Abstract

We present a method for producing laser beams of nonuniform polarization where the polarization direction rotates on a trajectory about the beam propagation direction. Our method uses a Sagnac interferometer that incorporates a spatial light modulator to combine beams that possess oppositely charged phase vortices in order to achieve the desired polarization vortex. We demonstrate the utility of our method by producing polarization vortices characterized by a fractional index, and we compare the results with calculations of the expected fields.

© 2009 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. S. Quabis, R. Dorn, M. Eberler, O. Glöckl, and G. Leuchs, Opt. Commun. 179, 1 (2000).
    [CrossRef]
  2. K. Venkatakrishnan and B. Tan, J. Micromech. Microeng. 16, 2603 (2006).
    [CrossRef]
  3. W. G. Kimura, G. H. Kim, R. D. Romea, L. C. Steinhauer, I. V. Pogorelsky, K. P. Kusche, R. C. Fernow, X. Wang, and Y. Liu, Phys. Rev. Lett. 74, 546 (1995).
    [CrossRef] [PubMed]
  4. Y. Saito, M. Kobayashi, D. Hiraga, K. Fujita, S. Kawano, N. I. Smith, Y. Inouye, and S. Kawata, J. Raman Spectrosc. 10.1002/jrs.1953 (2008).
  5. M. Stalder and M. Schadt, Opt. Lett. 21, 1948 (1996).
    [CrossRef] [PubMed]
  6. G. Machavariani, Y. Lumer, I. Moshe, A. Meir, and S. Jackel, Opt. Lett. 32, 1468 (2007).
    [CrossRef] [PubMed]
  7. V. G. Niziev, R. S. Chang, and A. V. Nesterov, Appl. Opt. 45, 8393 (2006).
    [CrossRef] [PubMed]
  8. X.-L. Wang, J. Ding, W.-J. Ni, C.-S. Guo, and H.-T. Wang, Opt. Lett. 32, 3549 (2007).
    [CrossRef] [PubMed]
  9. C. Maurer, A. Jesacher, S. Fürhapter, S. Bernet, and M. Ritsch-Marte, New J. Phys. 9, 78 (2007).
    [CrossRef]
  10. M. Rashid, O. M. Maragò, and P. H. Jones, J. Opt. A, Pure Appl. Opt. 11, 065204 (2009).
    [CrossRef]
  11. J. Arlt, K. Dholakia, L. Allen, and M. J. Padgett, J. Mod. Opt. 45, 1231 (1998).
    [CrossRef]
  12. T. Grosjean, D. Courjon, and D. Van Labeke, J. Microsc. 210, 319 (2003).
    [CrossRef] [PubMed]
  13. M. V. Berry, J. Opt. A, Pure Appl. Opt. 6, 259 (2004).
    [CrossRef]
  14. J. Leach, E. Yao, and M. Padgett, New J. Phys. 6, 71 (2004).
    [CrossRef]
  15. J. F. Nye, Natural Focusing and Fine Structure of Light (IOP, 1999).
  16. A. Niv, G. Biener, V. Kleiner, and E. Hasman, Opt. Express 14, 4208 (2006).
    [CrossRef] [PubMed]
  17. W. M. Lee, X.-C. Yuan, and K. Dholakia, Opt. Commun. 239, 129 (2004).
    [CrossRef]
  18. M. F. Andersen, C. Ryu, P. Cladé, V. Natarajan, A. Vaziri, K. Helmerson, and W. D. Phillips, Phys. Rev. Lett. 97, 170406 (2006).
    [CrossRef] [PubMed]
  19. K. C. Wright, L. S. Leslie, and N. P. Bigelow, Phys. Rev. A 77, 041601(R) (2008).
    [CrossRef]
  20. R. P. Huebner, N. Schopohl, and G. E. Volovik, Vortices in Unconventional Superconductors and Superfluids (Springer-Verlag, 2002).

2009

M. Rashid, O. M. Maragò, and P. H. Jones, J. Opt. A, Pure Appl. Opt. 11, 065204 (2009).
[CrossRef]

2008

K. C. Wright, L. S. Leslie, and N. P. Bigelow, Phys. Rev. A 77, 041601(R) (2008).
[CrossRef]

2007

2006

K. Venkatakrishnan and B. Tan, J. Micromech. Microeng. 16, 2603 (2006).
[CrossRef]

A. Niv, G. Biener, V. Kleiner, and E. Hasman, Opt. Express 14, 4208 (2006).
[CrossRef] [PubMed]

V. G. Niziev, R. S. Chang, and A. V. Nesterov, Appl. Opt. 45, 8393 (2006).
[CrossRef] [PubMed]

M. F. Andersen, C. Ryu, P. Cladé, V. Natarajan, A. Vaziri, K. Helmerson, and W. D. Phillips, Phys. Rev. Lett. 97, 170406 (2006).
[CrossRef] [PubMed]

2004

M. V. Berry, J. Opt. A, Pure Appl. Opt. 6, 259 (2004).
[CrossRef]

J. Leach, E. Yao, and M. Padgett, New J. Phys. 6, 71 (2004).
[CrossRef]

W. M. Lee, X.-C. Yuan, and K. Dholakia, Opt. Commun. 239, 129 (2004).
[CrossRef]

2003

T. Grosjean, D. Courjon, and D. Van Labeke, J. Microsc. 210, 319 (2003).
[CrossRef] [PubMed]

2000

S. Quabis, R. Dorn, M. Eberler, O. Glöckl, and G. Leuchs, Opt. Commun. 179, 1 (2000).
[CrossRef]

1998

J. Arlt, K. Dholakia, L. Allen, and M. J. Padgett, J. Mod. Opt. 45, 1231 (1998).
[CrossRef]

1996

1995

W. G. Kimura, G. H. Kim, R. D. Romea, L. C. Steinhauer, I. V. Pogorelsky, K. P. Kusche, R. C. Fernow, X. Wang, and Y. Liu, Phys. Rev. Lett. 74, 546 (1995).
[CrossRef] [PubMed]

Allen, L.

J. Arlt, K. Dholakia, L. Allen, and M. J. Padgett, J. Mod. Opt. 45, 1231 (1998).
[CrossRef]

Andersen, M. F.

M. F. Andersen, C. Ryu, P. Cladé, V. Natarajan, A. Vaziri, K. Helmerson, and W. D. Phillips, Phys. Rev. Lett. 97, 170406 (2006).
[CrossRef] [PubMed]

Arlt, J.

J. Arlt, K. Dholakia, L. Allen, and M. J. Padgett, J. Mod. Opt. 45, 1231 (1998).
[CrossRef]

Bernet, S.

C. Maurer, A. Jesacher, S. Fürhapter, S. Bernet, and M. Ritsch-Marte, New J. Phys. 9, 78 (2007).
[CrossRef]

Berry, M. V.

M. V. Berry, J. Opt. A, Pure Appl. Opt. 6, 259 (2004).
[CrossRef]

Biener, G.

Bigelow, N. P.

K. C. Wright, L. S. Leslie, and N. P. Bigelow, Phys. Rev. A 77, 041601(R) (2008).
[CrossRef]

Chang, R. S.

Cladé, P.

M. F. Andersen, C. Ryu, P. Cladé, V. Natarajan, A. Vaziri, K. Helmerson, and W. D. Phillips, Phys. Rev. Lett. 97, 170406 (2006).
[CrossRef] [PubMed]

Courjon, D.

T. Grosjean, D. Courjon, and D. Van Labeke, J. Microsc. 210, 319 (2003).
[CrossRef] [PubMed]

Dholakia, K.

W. M. Lee, X.-C. Yuan, and K. Dholakia, Opt. Commun. 239, 129 (2004).
[CrossRef]

J. Arlt, K. Dholakia, L. Allen, and M. J. Padgett, J. Mod. Opt. 45, 1231 (1998).
[CrossRef]

Ding, J.

Dorn, R.

S. Quabis, R. Dorn, M. Eberler, O. Glöckl, and G. Leuchs, Opt. Commun. 179, 1 (2000).
[CrossRef]

Eberler, M.

S. Quabis, R. Dorn, M. Eberler, O. Glöckl, and G. Leuchs, Opt. Commun. 179, 1 (2000).
[CrossRef]

Fernow, R. C.

W. G. Kimura, G. H. Kim, R. D. Romea, L. C. Steinhauer, I. V. Pogorelsky, K. P. Kusche, R. C. Fernow, X. Wang, and Y. Liu, Phys. Rev. Lett. 74, 546 (1995).
[CrossRef] [PubMed]

Fujita, K.

Y. Saito, M. Kobayashi, D. Hiraga, K. Fujita, S. Kawano, N. I. Smith, Y. Inouye, and S. Kawata, J. Raman Spectrosc. 10.1002/jrs.1953 (2008).

Fürhapter, S.

C. Maurer, A. Jesacher, S. Fürhapter, S. Bernet, and M. Ritsch-Marte, New J. Phys. 9, 78 (2007).
[CrossRef]

Glöckl, O.

S. Quabis, R. Dorn, M. Eberler, O. Glöckl, and G. Leuchs, Opt. Commun. 179, 1 (2000).
[CrossRef]

Grosjean, T.

T. Grosjean, D. Courjon, and D. Van Labeke, J. Microsc. 210, 319 (2003).
[CrossRef] [PubMed]

Guo, C.-S.

Hasman, E.

Helmerson, K.

M. F. Andersen, C. Ryu, P. Cladé, V. Natarajan, A. Vaziri, K. Helmerson, and W. D. Phillips, Phys. Rev. Lett. 97, 170406 (2006).
[CrossRef] [PubMed]

Hiraga, D.

Y. Saito, M. Kobayashi, D. Hiraga, K. Fujita, S. Kawano, N. I. Smith, Y. Inouye, and S. Kawata, J. Raman Spectrosc. 10.1002/jrs.1953 (2008).

Huebner, R. P.

R. P. Huebner, N. Schopohl, and G. E. Volovik, Vortices in Unconventional Superconductors and Superfluids (Springer-Verlag, 2002).

Inouye, Y.

Y. Saito, M. Kobayashi, D. Hiraga, K. Fujita, S. Kawano, N. I. Smith, Y. Inouye, and S. Kawata, J. Raman Spectrosc. 10.1002/jrs.1953 (2008).

Jackel, S.

Jesacher, A.

C. Maurer, A. Jesacher, S. Fürhapter, S. Bernet, and M. Ritsch-Marte, New J. Phys. 9, 78 (2007).
[CrossRef]

Jones, P. H.

M. Rashid, O. M. Maragò, and P. H. Jones, J. Opt. A, Pure Appl. Opt. 11, 065204 (2009).
[CrossRef]

Kawano, S.

Y. Saito, M. Kobayashi, D. Hiraga, K. Fujita, S. Kawano, N. I. Smith, Y. Inouye, and S. Kawata, J. Raman Spectrosc. 10.1002/jrs.1953 (2008).

Kawata, S.

Y. Saito, M. Kobayashi, D. Hiraga, K. Fujita, S. Kawano, N. I. Smith, Y. Inouye, and S. Kawata, J. Raman Spectrosc. 10.1002/jrs.1953 (2008).

Kim, G. H.

W. G. Kimura, G. H. Kim, R. D. Romea, L. C. Steinhauer, I. V. Pogorelsky, K. P. Kusche, R. C. Fernow, X. Wang, and Y. Liu, Phys. Rev. Lett. 74, 546 (1995).
[CrossRef] [PubMed]

Kimura, W. G.

W. G. Kimura, G. H. Kim, R. D. Romea, L. C. Steinhauer, I. V. Pogorelsky, K. P. Kusche, R. C. Fernow, X. Wang, and Y. Liu, Phys. Rev. Lett. 74, 546 (1995).
[CrossRef] [PubMed]

Kleiner, V.

Kobayashi, M.

Y. Saito, M. Kobayashi, D. Hiraga, K. Fujita, S. Kawano, N. I. Smith, Y. Inouye, and S. Kawata, J. Raman Spectrosc. 10.1002/jrs.1953 (2008).

Kusche, K. P.

W. G. Kimura, G. H. Kim, R. D. Romea, L. C. Steinhauer, I. V. Pogorelsky, K. P. Kusche, R. C. Fernow, X. Wang, and Y. Liu, Phys. Rev. Lett. 74, 546 (1995).
[CrossRef] [PubMed]

Leach, J.

J. Leach, E. Yao, and M. Padgett, New J. Phys. 6, 71 (2004).
[CrossRef]

Lee, W. M.

W. M. Lee, X.-C. Yuan, and K. Dholakia, Opt. Commun. 239, 129 (2004).
[CrossRef]

Leslie, L. S.

K. C. Wright, L. S. Leslie, and N. P. Bigelow, Phys. Rev. A 77, 041601(R) (2008).
[CrossRef]

Leuchs, G.

S. Quabis, R. Dorn, M. Eberler, O. Glöckl, and G. Leuchs, Opt. Commun. 179, 1 (2000).
[CrossRef]

Liu, Y.

W. G. Kimura, G. H. Kim, R. D. Romea, L. C. Steinhauer, I. V. Pogorelsky, K. P. Kusche, R. C. Fernow, X. Wang, and Y. Liu, Phys. Rev. Lett. 74, 546 (1995).
[CrossRef] [PubMed]

Lumer, Y.

Machavariani, G.

Maragò, O. M.

M. Rashid, O. M. Maragò, and P. H. Jones, J. Opt. A, Pure Appl. Opt. 11, 065204 (2009).
[CrossRef]

Maurer, C.

C. Maurer, A. Jesacher, S. Fürhapter, S. Bernet, and M. Ritsch-Marte, New J. Phys. 9, 78 (2007).
[CrossRef]

Meir, A.

Moshe, I.

Natarajan, V.

M. F. Andersen, C. Ryu, P. Cladé, V. Natarajan, A. Vaziri, K. Helmerson, and W. D. Phillips, Phys. Rev. Lett. 97, 170406 (2006).
[CrossRef] [PubMed]

Nesterov, A. V.

Ni, W.-J.

Niv, A.

Niziev, V. G.

Nye, J. F.

J. F. Nye, Natural Focusing and Fine Structure of Light (IOP, 1999).

Padgett, M.

J. Leach, E. Yao, and M. Padgett, New J. Phys. 6, 71 (2004).
[CrossRef]

Padgett, M. J.

J. Arlt, K. Dholakia, L. Allen, and M. J. Padgett, J. Mod. Opt. 45, 1231 (1998).
[CrossRef]

Phillips, W. D.

M. F. Andersen, C. Ryu, P. Cladé, V. Natarajan, A. Vaziri, K. Helmerson, and W. D. Phillips, Phys. Rev. Lett. 97, 170406 (2006).
[CrossRef] [PubMed]

Pogorelsky, I. V.

W. G. Kimura, G. H. Kim, R. D. Romea, L. C. Steinhauer, I. V. Pogorelsky, K. P. Kusche, R. C. Fernow, X. Wang, and Y. Liu, Phys. Rev. Lett. 74, 546 (1995).
[CrossRef] [PubMed]

Quabis, S.

S. Quabis, R. Dorn, M. Eberler, O. Glöckl, and G. Leuchs, Opt. Commun. 179, 1 (2000).
[CrossRef]

Rashid, M.

M. Rashid, O. M. Maragò, and P. H. Jones, J. Opt. A, Pure Appl. Opt. 11, 065204 (2009).
[CrossRef]

Ritsch-Marte, M.

C. Maurer, A. Jesacher, S. Fürhapter, S. Bernet, and M. Ritsch-Marte, New J. Phys. 9, 78 (2007).
[CrossRef]

Romea, R. D.

W. G. Kimura, G. H. Kim, R. D. Romea, L. C. Steinhauer, I. V. Pogorelsky, K. P. Kusche, R. C. Fernow, X. Wang, and Y. Liu, Phys. Rev. Lett. 74, 546 (1995).
[CrossRef] [PubMed]

Ryu, C.

M. F. Andersen, C. Ryu, P. Cladé, V. Natarajan, A. Vaziri, K. Helmerson, and W. D. Phillips, Phys. Rev. Lett. 97, 170406 (2006).
[CrossRef] [PubMed]

Saito, Y.

Y. Saito, M. Kobayashi, D. Hiraga, K. Fujita, S. Kawano, N. I. Smith, Y. Inouye, and S. Kawata, J. Raman Spectrosc. 10.1002/jrs.1953 (2008).

Schadt, M.

Schopohl, N.

R. P. Huebner, N. Schopohl, and G. E. Volovik, Vortices in Unconventional Superconductors and Superfluids (Springer-Verlag, 2002).

Smith, N. I.

Y. Saito, M. Kobayashi, D. Hiraga, K. Fujita, S. Kawano, N. I. Smith, Y. Inouye, and S. Kawata, J. Raman Spectrosc. 10.1002/jrs.1953 (2008).

Stalder, M.

Steinhauer, L. C.

W. G. Kimura, G. H. Kim, R. D. Romea, L. C. Steinhauer, I. V. Pogorelsky, K. P. Kusche, R. C. Fernow, X. Wang, and Y. Liu, Phys. Rev. Lett. 74, 546 (1995).
[CrossRef] [PubMed]

Tan, B.

K. Venkatakrishnan and B. Tan, J. Micromech. Microeng. 16, 2603 (2006).
[CrossRef]

Van Labeke, D.

T. Grosjean, D. Courjon, and D. Van Labeke, J. Microsc. 210, 319 (2003).
[CrossRef] [PubMed]

Vaziri, A.

M. F. Andersen, C. Ryu, P. Cladé, V. Natarajan, A. Vaziri, K. Helmerson, and W. D. Phillips, Phys. Rev. Lett. 97, 170406 (2006).
[CrossRef] [PubMed]

Venkatakrishnan, K.

K. Venkatakrishnan and B. Tan, J. Micromech. Microeng. 16, 2603 (2006).
[CrossRef]

Volovik, G. E.

R. P. Huebner, N. Schopohl, and G. E. Volovik, Vortices in Unconventional Superconductors and Superfluids (Springer-Verlag, 2002).

Wang, H.-T.

Wang, X.

W. G. Kimura, G. H. Kim, R. D. Romea, L. C. Steinhauer, I. V. Pogorelsky, K. P. Kusche, R. C. Fernow, X. Wang, and Y. Liu, Phys. Rev. Lett. 74, 546 (1995).
[CrossRef] [PubMed]

Wang, X.-L.

Wright, K. C.

K. C. Wright, L. S. Leslie, and N. P. Bigelow, Phys. Rev. A 77, 041601(R) (2008).
[CrossRef]

Yao, E.

J. Leach, E. Yao, and M. Padgett, New J. Phys. 6, 71 (2004).
[CrossRef]

Yuan, X.-C.

W. M. Lee, X.-C. Yuan, and K. Dholakia, Opt. Commun. 239, 129 (2004).
[CrossRef]

Appl. Opt.

J. Micromech. Microeng.

K. Venkatakrishnan and B. Tan, J. Micromech. Microeng. 16, 2603 (2006).
[CrossRef]

J. Microsc.

T. Grosjean, D. Courjon, and D. Van Labeke, J. Microsc. 210, 319 (2003).
[CrossRef] [PubMed]

J. Mod. Opt.

J. Arlt, K. Dholakia, L. Allen, and M. J. Padgett, J. Mod. Opt. 45, 1231 (1998).
[CrossRef]

J. Opt. A, Pure Appl. Opt.

M. Rashid, O. M. Maragò, and P. H. Jones, J. Opt. A, Pure Appl. Opt. 11, 065204 (2009).
[CrossRef]

M. V. Berry, J. Opt. A, Pure Appl. Opt. 6, 259 (2004).
[CrossRef]

New J. Phys.

J. Leach, E. Yao, and M. Padgett, New J. Phys. 6, 71 (2004).
[CrossRef]

C. Maurer, A. Jesacher, S. Fürhapter, S. Bernet, and M. Ritsch-Marte, New J. Phys. 9, 78 (2007).
[CrossRef]

Opt. Commun.

S. Quabis, R. Dorn, M. Eberler, O. Glöckl, and G. Leuchs, Opt. Commun. 179, 1 (2000).
[CrossRef]

W. M. Lee, X.-C. Yuan, and K. Dholakia, Opt. Commun. 239, 129 (2004).
[CrossRef]

Opt. Express

Opt. Lett.

Phys. Rev. A

K. C. Wright, L. S. Leslie, and N. P. Bigelow, Phys. Rev. A 77, 041601(R) (2008).
[CrossRef]

Phys. Rev. Lett.

M. F. Andersen, C. Ryu, P. Cladé, V. Natarajan, A. Vaziri, K. Helmerson, and W. D. Phillips, Phys. Rev. Lett. 97, 170406 (2006).
[CrossRef] [PubMed]

W. G. Kimura, G. H. Kim, R. D. Romea, L. C. Steinhauer, I. V. Pogorelsky, K. P. Kusche, R. C. Fernow, X. Wang, and Y. Liu, Phys. Rev. Lett. 74, 546 (1995).
[CrossRef] [PubMed]

Other

Y. Saito, M. Kobayashi, D. Hiraga, K. Fujita, S. Kawano, N. I. Smith, Y. Inouye, and S. Kawata, J. Raman Spectrosc. 10.1002/jrs.1953 (2008).

R. P. Huebner, N. Schopohl, and G. E. Volovik, Vortices in Unconventional Superconductors and Superfluids (Springer-Verlag, 2002).

J. F. Nye, Natural Focusing and Fine Structure of Light (IOP, 1999).

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 (4)

Fig. 1
Fig. 1

Sagnac interferometer arrangement for producing cylindrical vector beams. Phase retardation pattern displayed by the SLM for a topological charge p = 1 : (b) LG profile, (f) Bessel–Gauss profile. Output of the interferometer: (c) LG profile, (g) Bessel–Gauss profile. Transmitted intensity through a linear polarizer with transmission axis vertical: (d) LG profile, (h) Bessel–Gauss profile. The same with transmission axis horizontal: (e) Laguerre-Gauss profile, (i) Bessel-Gauss profile.

Fig. 2
Fig. 2

Intensity distribution for p = 1 2 phase vortex: (a) calculated, (d) experimental. Intensity distribution at the output of the Sagnac interferometer for combining p = 1 2 and p = 1 2 phase vortices: (b) calculated, (e) experimental. Interference pattern between a linearly polarized plane wave and the p = 1 2 polarization vortex beam: (c) calculated, (f) experimental.

Fig. 3
Fig. 3

Comparison of theory (upper row) and experiment (lower row) for the case when p = 5 2 . (a), (e) p = 5 2 phase vortex, i.e., the beam along one path of the interferometer. (b), (f) p = 5 2 polarization vortex (i.e., the output of the interferometer). (c), (g) Vertically polarized component. (d), (h) Horizontally polarized component.

Fig. 4
Fig. 4

Evolution of polarization distribution with increasing order number p: (a) p = 1.0 , (b) p = 1.4 , (c) p = 1.6 , (d) p = 2.0 . (e) Number of intensity zeros arising from the insertion of the linear polarizer as a function of the polarization order p. The number of zeros is given by the number of polarization rotations, determined by the net vorticity of the interfering beams. The increase in the number of zeros at half-integer values of p corresponds to the seeding of one more phase vortex in each beam.

Equations (1)

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

ψ p = exp [ i ( z + p π ) ] sin p π π n = exp [ i n ϕ P n ( ρ ) ] p n .

Metrics