 8(1), 90 (2019).
[Crossref]

Yue, F.

F. Yue, D. Wen, C. Zhang, B. D. Gerardot, W. Wang, S. Zhang, and X. Chen, “Multichannel Polarization-Controllable Superpositions of Orbital Angular Momentum States,” Adv. Mater. 29(15), 1603838 (2017).
[Crossref]

Zeilinger, A.

R. Fickler, G. Campbell, B. Buchler, P. K. Lam, and A. Zeilinger, “Quantum entanglement of angular momentum states with quantum numbers up to 10,010,” Proc. Natl. Acad. Sci. 113(48), 13642–13647 (2016).
[Crossref]

Zhai, Y.

S. Fu, C. Gao, T. Wang, Y. Zhai, and C. Yin, “Anisotropic polarization modulation for the production of arbitrary Poincaré beams,” J. Opt. Soc. Am. B 35(1), 1–7 (2018).
[Crossref]

S. Fu, Y. Zhai, T. Wang, C. Yin, and C. Gao, “Tailoring arbitrary hybrid Poincaré beams through a single hologram,” Appl. Phys. Lett. 111(21), 211101 (2017).
[Crossref]

Zhan, Q.

J. Chen, C. Wan, and Q. Zhan, “Vectorial optical fields: recent advances and future prospects,” Sci. Bull. 63(1), 54–74 (2018).
[Crossref]

Q. Zhan, “Cylindrical vector beams: from mathematical concepts to applications,” Adv. Opt. Photonics 1(1), 1–57 (2009).
[Crossref]

W. Chen and Q. Zhan, “Three-dimensional focus shaping with cylindrical vector beams,” Opt. Commun. 265(2), 411–417 (2006).
[Crossref]

Zhang, C.

F. Yue, D. Wen, C. Zhang, B. D. Gerardot, W. Wang, S. Zhang, and X. Chen, “Multichannel Polarization-Controllable Superpositions of Orbital Angular Momentum States,” Adv. Mater. 29(15), 1603838 (2017).
[Crossref]

Zhang, R.

Zhang, S.

Zhang, X.

Zhang, Y.

S. Liu, S. Qi, Y. Zhang, P. Li, D. Wu, L. Han, and J. Zhao, “Highly efficient generation of arbitrary vector beams with tunable polarization, phase, and amplitude,” Photonics Res. 6(4), 228–233 (2018).
[Crossref]

Y. Zhang, R. Zhang, X. Li, L. Ma, C. Liu, C. He, and C. Cheng, “Radially polarized plasmonic vector vortex generated by a metasurface spiral in gold film,” Opt. Express 25(25), 32150–32160 (2017).
[Crossref]

B. Ndagano, B. Perez-Garcia, F. S. Roux, M. McLaren, C. Rosales-Guzman, Y. Zhang, O. Mouane, R. I. Hernandez-Aranda, T. Konrad, and A. Forbes, “Characterizing quantum channels with non-separable states of classical light,” Nat. Phys. 13(4), 397–402 (2017).
[Crossref]

Zhao, J.

S. Liu, S. Qi, Y. Zhang, P. Li, D. Wu, L. Han, and J. Zhao, “Highly efficient generation of arbitrary vector beams with tunable polarization, phase, and amplitude,” Photonics Res. 6(4), 228–233 (2018).
[Crossref]

Zhong, L.

Zhong, M.

L. Gong, Y. Ren, W. Liu, M. Wang, M. Zhong, Z. Wang, and Y. Li, “Generation of cylindrically polarized vector vortex beams with digital micromirror device,” J. Appl. Phys. 116(18), 183105 (2014).
[Crossref]

Zhou, X.

X. Yi, Y. Liu, X. Ling, X. Zhou, Y. Ke, H. Luo, S. Wen, and D. Fan, “Hybrid-order Poincaré sphere,” Phys. Rev. A 91(2), 023801 (2015).
[Crossref]

S. Chen, X. Zhou, Y. Liu, X. Ling, H. Luo, and S. Wen, “Generation of arbitrary cylindrical vector beams on the higher order Poincaré sphere,” Opt. Lett. 39(18), 5274–5276 (2014).
[Crossref]

Adv. Mater. (1)

F. Yue, D. Wen, C. Zhang, B. D. Gerardot, W. Wang, S. Zhang, and X. Chen, “Multichannel Polarization-Controllable Superpositions of Orbital Angular Momentum States,” Adv. Mater. 29(15), 1603838 (2017).
[Crossref]

Adv. Opt. Photonics (1)

Q. Zhan, “Cylindrical vector beams: from mathematical concepts to applications,” Adv. Opt. Photonics 1(1), 1–57 (2009).
[Crossref]

Appl. Opt. (1)

Appl. Phys. Lett. (1)

S. Fu, Y. Zhai, T. Wang, C. Yin, and C. Gao, “Tailoring arbitrary hybrid Poincaré beams through a single hologram,” Appl. Phys. Lett. 111(21), 211101 (2017).
[Crossref]

J. Appl. Phys. (1)

L. Gong, Y. Ren, W. Liu, M. Wang, M. Zhong, Z. Wang, and Y. Li, “Generation of cylindrically polarized vector vortex beams with digital micromirror device,” J. Appl. Phys. 116(18), 183105 (2014).
[Crossref]

J. Opt. (1)

C. Rosales-Guzmán, B. Ndagano, and A. Forbes, “A review of complex vector light fields and their applications,” J. Opt. 20(12), 123001 (2018).
[Crossref]

J. Opt. Soc. Am. B (1)

J. Phys. D: Appl. Phys. (1)

V. G. Niziev and A. V. Nesterov, “Influence of beam polarization on laser cutting efficiency,” J. Phys. D: Appl. Phys. 32(13), 1455–1461 (1999).
[Crossref]

Laser Photonics Rev. (1)

Z. Qiao, G. Xie, Y. Wu, P. Yuan, J. Ma, L. Qian, and D. Fan, “Generating High-Charge Optical Vortices Directly from Laser Up to 288th Order,” Laser Photonics Rev. 12(8), 1800019 (2018).
[Crossref]

Light: Sci. Appl. (1)

Y. Shen, X. Wang, Z. Xie, C. Min, X. Fu, Q. Liu, M. Gong, and X. Yuan, “Optical vortices 30 years on: OAM manipulation from topological charge to multiple singularities,” Light: Sci. Appl. 8(1), 90 (2019).
[Crossref]

Nat. Commun. (1)

M. Neugebauer, P. Woźniak, A. Bag, G. Leuchs, and P. Banzer, “Polarization-controlled directional scattering for nanoscopic position sensing,” Nat. Commun. 7(1), 11286 (2016).
[Crossref]

Nat. Nanotechnol. (1)

O. M. Maragò, P. H. Jones, P. G. Gucciardi, G. Volpe, and A. C. Ferrari, “Optical trapping and manipulation of nanostructures,” Nat. Nanotechnol. 8(11), 807–819 (2013).
[Crossref]

Nat. Phys. (2)

J. T. Barreiro, T.-C. Wei, and P. G. Kwiat, “Beating the channel capacity limit for linear photonic superdense coding,” Nat. Phys. 4(4), 282–286 (2008).
[Crossref]

B. Ndagano, B. Perez-Garcia, F. S. Roux, M. McLaren, C. Rosales-Guzman, Y. Zhang, O. Mouane, R. I. Hernandez-Aranda, T. Konrad, and A. Forbes, “Characterizing quantum channels with non-separable states of classical light,” Nat. Phys. 13(4), 397–402 (2017).
[Crossref]

Nature (1)

X.-L. Wang, X.-D. Cai, Z.-E. Su, M.-C. Chen, D. Wu, L. Li, N.-L. Liu, C.-Y. Lu, and J.-W. Pan, “Quantum teleportation of multiple degrees of freedom of a single photon,” Nature 518(7540), 516–519 (2015).
[Crossref]

New J. Phys. (1)

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

Opt. Commun. (1)

W. Chen and Q. Zhan, “Three-dimensional focus shaping with cylindrical vector beams,” Opt. Commun. 265(2), 411–417 (2006).
[Crossref]

Opt. Eng. (1)

Y. Liang, S. Yan, B. Yao, M. Lei, J. Min, and X. Yu, “Generation of cylindrical vector beams based on common-path interferometer with a vortex phase plate,” Opt. Eng. 55(4), 046117 (2016).
[Crossref]

Opt. Express (10)

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]

H.-F. Xu, R. Zhang, Z.-Q. Sheng, and J. Qu, “Focus shaping of partially coherent radially polarized vortex beam with tunable topological charge,” Opt. Express 27(17), 23959–23969 (2019).
[Crossref]

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]

P. Li, B. Wang, and X. Zhang, “High-dimensional encoding based on classical nonseparability,” Opt. Express 24(13), 15143–15159 (2016).
[Crossref]

Y. Kozawa and S. Sato, “Optical trapping of micrometer-sized dielectric particles by cylindrical vector beams,” Opt. Express 18(10), 10828–10833 (2010).
[Crossref]

S. Fu, S. Zhang, T. Wang, and C. Gao, “Rectilinear lattices of polarization vortices with various spatial polarization distributions,” Opt. Express 24(16), 18486–18491 (2016).
[Crossref]

E. Otte, K. Tekce, and C. Denz, “Tailored intensity landscapes by tight focusing of singular vector beams,” Opt. Express 25(17), 20194–20201 (2017).
[Crossref]

K. S. Youngworth and T. G. Brown, “Focusing of high numerical aperture cylindrical-vector beams,” Opt. Express 7(2), 77–87 (2000).
[Crossref]

P. Török and P. Munro, “The use of Gauss-Laguerre vector beams in STED microscopy,” Opt. Express 12(15), 3605–3617 (2004).
[Crossref]

Y. Zhang, R. Zhang, X. Li, L. Ma, C. Liu, C. He, and C. Cheng, “Radially polarized plasmonic vector vortex generated by a metasurface spiral in gold film,” Opt. Express 25(25), 32150–32160 (2017).
[Crossref]

Opt. Lett. (9)

S. Segawa, Y. Kozawa, and S. Sato, “Resolution enhancement of confocal microscopy by subtraction method with vector beams,” Opt. Lett. 39(11), 3118–3121 (2014).
[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]

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]

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).
[Crossref]

V. V. Kotlyar, S. N. Khonina, A. A. Kovalev, V. A. Soifer, H. Elfstrom, and J. Turunen, “Diffraction of a plane, finite-radius wave by a spiral phase plate,” Opt. Lett. 31(11), 1597–1599 (2006).
[Crossref]

S. Fu, C. Gao, Y. Shi, K. Dai, L. Zhong, and S. Zhang, “Generating polarization vortices by using helical beams and a Twyman Green interferometer,” Opt. Lett. 40(8), 1775–1778 (2015).
[Crossref]

S. Chen, X. Zhou, Y. Liu, X. Ling, H. Luo, and S. Wen, “Generation of arbitrary cylindrical vector beams on the higher order Poincaré sphere,” Opt. Lett. 39(18), 5274–5276 (2014).
[Crossref]

O. Emile and J. Emile, “Naked eye picometer resolution in a Michelson interferometer using conjugated twisted beams,” Opt. Lett. 42(2), 354–357 (2017).
[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]

Optica (2)

Photonics Res. (1)

S. Liu, S. Qi, Y. Zhang, P. Li, D. Wu, L. Han, and J. Zhao, “Highly efficient generation of arbitrary vector beams with tunable polarization, phase, and amplitude,” Photonics Res. 6(4), 228–233 (2018).
[Crossref]

Phys. Rev. A (2)

V. D’Ambrosio, G. Carvacho, F. Graffitti, C. Vitelli, B. Piccirillo, L. Marrucci, and F. Sciarrino, “Entangled vector vortex beams,” Phys. Rev. A 94(3), 030304 (2016).
[Crossref]

X. Yi, Y. Liu, X. Ling, X. Zhou, Y. Ke, H. Luo, S. Wen, and D. Fan, “Hybrid-order Poincaré sphere,” Phys. Rev. A 91(2), 023801 (2015).
[Crossref]

Phys. Rev. Lett. (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]

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]

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

Proc. Natl. Acad. Sci. (1)

R. Fickler, G. Campbell, B. Buchler, P. K. Lam, and A. Zeilinger, “Quantum entanglement of angular momentum states with quantum numbers up to 10,010,” Proc. Natl. Acad. Sci. 113(48), 13642–13647 (2016).
[Crossref]

Sci. Bull. (1)

J. Chen, C. Wan, and Q. Zhan, “Vectorial optical fields: recent advances and future prospects,” Sci. Bull. 63(1), 54–74 (2018).
[Crossref]

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 (5)

Fig. 1.
Fig. 1. Schematic diagram of the experimental setup to generated arbitrary HOP beams. SPF: spatial pinhole filter; A1 and A2: circular apertures; L1, L2 and L3: lens; SPP: spiral phase plate; HWP: half-wave plate; PBS: polarizing beam splitter; M1 and M2: mirrors; QWP1 and QWP2: quarter-wave plate; BS: beam splitter; P: polarized analyzer.
Fig. 2.
Fig. 2. Vector beams at HOP sphere of l = +3 and −3. (a) HOP sphere of l = +3. The eight labeled points from A1 to A4, and from A1′ to A4′ are distributed evenly with constant longitude increment on equator (labeled in red). (b) Simulated and experimental intensity patterns of vector beams on HOP sphere l = +3 at points from A1 to A4 with the longitudes ϕn = /4 (n = 1, 2, 3 and 4) and from A1′ to A4′ with the longitudes ϕn′ = π+/4, respectively. The left part in each figure is superposed intensity of the simulated horizontally and vertically polarized components, overlaid with the polarization state; the right part is experimental pattern of x-polarized component. The insert map is the corresponding simulated pattern. (c) HOP sphere of l = −3. Eight labeled points from B1 to B4, and from B1′ to B4′ are distributed evenly on the circle of latitude θ = 3π/4 (labeled in blue). (d) Simulated and experimental intensity patterns of vector beams on HOP sphere l = −3 at points from B1 to B4, and from B1′ to B4′, respectively.
Fig. 3.
Fig. 3. Simulated and experimental intensity patterns and the experimental Stokes parameters distributions of eight Bell states. (a) Bell states for |l| = 1. The patterns from top to bottom rows are the intensities of |TM>1, |TE>1, |HE e >1 and |HE o >1, corresponding to the vector beams and the π-vector beams of linear polarizations at the points (0, 0) and (0, π) on both HOP spheres of l = 1 and –1, respectively. (b) Bell states for |l| = 2. The patterns from top to bottom rows are the intensities of |TM>2, |TE>2 with l = 2, and |HE e >2, |HE o >2 with l = –2, respectively. From left to right columns, the patterns are the simulated intensities overlaid with polarization states, experimental intensities and the component intensities of x-, 45°-, y-, 135°-polarizations, respectively. Insets are the corresponding patterns of simulations. (c) Stokes parameters distribution S1 1 , S2 1 and S3 1 . From top to bottom, the patterns are for Bell states |TM>1, |TE>1, |HE e >1 and |HE o >1, respectively. (d) Stokes parameters distribution S1 2 , S2 2 and S3 2 . From top to bottom, the patterns are for Bell states |TM>2, |TE>2, |HE e >2 and |HE o >2, respectively.
Fig. 4.
Fig. 4. Simulated and experimental results of vector beams at the points in a meridian of longitude ϕ = 0. (a) Simulated and experimental intensity patterns of seven vector beams on HOP sphere l = +3 at points from C1 to C7 with the latitudes θn = /8 (n = 1, 2, 3, …, 7). In each row, from left to right, the patterns are simulated intensities with overlaid polarization states, experimental component intensities of x-polarized and y-polarized, and the insets are the corresponding simulational patterns. (b) HOP sphere of l = +3. The seven labeled points from C1 to C7 are distributed evenly in one meridian with fixed longitude ϕ = 0. (c) Theoretical curves and experimental data of the ratio η(θ). (d) The experimental intensity curves of the first ring versus azimuth angle φ taken from the x-component patterns from C1 to C4, and the corresponding fit curves. (e) The experimental intensity curves versus azimuth angle φ taken from the y-component patterns from C4 to C7, and the corresponding fit curves.
Fig. 5.
Fig. 5. Simulation and experimental results for the radially polarized CV beams on HOP sphere of l = 8 (the first two rows) and l = 16 (the last two rows). In each row, the images from left to right are the simulated superposed intensity overlaid with polarization distribution or the experimental superposed intensity, and the component field polarizing in x-, 45°-, y-, 135°-directions, respectively.

Tables (1)

Tables Icon

Table 1. Theoretical and experimental values of generated HOPs modes under different conditions

Equations (11)

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

u l ( r , φ ) = e i δ /2 [ cos ( 2 α ) e i ( l φ + δ /2 ) + sin ( 2 α ) e i ( l φ + δ /2 ) i cos ( 2 α ) e i ( l φ + δ /2 )  -  i sin ( 2 α ) e i ( l φ + δ /2 ) ] circ( r R ,
U ( ρ , γ ) = cos( 2 α ) [ 1 i ] [ k = + ( i ) k 0 2 π e i k γ e i l φ e i k φ d φ 0 R r J l ( 2 π r ρ ) d r ]  + sin( 2 α ) e i δ [ 1 i ] [ k = + ( i ) k 0 2 π e i k γ e i l φ e i k φ d φ 0 R r J l ( 2 π r ρ ) d r ]   .
U ( ρ , γ ) = ( i ) l + 1 2 k f 1 e i δ / 2 P l ( γ ) 0 R J l ( k r ρ / f ) r d r ,
P l ( γ ) =  2 2 [ cos ( 2 α ) e i ( l γ + δ /2) + sin ( 2 α ) e i ( l γ + δ /2) i cos ( 2 α ) e i ( l γ + δ /2)  -  i sin ( 2 α ) e i ( l γ + δ /2) ] ,
U ( ρ , γ ) = ( i ) l + 1 2 e i δ / 2 ( l + 2 ) l ! ( k R 2 f ) ( k R ρ 2 f ) l 1 F 2 [ l  +  2 2 , l  + 4 2 , l  + 1; ( k R ρ 2 f ) 2 ] P l ( γ ) ,
I l ( ρ l ) = k 2 R 4 2 f 2 J l 2 ( k R ρ l f ) ,
E ( r ; θ , ϕ )  =  E 0 ( r ) | ψ m ( θ , ϕ ) = 2 2 E 0 ( r ) [ cos ( θ / 2 ) e i ( m φ + ϕ / 2 ) + sin ( θ / 2 ) e i ( m φ + ϕ / 2 ) i cos ( θ / 2 ) e i ( m φ + ϕ / 2 )  -  i sin ( θ / 2 ) e i ( m φ + ϕ / 2 ) ] ,
θ  =  4 α ;   ϕ  =  δ ;   m  =  l ,
E 0 ( r ) = ( i ) l + 1 2 e i δ / 2 ( l + 2 ) l ! ( k R 2 f ) ( k R ρ 2 f ) l 1 F 2 [ l  +  2 2 , l  + 4 2 , l  + 1; ( k R ρ 2 f ) 2 ]   .
P l ( γ )  =  [ cos ( l γ + δ / δ 2 2 ) sin ( l γ + δ / δ 2 2 ) ]   .
[ I x ( φ ) I y ( φ ) ] = k 2 R 4 J l 2 ( k R ρ l / k R ρ l f f ) 4 f 2 [ 1 + sin ( θ ) cos ( 2 l φ + ϕ ) 1 sin ( θ ) cos ( 2 l φ + ϕ ) ] ,

Metrics