Abstract

We propose and experimentally demonstrate the complete and simultaneous modulation of the amplitude, phase and arbitrary state of polarization of optical beams. Based on a 4-f system including a spatial light modulator (SLM), two orthogonally polarized beams serving as the base vector components are produced by a computer generated hologram. The complex amplitude of orthogonal components is realized by a macro-pixel encoding technique purposely designed for phase-only SLMs. Vector beams can be created from the coaxial superposition of the two base beams. This enables us to design optical fields with arbitrarily structured amplitude, phase and polarization by using only one SLM, and thus provides an easy-to-implement route for exploring the novel effects and expanding the functionality of vector beams with space-variant parameters.

© 2015 Optical Society of America

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References

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  1. D. G. Grier, “A revolution in optical manipulation,” Nature 424(6950), 810–816 (2003).
    [Crossref] [PubMed]
  2. A. M. Yao and M. J. Padgett, “Orbital angular momentum: origins, behavior and applications,” Adv. Opt. Photonics 3(2), 161–204 (2011).
    [Crossref]
  3. 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] [PubMed]
  4. G. A. Siviloglou, J. Broky, A. Dogariu, and D. N. Christodoulides, “Observation of Accelerating Airy Beams,” Phys. Rev. Lett. 99(21), 213901 (2007).
    [Crossref] [PubMed]
  5. J. Durnin, “Exact solutions for nondiffracting beams. I. The scalar theory,” J. Opt. Soc. Am. A 4(4), 651–654 (1987).
    [Crossref]
  6. Q. Zhan, “Cylindrical vector beams: from mathematical concepts to applications,” Adv. Opt. Photonics 1(1), 1–57 (2009).
    [Crossref]
  7. F. Kenny, D. Lara, O. G. Rodríguez-Herrera, and C. Dainty, “Complete polarization and phase control for focus-shaping in high-NA microscopy,” Opt. Express 20(13), 14015–14029 (2012).
    [Crossref] [PubMed]
  8. W. Chen and Q. Zhan, “Diffraction limited focusing with controllable arbitrary three-dimensional polarization,” J. Opt. 12(4), 045707 (2010).
    [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] [PubMed]
  10. K. J. Moh, X.-C. Yuan, J. Bu, S. W. Zhu, and B. Z. Gao, “Radial polarization induced surface plasmon virtual probe for two-photon fluorescence microscopy,” Opt. Lett. 34(7), 971–973 (2009).
    [Crossref] [PubMed]
  11. K. Lou, S. X. Qian, Z. C. Ren, C. Tu, Y. Li, and H. T. Wang, “Femtosecond Laser Processing by Using Patterned Vector Optical Fields,” Sci. Rep. 3, 2281 (2013).
    [Crossref] [PubMed]
  12. D. B. Ruffner and D. G. Grier, “Optical Forces and Torques in Nonuniform Beams of Light,” Phys. Rev. Lett. 108(17), 173602 (2012).
    [Crossref] [PubMed]
  13. M. I. Marqués, “Beam configuration proposal to verify that scattering forces come from the orbital part of the Poynting vector,” Opt. Lett. 39(17), 5122–5125 (2014).
    [Crossref] [PubMed]
  14. V. Arrizón, G. Méndez, and D. Sánchez-de-La-Llave, “Accurate encoding of arbitrary complex fields with amplitude-only liquid crystal spatial light modulators,” Opt. Express 13(20), 7913–7927 (2005).
    [Crossref] [PubMed]
  15. E. G. van Putten, I. M. Vellekoop, and A. P. Mosk, “Spatial amplitude and phase modulation using commercial twisted nematic LCDs,” Appl. Opt. 47(12), 2076–2081 (2008).
    [Crossref] [PubMed]
  16. H. Chen, J. Hao, B.-F. Zhang, J. Xu, J. Ding, and H.-T. Wang, “Generation of vector beam with space-variant distribution of both polarization and phase,” Opt. Lett. 36(16), 3179–3181 (2011).
    [Crossref] [PubMed]
  17. F. Kenny, D. Lara, O. G. Rodríguez-Herrera, and C. Dainty, “Complete polarization and phase control for focus-shaping in high-NA microscopy,” Opt. Express 20(13), 14015–14029 (2012).
    [Crossref] [PubMed]
  18. W. Han, Y. Yang, W. Cheng, and Q. Zhan, “Vectorial optical field generator for the creation of arbitrarily complex fields,” Opt. Express 21(18), 20692–20706 (2013).
    [Crossref] [PubMed]
  19. E. H. Waller and G. von Freymann, “Independent spatial intensity, phase and polarization distributions,” Opt. Express 21(23), 28167–28174 (2013).
    [Crossref] [PubMed]
  20. I. Moreno, J. A. Davis, T. M. Hernandez, D. M. Cottrell, and D. Sand, “Complete polarization control of light from a liquid crystal spatial light modulator,” Opt. Express 20(1), 364–376 (2012).
    [Crossref] [PubMed]
  21. D. Goldstein, Polarized Light, (Marcel Dekker Inc., 2003).
  22. V. Bagnoud and J. D. Zuegel, “Independent phase and amplitude control of a laser beam by use of a single-phase-only spatial light modulator,” Opt. Lett. 29(3), 295–297 (2004).
    [Crossref] [PubMed]
  23. L. Z. Liu, K. O’Keeffe, D. T. Lloyd, and S. M. Hooker, “General analytic solution for far-field phase and amplitude control, with a phase-only spatial light modulator,” Opt. Lett. 39(7), 2137–2140 (2014).
    [Crossref] [PubMed]
  24. S. Ngcobo, I. Litvin, L. Burger, and A. Forbes, “A digital laser for on-demand laser modes,” Nat. Commun. 4, 2289 (2013).
    [Crossref] [PubMed]
  25. D. Mendlovic, G. Shabtay, U. Levi, Z. Zalevsky, and E. Marom, “Encoding technique for design of zero-order (on-axis) Fraunhofer computer-generated holograms,” Appl. Opt. 36(32), 8427–8434 (1997).
    [Crossref] [PubMed]
  26. M. Yang and J. Ding, “Area encoding for design of phase-only computer-generated holograms,” Opt. Commun. 203(1-2), 51–60 (2002).
    [Crossref]
  27. S. Choi, J. Roh, H. Song, G. Sung, J. An, W. Seo, K. Won, J. Ungnapatanin, M. Jung, Y. Yoon, H. S. Lee, C. H. Oh, J. Hahn, and H. Kim, “Modulation efficiency of double-phase hologram complex light modulation macro-pixels,” Opt. Express 22(18), 21460–21470 (2014).
    [Crossref] [PubMed]
  28. A. M. Beckley, T. G. Brown, and M. A. Alonso, “Full Poincaré beams,” Opt. Express 18(10), 10777–10785 (2010).
    [Crossref] [PubMed]
  29. J. E. Curtis and D. G. Grier, “Structure of Optical Vortices,” Phys. Rev. Lett. 90(13), 133901 (2003).
    [Crossref] [PubMed]
  30. A. S. Ostrovsky, C. Rickenstorff-Parrao, and V. Arrizón, “Generation of the “perfect” optical vortex using a liquid-crystal spatial light modulator,” Opt. Lett. 38(4), 534–536 (2013).
    [Crossref] [PubMed]
  31. 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]
  32. 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]

2015 (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] [PubMed]

2014 (4)

2013 (5)

2012 (4)

2011 (3)

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]

A. M. Yao and M. J. Padgett, “Orbital angular momentum: origins, behavior and applications,” Adv. Opt. Photonics 3(2), 161–204 (2011).
[Crossref]

H. Chen, J. Hao, B.-F. Zhang, J. Xu, J. Ding, and H.-T. Wang, “Generation of vector beam with space-variant distribution of both polarization and phase,” Opt. Lett. 36(16), 3179–3181 (2011).
[Crossref] [PubMed]

2010 (3)

2009 (2)

2008 (1)

2007 (1)

G. A. Siviloglou, J. Broky, A. Dogariu, and D. N. Christodoulides, “Observation of Accelerating Airy Beams,” Phys. Rev. Lett. 99(21), 213901 (2007).
[Crossref] [PubMed]

2005 (1)

2004 (1)

2003 (2)

J. E. Curtis and D. G. Grier, “Structure of Optical Vortices,” Phys. Rev. Lett. 90(13), 133901 (2003).
[Crossref] [PubMed]

D. G. Grier, “A revolution in optical manipulation,” Nature 424(6950), 810–816 (2003).
[Crossref] [PubMed]

2002 (1)

M. Yang and J. Ding, “Area encoding for design of phase-only computer-generated holograms,” Opt. Commun. 203(1-2), 51–60 (2002).
[Crossref]

1997 (1)

1987 (1)

Alfano, R. R.

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]

Alonso, M. A.

An, J.

Arrizón, V.

Bagnoud, V.

Beckley, A. M.

Broky, J.

G. A. Siviloglou, J. Broky, A. Dogariu, and D. N. Christodoulides, “Observation of Accelerating Airy Beams,” Phys. Rev. Lett. 99(21), 213901 (2007).
[Crossref] [PubMed]

Brown, T. G.

Bu, J.

Burger, L.

S. Ngcobo, I. Litvin, L. Burger, and A. Forbes, “A digital laser for on-demand laser modes,” Nat. Commun. 4, 2289 (2013).
[Crossref] [PubMed]

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] [PubMed]

Chen, H.

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] [PubMed]

Chen, S.

Chen, W.

W. Chen and Q. Zhan, “Diffraction limited focusing with controllable arbitrary three-dimensional polarization,” J. Opt. 12(4), 045707 (2010).
[Crossref]

Cheng, W.

Choi, S.

Christodoulides, D. N.

G. A. Siviloglou, J. Broky, A. Dogariu, and D. N. Christodoulides, “Observation of Accelerating Airy Beams,” Phys. Rev. Lett. 99(21), 213901 (2007).
[Crossref] [PubMed]

Cottrell, D. M.

Curtis, J. E.

J. E. Curtis and D. G. Grier, “Structure of Optical Vortices,” Phys. Rev. Lett. 90(13), 133901 (2003).
[Crossref] [PubMed]

Dainty, C.

Davis, J. A.

Ding, J.

Dogariu, A.

G. A. Siviloglou, J. Broky, A. Dogariu, and D. N. Christodoulides, “Observation of Accelerating Airy Beams,” Phys. Rev. Lett. 99(21), 213901 (2007).
[Crossref] [PubMed]

Durnin, J.

Forbes, A.

S. Ngcobo, I. Litvin, L. Burger, and A. Forbes, “A digital laser for on-demand laser modes,” Nat. Commun. 4, 2289 (2013).
[Crossref] [PubMed]

Gao, B. Z.

Grier, D. G.

D. B. Ruffner and D. G. Grier, “Optical Forces and Torques in Nonuniform Beams of Light,” Phys. Rev. Lett. 108(17), 173602 (2012).
[Crossref] [PubMed]

J. E. Curtis and D. G. Grier, “Structure of Optical Vortices,” Phys. Rev. Lett. 90(13), 133901 (2003).
[Crossref] [PubMed]

D. G. Grier, “A revolution in optical manipulation,” Nature 424(6950), 810–816 (2003).
[Crossref] [PubMed]

Hahn, J.

Han, W.

Hao, J.

Hernandez, T. M.

Hooker, S. M.

Jung, M.

Kenny, F.

Kim, H.

Kozawa, Y.

Lara, D.

Lee, H. S.

Levi, U.

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] [PubMed]

Li, Y.

K. Lou, S. X. Qian, Z. C. Ren, C. Tu, Y. Li, and H. T. Wang, “Femtosecond Laser Processing by Using Patterned Vector Optical Fields,” Sci. Rep. 3, 2281 (2013).
[Crossref] [PubMed]

Ling, X.

Litvin, I.

S. Ngcobo, I. Litvin, L. Burger, and A. Forbes, “A digital laser for on-demand laser modes,” Nat. Commun. 4, 2289 (2013).
[Crossref] [PubMed]

Liu, L. Z.

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] [PubMed]

Liu, Y.

Lloyd, D. T.

Lou, K.

K. Lou, S. X. Qian, Z. C. Ren, C. Tu, Y. Li, and H. T. Wang, “Femtosecond Laser Processing by Using Patterned Vector Optical Fields,” Sci. Rep. 3, 2281 (2013).
[Crossref] [PubMed]

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] [PubMed]

Luo, H.

Marom, E.

Marqués, M. I.

Méndez, G.

Mendlovic, D.

Milione, G.

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]

Moh, K. J.

Moreno, I.

Mosk, A. P.

Ngcobo, S.

S. Ngcobo, I. Litvin, L. Burger, and A. Forbes, “A digital laser for on-demand laser modes,” Nat. Commun. 4, 2289 (2013).
[Crossref] [PubMed]

Nolan, D. A.

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]

O’Keeffe, K.

Oh, C. H.

Ostrovsky, A. S.

Padgett, M. J.

A. M. Yao and M. J. Padgett, “Orbital angular momentum: origins, behavior and applications,” Adv. Opt. Photonics 3(2), 161–204 (2011).
[Crossref]

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] [PubMed]

Qian, S. X.

K. Lou, S. X. Qian, Z. C. Ren, C. Tu, Y. Li, and H. T. Wang, “Femtosecond Laser Processing by Using Patterned Vector Optical Fields,” Sci. Rep. 3, 2281 (2013).
[Crossref] [PubMed]

Ren, Z. C.

K. Lou, S. X. Qian, Z. C. Ren, C. Tu, Y. Li, and H. T. Wang, “Femtosecond Laser Processing by Using Patterned Vector Optical Fields,” Sci. Rep. 3, 2281 (2013).
[Crossref] [PubMed]

Rickenstorff-Parrao, C.

Rodríguez-Herrera, O. G.

Roh, J.

Ruffner, D. B.

D. B. Ruffner and D. G. Grier, “Optical Forces and Torques in Nonuniform Beams of Light,” Phys. Rev. Lett. 108(17), 173602 (2012).
[Crossref] [PubMed]

Sánchez-de-La-Llave, D.

Sand, D.

Sato, S.

Seo, W.

Shabtay, G.

Siviloglou, G. A.

G. A. Siviloglou, J. Broky, A. Dogariu, and D. N. Christodoulides, “Observation of Accelerating Airy Beams,” Phys. Rev. Lett. 99(21), 213901 (2007).
[Crossref] [PubMed]

Song, H.

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] [PubMed]

Sung, G.

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] [PubMed]

Tu, C.

K. Lou, S. X. Qian, Z. C. Ren, C. Tu, Y. Li, and H. T. Wang, “Femtosecond Laser Processing by Using Patterned Vector Optical Fields,” Sci. Rep. 3, 2281 (2013).
[Crossref] [PubMed]

Ungnapatanin, J.

van Putten, E. G.

Vellekoop, I. M.

von Freymann, G.

Waller, E. H.

Wang, H. T.

K. Lou, S. X. Qian, Z. C. Ren, C. Tu, Y. Li, and H. T. Wang, “Femtosecond Laser Processing by Using Patterned Vector Optical Fields,” Sci. Rep. 3, 2281 (2013).
[Crossref] [PubMed]

Wang, H.-T.

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] [PubMed]

Wen, S.

Won, K.

Wu, 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] [PubMed]

Xu, J.

Yang, M.

M. Yang and J. Ding, “Area encoding for design of phase-only computer-generated holograms,” Opt. Commun. 203(1-2), 51–60 (2002).
[Crossref]

Yang, Y.

Yao, A. M.

A. M. Yao and M. J. Padgett, “Orbital angular momentum: origins, behavior and applications,” Adv. Opt. Photonics 3(2), 161–204 (2011).
[Crossref]

Yoon, Y.

Yuan, X.-C.

Zalevsky, Z.

Zhan, Q.

W. Han, Y. Yang, W. Cheng, and Q. Zhan, “Vectorial optical field generator for the creation of arbitrarily complex fields,” Opt. Express 21(18), 20692–20706 (2013).
[Crossref] [PubMed]

W. Chen and Q. Zhan, “Diffraction limited focusing with controllable arbitrary three-dimensional polarization,” J. Opt. 12(4), 045707 (2010).
[Crossref]

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

Zhang, B.-F.

Zhou, X.

Zhu, S. W.

Zuegel, J. D.

Adv. Opt. Photonics (2)

A. M. Yao and M. J. Padgett, “Orbital angular momentum: origins, behavior and applications,” Adv. Opt. Photonics 3(2), 161–204 (2011).
[Crossref]

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

Appl. Opt. (2)

J. Opt. (1)

W. Chen and Q. Zhan, “Diffraction limited focusing with controllable arbitrary three-dimensional polarization,” J. Opt. 12(4), 045707 (2010).
[Crossref]

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

Nat. Commun. (1)

S. Ngcobo, I. Litvin, L. Burger, and A. Forbes, “A digital laser for on-demand laser modes,” Nat. Commun. 4, 2289 (2013).
[Crossref] [PubMed]

Nature (2)

D. G. Grier, “A revolution in optical manipulation,” Nature 424(6950), 810–816 (2003).
[Crossref] [PubMed]

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] [PubMed]

Opt. Commun. (1)

M. Yang and J. Ding, “Area encoding for design of phase-only computer-generated holograms,” Opt. Commun. 203(1-2), 51–60 (2002).
[Crossref]

Opt. Express (9)

S. Choi, J. Roh, H. Song, G. Sung, J. An, W. Seo, K. Won, J. Ungnapatanin, M. Jung, Y. Yoon, H. S. Lee, C. H. Oh, J. Hahn, and H. Kim, “Modulation efficiency of double-phase hologram complex light modulation macro-pixels,” Opt. Express 22(18), 21460–21470 (2014).
[Crossref] [PubMed]

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

V. Arrizón, G. Méndez, and D. Sánchez-de-La-Llave, “Accurate encoding of arbitrary complex fields with amplitude-only liquid crystal spatial light modulators,” Opt. Express 13(20), 7913–7927 (2005).
[Crossref] [PubMed]

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

F. Kenny, D. Lara, O. G. Rodríguez-Herrera, and C. Dainty, “Complete polarization and phase control for focus-shaping in high-NA microscopy,” Opt. Express 20(13), 14015–14029 (2012).
[Crossref] [PubMed]

F. Kenny, D. Lara, O. G. Rodríguez-Herrera, and C. Dainty, “Complete polarization and phase control for focus-shaping in high-NA microscopy,” Opt. Express 20(13), 14015–14029 (2012).
[Crossref] [PubMed]

W. Han, Y. Yang, W. Cheng, and Q. Zhan, “Vectorial optical field generator for the creation of arbitrarily complex fields,” Opt. Express 21(18), 20692–20706 (2013).
[Crossref] [PubMed]

E. H. Waller and G. von Freymann, “Independent spatial intensity, phase and polarization distributions,” Opt. Express 21(23), 28167–28174 (2013).
[Crossref] [PubMed]

I. Moreno, J. A. Davis, T. M. Hernandez, D. M. Cottrell, and D. Sand, “Complete polarization control of light from a liquid crystal spatial light modulator,” Opt. Express 20(1), 364–376 (2012).
[Crossref] [PubMed]

Opt. Lett. (7)

Phys. Rev. Lett. (4)

J. E. Curtis and D. G. Grier, “Structure of Optical Vortices,” Phys. Rev. Lett. 90(13), 133901 (2003).
[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]

G. A. Siviloglou, J. Broky, A. Dogariu, and D. N. Christodoulides, “Observation of Accelerating Airy Beams,” Phys. Rev. Lett. 99(21), 213901 (2007).
[Crossref] [PubMed]

D. B. Ruffner and D. G. Grier, “Optical Forces and Torques in Nonuniform Beams of Light,” Phys. Rev. Lett. 108(17), 173602 (2012).
[Crossref] [PubMed]

Sci. Rep. (1)

K. Lou, S. X. Qian, Z. C. Ren, C. Tu, Y. Li, and H. T. Wang, “Femtosecond Laser Processing by Using Patterned Vector Optical Fields,” Sci. Rep. 3, 2281 (2013).
[Crossref] [PubMed]

Other (1)

D. Goldstein, Polarized Light, (Marcel Dekker Inc., 2003).

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Figures (8)

Fig. 1
Fig. 1 (a) Poincaré sphere and (b) different SoPs on Poincaré sphere.
Fig. 2
Fig. 2 Phasor diagram of decomposing a complex amplitude A mn exp(i ϕ mn ) into two constituent phasors ( aexp(i ϕ mn 1 ) and aexp(i ϕ mn 2 ) ).
Fig. 3
Fig. 3 Symmetric structure of the (m, n)-th macro-pixel synthesized from four sub-pixels with phase-only terms ϕ mn 1 and ϕ mn 2 .
Fig. 4
Fig. 4 Schematic of the experimental setup.
Fig. 5
Fig. 5 Experimental results of optical vortex field with circular and square intensity distribution.
Fig. 6
Fig. 6 Theoretical (first row) and experimental (second row) results of space-variant polarization field to be designed: (a) SoPs in the cross-section, (b-d) simulated values of the Stokes parameters, (e) recorded intensity (or S0), and (f-h) measured values of the Stokes parameters of S1, S2 and S3.
Fig. 7
Fig. 7 (a) Higher-order PS for the TC of l = −1, (b) SoP of the field to be produced: four regions denoted by A, B, C and D carrying the SoPs marked by the corresponding letters on the HOPS. The outer annulus (A), middle annulus (B), and inner ring-shaped zone (C and D) are endowed with different intensities; the respective values are 1, 2 and 4.
Fig. 8
Fig. 8 Theoretical and experimental results of the higher-order PS field illustrated in Fig. 7(b): (a) theoretical intensity I in the cross-section, (b-d) simulated values of the Stokes parameters, (e) recorded intensity I in the cross-section, (f-h) measured values of the Stokes parameters, (i) and (k) experimental interference patterns between the generated field with right and left circularly polarized plane waves, (j) and (l) theoretical phases carried by right and left circularly polarized components.

Equations (10)

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E (x,y)=( E x ( x,y ) E y ( x,y ) )=( A x (x,y)exp(i ϕ x (x,y)) A y (x,y)exp(i ϕ y (x,y)) ),
S 1 = A x 2 A y 2 , S 2 =2 A x A y cosδ, S 3 =2 A x A y sinδ,
χ= 1 2 sin 1 ( S 3 S 0 ), - π 4 χ π 4 , ψ= 1 2 tan 1 ( S 2 S 0 ), 0ψ<π,
E ( x,y )= S 0 ( x,y ) e iβ( x,y ) [ cosα( x,y ) sinα( x,y ) e iδ( x,y ) ],
A mn exp(i ϕ mn )=aexp(i ϕ mn 1 )+aexp(i ϕ mn 2 )
t i,j (m,n)=( 1 2 + 1 4 { cos[ 2π f 0 m( 2Δ )+ φ x,mn i,j ]+cos[ 2π f 0 n( 2Δ )+ φ y,mn i,j ] } ),
φ x,mn i,j = ϕ x,mn 1 δ ij + ϕ x,mn 2 ( 1 δ ij ), φ y,mn i,j = ϕ y,mn 1 δ ij + ϕ y,mn 2 ( 1 δ ij ),
E = A L L ^ l + A R R ^ l ,
L ^ l = 1 2 e ilφ ( 1 i ), R ^ l = 1 2 e ilφ ( 1 i )
E A =0.707 R ^ 1 +0.707 L ^ 1 , E B =1.307 R ^ 1 +0.541exp(iπ/2) L ^ 1 , E C =2 R ^ 1 , E D =2 L ^ 1

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