Abstract

We present a detailed theoretical analysis of the formation of standing waves using cylindrically polarized vector Laguerre-Gaussian (LG) beams. It is shown that complex interplay between the radial and azimuthal polarization state can be used to realize different kinds of polarization gradients with cylindrically symmetric polarization distribution. Expressions for four different cases are presented and local dynamics of spatial polarization distribution is studied. We show cylindrically symmetric Sisyphus and corkscrew type polarization gradients can be obtained from vector LG beams. The optical landscape presented here with spatially periodic polarization patterns may find important applications in the field of atom optics, atom interferometry, atom lithography, and optical trapping.

© 2015 Optical Society of America

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References

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    [Crossref]
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    [Crossref]
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    [Crossref]
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    [Crossref]
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    [Crossref] [PubMed]
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    [Crossref] [PubMed]
  26. S. A. Schulz, T. Machula, E. Karimi, and R. W. Boyd, “Integrated multi vector vortex beam generator,” Opt. Express 21(13), 16130–16141 (2013).
    [Crossref] [PubMed]
  27. S. Ngcobo, I. Litvin, L. Burger, and A. Forbes, “A digital laser for on-demand laser modes,” Nat. Commun. 4, 2289 (2013).
    [Crossref] [PubMed]
  28. T. Bauer, S. Orlov, U. Peschel, P. Banzer, and G. Leuchs, “Nanointerfereometric amplitude and phase reconstruction of tightly focused vector beams,” Nat. Photonics 8(1), 23–27 (2013).
    [Crossref]
  29. T. Bauer, P. Banzer, E. Karimi, S. Orlov, A. Rubano, L. Marrucci, E. Santamato, R. W. Boyd, and G. Leuchs, “Observation of optical polarization Möbius strips,” Science 347(6225), 964–966 (2015).
    [Crossref] [PubMed]
  30. T. Čižmár, V. Garcés-Chávez, K. Dholakia, and P. Zemánek, “Optical conveyor belt for delivery of submicron objects,” Appl. Phys. Lett. 86(17), 174101 (2005).
    [Crossref]

2015 (4)

V. Parigi, V. D’Ambrosio, C. Arnold, L. Marrucci, F. Sciarrino, and J. Laurat, “Storage and retrieval of vector beams of light in a multiple-degree-of-freedom quantum memory,” Nat. Commun. 6, 7706 (2015).
[Crossref] [PubMed]

T. Bauer, P. Banzer, E. Karimi, S. Orlov, A. Rubano, L. Marrucci, E. Santamato, R. W. Boyd, and G. Leuchs, “Observation of optical polarization Möbius strips,” Science 347(6225), 964–966 (2015).
[Crossref] [PubMed]

O. Brzobohatý, A. V. Arzola, M. Šiler, L. Chvátal, P. Jákl, S. Simpson, and P. Zemánek, “Complex rotational dynamics of multiple spheroidal particles in a circularly polarized, dual beam trap,” Opt. Express 23(6), 7273–7287 (2015).
[Crossref] [PubMed]

I. Moreno, J. A. Davis, M. M. Sánchez-López, K. Badham, and D. M. Cottrell, “Nondiffracting Bessel beams with polarization state that varies with propagation distance,” Opt. Lett. 40(23), 5451–5454 (2015).
[Crossref] [PubMed]

2014 (2)

R. Zhang and H. Guo, “Phase gradients from intensity gradients: a method of spatial carrier fringe pattern analysis,” Opt. Express 22(19), 22432–22445 (2014).
[Crossref] [PubMed]

F. Töppel, A. Aiello, C. Marquardt, E. Giacobino, and G. Leuchs, “Classical entanglement in polarization metrology,” New J. Phys. 16(7), 073019 (2014).
[Crossref]

2013 (4)

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

T. Bauer, S. Orlov, U. Peschel, P. Banzer, and G. Leuchs, “Nanointerfereometric amplitude and phase reconstruction of tightly focused vector beams,” Nat. Photonics 8(1), 23–27 (2013).
[Crossref]

S. Vyas, Y. Kozawa, and S. Sato, “Polarization singularities in superposition of vector beams,” Opt. Express 21(7), 8972–8986 (2013).
[Crossref] [PubMed]

S. A. Schulz, T. Machula, E. Karimi, and R. W. Boyd, “Integrated multi vector vortex beam generator,” Opt. Express 21(13), 16130–16141 (2013).
[Crossref] [PubMed]

2011 (4)

Y. Kozawa, T. Hibi, A. Sato, H. Horanai, M. Kurihara, N. Hashimoto, H. Yokoyama, T. Nemoto, and S. Sato, “Lateral resolution enhancement of laser scanning microscopy by a higher-order radially polarized mode beam,” Opt. Express 19(17), 15947–15954 (2011).
[Crossref] [PubMed]

J. Xavier, S. Vyas, P. Senthilkumaran, C. Denz, and J. Joseph, “Sculptured 3D twister superlattices embedded with tunable vortex spirals,” Opt. Lett. 36(17), 3512–3514 (2011).
[Crossref] [PubMed]

V. E. Lembessis, D. Ellinas, and M. Babiker, “Azimuthal Sisyphus effect for atoms in a toroidal all optical trap,” Phys. Rev. A 84(4), 043422 (2011).
[Crossref]

A. Ramanathan, K. C. Wright, S. R. Muniz, M. Zelan, W. T. Hill, C. J. Lobb, K. Helmerson, W. D. Phillips, and G. K. Campbell, “Superflow in a toroidal Bose-Einstein condensate: an atom circuit with a tunable weak link,” Phys. Rev. Lett. 106(13), 130401 (2011).
[Crossref] [PubMed]

2010 (1)

V. E. Lembessis and M. Babiker, “Spatiotemporal polarization gradients in phase-bearing light,” Phys. Rev. A 81(3), 033811 (2010).
[Crossref]

2009 (2)

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

K. Volke-Sepulveda and R. Jauregui, “All-optical 3D atomic loops generated with Bessel light fields,” J. Phys. At. Mol. Opt. Phys. 42(8), 085303 (2009).
[Crossref]

2007 (1)

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]

2006 (1)

2005 (2)

E. Kolenović, “Correlation between intensity and phase in monochromatic light,” J. Opt. Soc. Am. A 22(5), 899–906 (2005).
[Crossref] [PubMed]

T. Čižmár, V. Garcés-Chávez, K. Dholakia, and P. Zemánek, “Optical conveyor belt for delivery of submicron objects,” Appl. Phys. Lett. 86(17), 174101 (2005).
[Crossref]

2003 (1)

D. Meschede and H. Metcalf, “Atomic nanofabrication: atomic deposition and lithography by laser and magnetic forces,” J. Phys. D Appl. Phys. 36(3), R17–R38 (2003).
[Crossref]

2002 (1)

I. Freund, “Polarization singularity indices in Gaussian laser beams,” Opt. Commun. 201(4-6), 251–270 (2002).
[Crossref]

1999 (2)

W. R. Anderson, C. C. Bradley, J. J. McClelland, and R. J. Celotta, “Minimizing features width in atom optically fabricated chromium nanostructures,” Phys. Rev. A 59(3), 2476–2485 (1999).
[Crossref]

J. W. R. Tabosa and D. V. Petrov, “Optical pumping of orbital angular momentum of light in cold Cerium atoms,” Phys. Rev. Lett. 83(24), 4967–4970 (1999).
[Crossref]

1997 (3)

S. A. Hopkins and A. V. Durrant, “Parameters for polarization gradients in three-dimensional electromagnetic standing waves,” Phys. Rev. A 56(5), 4012–4022 (1997).
[Crossref]

C. S. Adams and E. Riis, “Laser cooling and trapping of neutral atoms,” Prog. Quantum Electron. 21(1), 1–79 (1997).
[Crossref]

T. Kuga, Y. Torii, N. Shiokawa, T. Hirano, Y. Shimizu, and H. Sasada, “Novel optical trap of atoms with a doughnut beam,” Phys. Rev. Lett. 78(25), 4713–4716 (1997).
[Crossref]

1989 (1)

Adams, C. S.

C. S. Adams and E. Riis, “Laser cooling and trapping of neutral atoms,” Prog. Quantum Electron. 21(1), 1–79 (1997).
[Crossref]

Aiello, A.

F. Töppel, A. Aiello, C. Marquardt, E. Giacobino, and G. Leuchs, “Classical entanglement in polarization metrology,” New J. Phys. 16(7), 073019 (2014).
[Crossref]

Anderson, W. R.

W. R. Anderson, C. C. Bradley, J. J. McClelland, and R. J. Celotta, “Minimizing features width in atom optically fabricated chromium nanostructures,” Phys. Rev. A 59(3), 2476–2485 (1999).
[Crossref]

Arnold, C.

V. Parigi, V. D’Ambrosio, C. Arnold, L. Marrucci, F. Sciarrino, and J. Laurat, “Storage and retrieval of vector beams of light in a multiple-degree-of-freedom quantum memory,” Nat. Commun. 6, 7706 (2015).
[Crossref] [PubMed]

Arzola, A. V.

Babiker, M.

V. E. Lembessis, D. Ellinas, and M. Babiker, “Azimuthal Sisyphus effect for atoms in a toroidal all optical trap,” Phys. Rev. A 84(4), 043422 (2011).
[Crossref]

V. E. Lembessis and M. Babiker, “Spatiotemporal polarization gradients in phase-bearing light,” Phys. Rev. A 81(3), 033811 (2010).
[Crossref]

Badham, K.

Banzer, P.

T. Bauer, P. Banzer, E. Karimi, S. Orlov, A. Rubano, L. Marrucci, E. Santamato, R. W. Boyd, and G. Leuchs, “Observation of optical polarization Möbius strips,” Science 347(6225), 964–966 (2015).
[Crossref] [PubMed]

T. Bauer, S. Orlov, U. Peschel, P. Banzer, and G. Leuchs, “Nanointerfereometric amplitude and phase reconstruction of tightly focused vector beams,” Nat. Photonics 8(1), 23–27 (2013).
[Crossref]

Bauer, T.

T. Bauer, P. Banzer, E. Karimi, S. Orlov, A. Rubano, L. Marrucci, E. Santamato, R. W. Boyd, and G. Leuchs, “Observation of optical polarization Möbius strips,” Science 347(6225), 964–966 (2015).
[Crossref] [PubMed]

T. Bauer, S. Orlov, U. Peschel, P. Banzer, and G. Leuchs, “Nanointerfereometric amplitude and phase reconstruction of tightly focused vector beams,” Nat. Photonics 8(1), 23–27 (2013).
[Crossref]

Bernet, S.

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]

Boyd, R. W.

T. Bauer, P. Banzer, E. Karimi, S. Orlov, A. Rubano, L. Marrucci, E. Santamato, R. W. Boyd, and G. Leuchs, “Observation of optical polarization Möbius strips,” Science 347(6225), 964–966 (2015).
[Crossref] [PubMed]

S. A. Schulz, T. Machula, E. Karimi, and R. W. Boyd, “Integrated multi vector vortex beam generator,” Opt. Express 21(13), 16130–16141 (2013).
[Crossref] [PubMed]

Bradley, C. C.

W. R. Anderson, C. C. Bradley, J. J. McClelland, and R. J. Celotta, “Minimizing features width in atom optically fabricated chromium nanostructures,” Phys. Rev. A 59(3), 2476–2485 (1999).
[Crossref]

Brzobohatý, O.

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]

Campbell, G. K.

A. Ramanathan, K. C. Wright, S. R. Muniz, M. Zelan, W. T. Hill, C. J. Lobb, K. Helmerson, W. D. Phillips, and G. K. Campbell, “Superflow in a toroidal Bose-Einstein condensate: an atom circuit with a tunable weak link,” Phys. Rev. Lett. 106(13), 130401 (2011).
[Crossref] [PubMed]

Celotta, R. J.

W. R. Anderson, C. C. Bradley, J. J. McClelland, and R. J. Celotta, “Minimizing features width in atom optically fabricated chromium nanostructures,” Phys. Rev. A 59(3), 2476–2485 (1999).
[Crossref]

Chvátal, L.

Cižmár, T.

T. Čižmár, V. Garcés-Chávez, K. Dholakia, and P. Zemánek, “Optical conveyor belt for delivery of submicron objects,” Appl. Phys. Lett. 86(17), 174101 (2005).
[Crossref]

Cohen-Tannoudji, C.

Cottrell, D. M.

D’Ambrosio, V.

V. Parigi, V. D’Ambrosio, C. Arnold, L. Marrucci, F. Sciarrino, and J. Laurat, “Storage and retrieval of vector beams of light in a multiple-degree-of-freedom quantum memory,” Nat. Commun. 6, 7706 (2015).
[Crossref] [PubMed]

Dalibard, J.

Davis, J. A.

Denz, C.

Dholakia, K.

T. Čižmár, V. Garcés-Chávez, K. Dholakia, and P. Zemánek, “Optical conveyor belt for delivery of submicron objects,” Appl. Phys. Lett. 86(17), 174101 (2005).
[Crossref]

Durrant, A. V.

S. A. Hopkins and A. V. Durrant, “Parameters for polarization gradients in three-dimensional electromagnetic standing waves,” Phys. Rev. A 56(5), 4012–4022 (1997).
[Crossref]

Ellinas, D.

V. E. Lembessis, D. Ellinas, and M. Babiker, “Azimuthal Sisyphus effect for atoms in a toroidal all optical trap,” Phys. Rev. A 84(4), 043422 (2011).
[Crossref]

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]

Freund, I.

I. Freund, “Polarization singularity indices in Gaussian laser beams,” Opt. Commun. 201(4-6), 251–270 (2002).
[Crossref]

Fürhapter, S.

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]

Garcés-Chávez, V.

T. Čižmár, V. Garcés-Chávez, K. Dholakia, and P. Zemánek, “Optical conveyor belt for delivery of submicron objects,” Appl. Phys. Lett. 86(17), 174101 (2005).
[Crossref]

Giacobino, E.

F. Töppel, A. Aiello, C. Marquardt, E. Giacobino, and G. Leuchs, “Classical entanglement in polarization metrology,” New J. Phys. 16(7), 073019 (2014).
[Crossref]

Guo, H.

Hashimoto, N.

Helmerson, K.

A. Ramanathan, K. C. Wright, S. R. Muniz, M. Zelan, W. T. Hill, C. J. Lobb, K. Helmerson, W. D. Phillips, and G. K. Campbell, “Superflow in a toroidal Bose-Einstein condensate: an atom circuit with a tunable weak link,” Phys. Rev. Lett. 106(13), 130401 (2011).
[Crossref] [PubMed]

Hibi, T.

Hill, W. T.

A. Ramanathan, K. C. Wright, S. R. Muniz, M. Zelan, W. T. Hill, C. J. Lobb, K. Helmerson, W. D. Phillips, and G. K. Campbell, “Superflow in a toroidal Bose-Einstein condensate: an atom circuit with a tunable weak link,” Phys. Rev. Lett. 106(13), 130401 (2011).
[Crossref] [PubMed]

Hirano, T.

T. Kuga, Y. Torii, N. Shiokawa, T. Hirano, Y. Shimizu, and H. Sasada, “Novel optical trap of atoms with a doughnut beam,” Phys. Rev. Lett. 78(25), 4713–4716 (1997).
[Crossref]

Hopkins, S. A.

S. A. Hopkins and A. V. Durrant, “Parameters for polarization gradients in three-dimensional electromagnetic standing waves,” Phys. Rev. A 56(5), 4012–4022 (1997).
[Crossref]

Horanai, H.

Jákl, P.

Jauregui, R.

K. Volke-Sepulveda and R. Jauregui, “All-optical 3D atomic loops generated with Bessel light fields,” J. Phys. At. Mol. Opt. Phys. 42(8), 085303 (2009).
[Crossref]

Jesacher, A.

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]

Joseph, J.

Karimi, E.

T. Bauer, P. Banzer, E. Karimi, S. Orlov, A. Rubano, L. Marrucci, E. Santamato, R. W. Boyd, and G. Leuchs, “Observation of optical polarization Möbius strips,” Science 347(6225), 964–966 (2015).
[Crossref] [PubMed]

S. A. Schulz, T. Machula, E. Karimi, and R. W. Boyd, “Integrated multi vector vortex beam generator,” Opt. Express 21(13), 16130–16141 (2013).
[Crossref] [PubMed]

Kolenovic, E.

Kozawa, Y.

Kuga, T.

T. Kuga, Y. Torii, N. Shiokawa, T. Hirano, Y. Shimizu, and H. Sasada, “Novel optical trap of atoms with a doughnut beam,” Phys. Rev. Lett. 78(25), 4713–4716 (1997).
[Crossref]

Kurihara, M.

Laurat, J.

V. Parigi, V. D’Ambrosio, C. Arnold, L. Marrucci, F. Sciarrino, and J. Laurat, “Storage and retrieval of vector beams of light in a multiple-degree-of-freedom quantum memory,” Nat. Commun. 6, 7706 (2015).
[Crossref] [PubMed]

Lembessis, V. E.

V. E. Lembessis, D. Ellinas, and M. Babiker, “Azimuthal Sisyphus effect for atoms in a toroidal all optical trap,” Phys. Rev. A 84(4), 043422 (2011).
[Crossref]

V. E. Lembessis and M. Babiker, “Spatiotemporal polarization gradients in phase-bearing light,” Phys. Rev. A 81(3), 033811 (2010).
[Crossref]

Leuchs, G.

T. Bauer, P. Banzer, E. Karimi, S. Orlov, A. Rubano, L. Marrucci, E. Santamato, R. W. Boyd, and G. Leuchs, “Observation of optical polarization Möbius strips,” Science 347(6225), 964–966 (2015).
[Crossref] [PubMed]

F. Töppel, A. Aiello, C. Marquardt, E. Giacobino, and G. Leuchs, “Classical entanglement in polarization metrology,” New J. Phys. 16(7), 073019 (2014).
[Crossref]

T. Bauer, S. Orlov, U. Peschel, P. Banzer, and G. Leuchs, “Nanointerfereometric amplitude and phase reconstruction of tightly focused vector beams,” Nat. Photonics 8(1), 23–27 (2013).
[Crossref]

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]

Lobb, C. J.

A. Ramanathan, K. C. Wright, S. R. Muniz, M. Zelan, W. T. Hill, C. J. Lobb, K. Helmerson, W. D. Phillips, and G. K. Campbell, “Superflow in a toroidal Bose-Einstein condensate: an atom circuit with a tunable weak link,” Phys. Rev. Lett. 106(13), 130401 (2011).
[Crossref] [PubMed]

Machula, T.

Marquardt, C.

F. Töppel, A. Aiello, C. Marquardt, E. Giacobino, and G. Leuchs, “Classical entanglement in polarization metrology,” New J. Phys. 16(7), 073019 (2014).
[Crossref]

Marrucci, L.

T. Bauer, P. Banzer, E. Karimi, S. Orlov, A. Rubano, L. Marrucci, E. Santamato, R. W. Boyd, and G. Leuchs, “Observation of optical polarization Möbius strips,” Science 347(6225), 964–966 (2015).
[Crossref] [PubMed]

V. Parigi, V. D’Ambrosio, C. Arnold, L. Marrucci, F. Sciarrino, and J. Laurat, “Storage and retrieval of vector beams of light in a multiple-degree-of-freedom quantum memory,” Nat. Commun. 6, 7706 (2015).
[Crossref] [PubMed]

Maurer, C.

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]

McClelland, J. J.

W. R. Anderson, C. C. Bradley, J. J. McClelland, and R. J. Celotta, “Minimizing features width in atom optically fabricated chromium nanostructures,” Phys. Rev. A 59(3), 2476–2485 (1999).
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D. Meschede and H. Metcalf, “Atomic nanofabrication: atomic deposition and lithography by laser and magnetic forces,” J. Phys. D Appl. Phys. 36(3), R17–R38 (2003).
[Crossref]

Metcalf, H.

D. Meschede and H. Metcalf, “Atomic nanofabrication: atomic deposition and lithography by laser and magnetic forces,” J. Phys. D Appl. Phys. 36(3), R17–R38 (2003).
[Crossref]

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Muniz, S. R.

A. Ramanathan, K. C. Wright, S. R. Muniz, M. Zelan, W. T. Hill, C. J. Lobb, K. Helmerson, W. D. Phillips, and G. K. Campbell, “Superflow in a toroidal Bose-Einstein condensate: an atom circuit with a tunable weak link,” Phys. Rev. Lett. 106(13), 130401 (2011).
[Crossref] [PubMed]

Nemoto, T.

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]

Orlov, S.

T. Bauer, P. Banzer, E. Karimi, S. Orlov, A. Rubano, L. Marrucci, E. Santamato, R. W. Boyd, and G. Leuchs, “Observation of optical polarization Möbius strips,” Science 347(6225), 964–966 (2015).
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T. Bauer, S. Orlov, U. Peschel, P. Banzer, and G. Leuchs, “Nanointerfereometric amplitude and phase reconstruction of tightly focused vector beams,” Nat. Photonics 8(1), 23–27 (2013).
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Parigi, V.

V. Parigi, V. D’Ambrosio, C. Arnold, L. Marrucci, F. Sciarrino, and J. Laurat, “Storage and retrieval of vector beams of light in a multiple-degree-of-freedom quantum memory,” Nat. Commun. 6, 7706 (2015).
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Peschel, U.

T. Bauer, S. Orlov, U. Peschel, P. Banzer, and G. Leuchs, “Nanointerfereometric amplitude and phase reconstruction of tightly focused vector beams,” Nat. Photonics 8(1), 23–27 (2013).
[Crossref]

Petrov, D. V.

J. W. R. Tabosa and D. V. Petrov, “Optical pumping of orbital angular momentum of light in cold Cerium atoms,” Phys. Rev. Lett. 83(24), 4967–4970 (1999).
[Crossref]

Phillips, W. D.

A. Ramanathan, K. C. Wright, S. R. Muniz, M. Zelan, W. T. Hill, C. J. Lobb, K. Helmerson, W. D. Phillips, and G. K. Campbell, “Superflow in a toroidal Bose-Einstein condensate: an atom circuit with a tunable weak link,” Phys. Rev. Lett. 106(13), 130401 (2011).
[Crossref] [PubMed]

Ramanathan, A.

A. Ramanathan, K. C. Wright, S. R. Muniz, M. Zelan, W. T. Hill, C. J. Lobb, K. Helmerson, W. D. Phillips, and G. K. Campbell, “Superflow in a toroidal Bose-Einstein condensate: an atom circuit with a tunable weak link,” Phys. Rev. Lett. 106(13), 130401 (2011).
[Crossref] [PubMed]

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C. S. Adams and E. Riis, “Laser cooling and trapping of neutral atoms,” Prog. Quantum Electron. 21(1), 1–79 (1997).
[Crossref]

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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]

Rubano, A.

T. Bauer, P. Banzer, E. Karimi, S. Orlov, A. Rubano, L. Marrucci, E. Santamato, R. W. Boyd, and G. Leuchs, “Observation of optical polarization Möbius strips,” Science 347(6225), 964–966 (2015).
[Crossref] [PubMed]

Sánchez-López, M. M.

Santamato, E.

T. Bauer, P. Banzer, E. Karimi, S. Orlov, A. Rubano, L. Marrucci, E. Santamato, R. W. Boyd, and G. Leuchs, “Observation of optical polarization Möbius strips,” Science 347(6225), 964–966 (2015).
[Crossref] [PubMed]

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T. Kuga, Y. Torii, N. Shiokawa, T. Hirano, Y. Shimizu, and H. Sasada, “Novel optical trap of atoms with a doughnut beam,” Phys. Rev. Lett. 78(25), 4713–4716 (1997).
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Sato, S.

Schulz, S. A.

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V. Parigi, V. D’Ambrosio, C. Arnold, L. Marrucci, F. Sciarrino, and J. Laurat, “Storage and retrieval of vector beams of light in a multiple-degree-of-freedom quantum memory,” Nat. Commun. 6, 7706 (2015).
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Shimizu, Y.

T. Kuga, Y. Torii, N. Shiokawa, T. Hirano, Y. Shimizu, and H. Sasada, “Novel optical trap of atoms with a doughnut beam,” Phys. Rev. Lett. 78(25), 4713–4716 (1997).
[Crossref]

Shiokawa, N.

T. Kuga, Y. Torii, N. Shiokawa, T. Hirano, Y. Shimizu, and H. Sasada, “Novel optical trap of atoms with a doughnut beam,” Phys. Rev. Lett. 78(25), 4713–4716 (1997).
[Crossref]

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Simpson, S.

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J. W. R. Tabosa and D. V. Petrov, “Optical pumping of orbital angular momentum of light in cold Cerium atoms,” Phys. Rev. Lett. 83(24), 4967–4970 (1999).
[Crossref]

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F. Töppel, A. Aiello, C. Marquardt, E. Giacobino, and G. Leuchs, “Classical entanglement in polarization metrology,” New J. Phys. 16(7), 073019 (2014).
[Crossref]

Torii, Y.

T. Kuga, Y. Torii, N. Shiokawa, T. Hirano, Y. Shimizu, and H. Sasada, “Novel optical trap of atoms with a doughnut beam,” Phys. Rev. Lett. 78(25), 4713–4716 (1997).
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K. Volke-Sepulveda and R. Jauregui, “All-optical 3D atomic loops generated with Bessel light fields,” J. Phys. At. Mol. Opt. Phys. 42(8), 085303 (2009).
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Wang, Z.

Wright, K. C.

A. Ramanathan, K. C. Wright, S. R. Muniz, M. Zelan, W. T. Hill, C. J. Lobb, K. Helmerson, W. D. Phillips, and G. K. Campbell, “Superflow in a toroidal Bose-Einstein condensate: an atom circuit with a tunable weak link,” Phys. Rev. Lett. 106(13), 130401 (2011).
[Crossref] [PubMed]

Xavier, J.

Yin, J.

Yokoyama, H.

Zelan, M.

A. Ramanathan, K. C. Wright, S. R. Muniz, M. Zelan, W. T. Hill, C. J. Lobb, K. Helmerson, W. D. Phillips, and G. K. Campbell, “Superflow in a toroidal Bose-Einstein condensate: an atom circuit with a tunable weak link,” Phys. Rev. Lett. 106(13), 130401 (2011).
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Zhan, Q.

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

Zhang, R.

Adv. Opt. Photonics (1)

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

Appl. Phys. Lett. (1)

T. Čižmár, V. Garcés-Chávez, K. Dholakia, and P. Zemánek, “Optical conveyor belt for delivery of submicron objects,” Appl. Phys. Lett. 86(17), 174101 (2005).
[Crossref]

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

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

J. Phys. At. Mol. Opt. Phys. (1)

K. Volke-Sepulveda and R. Jauregui, “All-optical 3D atomic loops generated with Bessel light fields,” J. Phys. At. Mol. Opt. Phys. 42(8), 085303 (2009).
[Crossref]

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

D. Meschede and H. Metcalf, “Atomic nanofabrication: atomic deposition and lithography by laser and magnetic forces,” J. Phys. D Appl. Phys. 36(3), R17–R38 (2003).
[Crossref]

Nat. Commun. (2)

V. Parigi, V. D’Ambrosio, C. Arnold, L. Marrucci, F. Sciarrino, and J. Laurat, “Storage and retrieval of vector beams of light in a multiple-degree-of-freedom quantum memory,” Nat. Commun. 6, 7706 (2015).
[Crossref] [PubMed]

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

Nat. Photonics (1)

T. Bauer, S. Orlov, U. Peschel, P. Banzer, and G. Leuchs, “Nanointerfereometric amplitude and phase reconstruction of tightly focused vector beams,” Nat. Photonics 8(1), 23–27 (2013).
[Crossref]

New J. Phys. (2)

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]

F. Töppel, A. Aiello, C. Marquardt, E. Giacobino, and G. Leuchs, “Classical entanglement in polarization metrology,” New J. Phys. 16(7), 073019 (2014).
[Crossref]

Opt. Commun. (1)

I. Freund, “Polarization singularity indices in Gaussian laser beams,” Opt. Commun. 201(4-6), 251–270 (2002).
[Crossref]

Opt. Express (6)

Opt. Lett. (2)

Phys. Rev. A (4)

W. R. Anderson, C. C. Bradley, J. J. McClelland, and R. J. Celotta, “Minimizing features width in atom optically fabricated chromium nanostructures,” Phys. Rev. A 59(3), 2476–2485 (1999).
[Crossref]

S. A. Hopkins and A. V. Durrant, “Parameters for polarization gradients in three-dimensional electromagnetic standing waves,” Phys. Rev. A 56(5), 4012–4022 (1997).
[Crossref]

V. E. Lembessis, D. Ellinas, and M. Babiker, “Azimuthal Sisyphus effect for atoms in a toroidal all optical trap,” Phys. Rev. A 84(4), 043422 (2011).
[Crossref]

V. E. Lembessis and M. Babiker, “Spatiotemporal polarization gradients in phase-bearing light,” Phys. Rev. A 81(3), 033811 (2010).
[Crossref]

Phys. Rev. Lett. (3)

A. Ramanathan, K. C. Wright, S. R. Muniz, M. Zelan, W. T. Hill, C. J. Lobb, K. Helmerson, W. D. Phillips, and G. K. Campbell, “Superflow in a toroidal Bose-Einstein condensate: an atom circuit with a tunable weak link,” Phys. Rev. Lett. 106(13), 130401 (2011).
[Crossref] [PubMed]

T. Kuga, Y. Torii, N. Shiokawa, T. Hirano, Y. Shimizu, and H. Sasada, “Novel optical trap of atoms with a doughnut beam,” Phys. Rev. Lett. 78(25), 4713–4716 (1997).
[Crossref]

J. W. R. Tabosa and D. V. Petrov, “Optical pumping of orbital angular momentum of light in cold Cerium atoms,” Phys. Rev. Lett. 83(24), 4967–4970 (1999).
[Crossref]

Prog. Quantum Electron. (1)

C. S. Adams and E. Riis, “Laser cooling and trapping of neutral atoms,” Prog. Quantum Electron. 21(1), 1–79 (1997).
[Crossref]

Science (1)

T. Bauer, P. Banzer, E. Karimi, S. Orlov, A. Rubano, L. Marrucci, E. Santamato, R. W. Boyd, and G. Leuchs, “Observation of optical polarization Möbius strips,” Science 347(6225), 964–966 (2015).
[Crossref] [PubMed]

Other (1)

D. L. Andrews and M. Babiker, The Angular Momentum of Light (Cambridge. Univ. Press, 2012).

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Figures (5)

Fig. 1
Fig. 1 (a) Intensity distribution for the vector LG beam with m = 1 and radial index p = 0. (b-e) Polarization distributions corresponding to type (I-IV) for vector LG beams with m = 1.
Fig. 2
Fig. 2 (a-h). Calculated intensity and polarization distributions on different z-planes for cylindrically polarized standing waves with radial symmetry.
Fig. 3
Fig. 3 (a-h). Calculated intensity and polarization distributions on different z-planes for cylindrically symmetric Sisyphus polarization gradient. Red and blue color represents right-handed and left-handed circular polarization, respectively.
Fig. 4
Fig. 4 (a-h). Calculated intensity and polarization distributions on different z-planes for corkscrew polarization gradient.
Fig. 5
Fig. 5 (a-h). Calculated intensity and polarization distributions on different z-planes for right handed circularly polarized standing wave.

Equations (19)

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E p,m ( r,ϕ,z )= U p,m ( r,z ) P m ( ϕ ),
U p,m ( r,z )= 2p! π( p+m )! 1 w(z) [ 2 r w( z ) ] | m | L p | m | [ 2 r 2 w 2 ( z ) ]exp[ r 2 w 2 ( z ) ]exp{ ik r 2 2R( z ) +ikzi( 2p+| m |+1 )η( z ) },
P m ( ϕ )={ [ cos( m1 )ϕ e ^ φ sin( m1 )ϕ e ^ r ] ( TypeI ) [ cos( m+1 )ϕ e ^ φ +sin( m+1 )ϕ e ^ r ] ( TypeII ) [ sin( m1 )ϕ e ^ φ +cos( m1 )ϕ e ^ r ] ( TypeIII ) [ sin( m+1 )ϕ e ^ φ +cos( m+1 )ϕ e ^ r ] ( TypeIV ) ,
E AP ( r,ϕ,z )= U 0,1 ( r,z ) e ^ ϕ .
E RP ( r,ϕ,z )= U 0,1 ( r,z ) e ^ r .
U 0,1 ( r,z )= 2 π 1 w(z) [ 2 r w( z ) ]exp[ r 2 w 2 ( z ) ]exp{ ik r 2 2R( z ) +ikzi2η( z ) }=Ψexp(iT)
E A P * ( r,ϕ,z )= U 0,1 * ( r,z ) e ^ ϕ ,
E R P * ( r,ϕ,z )= U 0,1 * ( r,z ) e ^ r ,
Ε= Ε RP + Ε R P *
E= E RP + E A P * .
E=Ψ[cos(kz)( e ^ r + e ^ ϕ )isin(kz)( e ^ ϕ e ^ r )],
σ = E RP i E AP ,
σ * = E R P * +i E A P * ,
E= σ + σ * .
E=2Ψ[cos(kz) e ^ r +sin(kz) e ^ φ ].
σ = E RP i E AP ,
σ +* = E R P * i E A P * .
E= σ + σ +* .
E=2Ψcos(kz)( e ^ r i e ^ φ ).

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