Abstract

We demonstrate a specially designed vortex sensing diffraction grating that generates multiple vortex patterns in the different diffracted orders. When this grating is illuminated with a separate vortex beam, the sign and order of the topological charge of the incident beam can be easily detected. Experimental results are shown for a variety of vortex beams including fractional values of the topological charge, and where both the diffraction grating and incident vortex illumination beam are generated by two different liquid crystal displays (LCDs). The programmability offered by the LCDs offers extremely convenient flexibility.

© 2009 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. P. A. M. Dirac, Proc. R. Soc. London Ser. A 133, 60 (1931).
  2. J. F. Nye and M. V. Berry, Proc. R. Soc. London Ser. A 336, 165 (1974).
  3. H. He, M. E. J. Friese, N. R. Heckenberg, and H. Rubinstein-Dunlop, Phys. Rev. Lett. 75, 826 (1995).
    [PubMed]
  4. K. T. Gahagan and G. A. Swartzlander, Jr., Opt. Lett. 21, 827 (1996).
    [PubMed]
  5. P. Coullet, L. Gil, and F. Rocca, Opt. Commun. 73, 403 (1989).
  6. N. R. Heckenberg, R. McDuff, C. P. Smith, and A. G. White, Opt. Lett. 17, 221 (1992).
    [PubMed]
  7. M. Reicherter, T. Haist, E. U. Wagemann, and H. J. Tiziani, Opt. Lett. 24, 608 (1999).
  8. M. V. Berry, J. Opt. A. 6, 259 (2004).
  9. K. Crabtree, J. A. Davis, and I. Moreno, Appl. Opt. 42, 1360 (2004).
  10. A. Mair, A. Vaziri, G. Weihs, and A. Zeilinger, Nature 412, 313 (2001).
    [PubMed]
  11. J. Leach, J. Courtial, K. Skeldon, S. M. Barnett, S. Franke-Arnold, and M. J. Padgett, Phys. Rev. Lett. 92, 013601 (2004).
    [PubMed]
  12. G. Gibson, J. Courtial, M. J. Padgett, M. Vasnetsov, V. Pas'ko, S. M. Barnett, and S. Franke-Arnold, Opt. Express 12, 5448 (2004).
    [PubMed]
  13. A. Niv, Y. Gorodetski, V. Kleiner, and E. Hasman, Opt. Lett. 33, 2910 (2008).
    [PubMed]
  14. A. Y. Bekshaev and A. I. Karamoch, Opt. Commun. 281, 1366 (2008).
  15. J. A. Davis, G. H. Evans, and I. Moreno, Appl. Opt. 44, 4049 (2005).
    [PubMed]
  16. J. E. Curtis and D. G. Grier, Opt. Lett. 28, 872 (2004).

2008 (2)

A. Y. Bekshaev and A. I. Karamoch, Opt. Commun. 281, 1366 (2008).

A. Niv, Y. Gorodetski, V. Kleiner, and E. Hasman, Opt. Lett. 33, 2910 (2008).
[PubMed]

2005 (1)

2004 (5)

2001 (1)

A. Mair, A. Vaziri, G. Weihs, and A. Zeilinger, Nature 412, 313 (2001).
[PubMed]

1999 (1)

1996 (1)

1995 (1)

H. He, M. E. J. Friese, N. R. Heckenberg, and H. Rubinstein-Dunlop, Phys. Rev. Lett. 75, 826 (1995).
[PubMed]

1992 (1)

1989 (1)

P. Coullet, L. Gil, and F. Rocca, Opt. Commun. 73, 403 (1989).

1974 (1)

J. F. Nye and M. V. Berry, Proc. R. Soc. London Ser. A 336, 165 (1974).

1931 (1)

P. A. M. Dirac, Proc. R. Soc. London Ser. A 133, 60 (1931).

Barnett, S. M.

G. Gibson, J. Courtial, M. J. Padgett, M. Vasnetsov, V. Pas'ko, S. M. Barnett, and S. Franke-Arnold, Opt. Express 12, 5448 (2004).
[PubMed]

J. Leach, J. Courtial, K. Skeldon, S. M. Barnett, S. Franke-Arnold, and M. J. Padgett, Phys. Rev. Lett. 92, 013601 (2004).
[PubMed]

Bekshaev, A. Y.

A. Y. Bekshaev and A. I. Karamoch, Opt. Commun. 281, 1366 (2008).

Berry, M. V.

M. V. Berry, J. Opt. A. 6, 259 (2004).

J. F. Nye and M. V. Berry, Proc. R. Soc. London Ser. A 336, 165 (1974).

Coullet, P.

P. Coullet, L. Gil, and F. Rocca, Opt. Commun. 73, 403 (1989).

Courtial, J.

G. Gibson, J. Courtial, M. J. Padgett, M. Vasnetsov, V. Pas'ko, S. M. Barnett, and S. Franke-Arnold, Opt. Express 12, 5448 (2004).
[PubMed]

J. Leach, J. Courtial, K. Skeldon, S. M. Barnett, S. Franke-Arnold, and M. J. Padgett, Phys. Rev. Lett. 92, 013601 (2004).
[PubMed]

Crabtree, K.

Curtis, J. E.

Davis, J. A.

Dirac, P. A. M.

P. A. M. Dirac, Proc. R. Soc. London Ser. A 133, 60 (1931).

Evans, G. H.

Franke-Arnold, S.

G. Gibson, J. Courtial, M. J. Padgett, M. Vasnetsov, V. Pas'ko, S. M. Barnett, and S. Franke-Arnold, Opt. Express 12, 5448 (2004).
[PubMed]

J. Leach, J. Courtial, K. Skeldon, S. M. Barnett, S. Franke-Arnold, and M. J. Padgett, Phys. Rev. Lett. 92, 013601 (2004).
[PubMed]

Friese, M. E. J.

H. He, M. E. J. Friese, N. R. Heckenberg, and H. Rubinstein-Dunlop, Phys. Rev. Lett. 75, 826 (1995).
[PubMed]

Gahagan, K. T.

Gibson, G.

Gil, L.

P. Coullet, L. Gil, and F. Rocca, Opt. Commun. 73, 403 (1989).

Gorodetski, Y.

Grier, D. G.

Haist, T.

Hasman, E.

He, H.

H. He, M. E. J. Friese, N. R. Heckenberg, and H. Rubinstein-Dunlop, Phys. Rev. Lett. 75, 826 (1995).
[PubMed]

Heckenberg, N. R.

H. He, M. E. J. Friese, N. R. Heckenberg, and H. Rubinstein-Dunlop, Phys. Rev. Lett. 75, 826 (1995).
[PubMed]

N. R. Heckenberg, R. McDuff, C. P. Smith, and A. G. White, Opt. Lett. 17, 221 (1992).
[PubMed]

Karamoch, A. I.

A. Y. Bekshaev and A. I. Karamoch, Opt. Commun. 281, 1366 (2008).

Kleiner, V.

Leach, J.

J. Leach, J. Courtial, K. Skeldon, S. M. Barnett, S. Franke-Arnold, and M. J. Padgett, Phys. Rev. Lett. 92, 013601 (2004).
[PubMed]

Mair, A.

A. Mair, A. Vaziri, G. Weihs, and A. Zeilinger, Nature 412, 313 (2001).
[PubMed]

McDuff, R.

Moreno, I.

Niv, A.

Nye, J. F.

J. F. Nye and M. V. Berry, Proc. R. Soc. London Ser. A 336, 165 (1974).

Padgett, M. J.

J. Leach, J. Courtial, K. Skeldon, S. M. Barnett, S. Franke-Arnold, and M. J. Padgett, Phys. Rev. Lett. 92, 013601 (2004).
[PubMed]

G. Gibson, J. Courtial, M. J. Padgett, M. Vasnetsov, V. Pas'ko, S. M. Barnett, and S. Franke-Arnold, Opt. Express 12, 5448 (2004).
[PubMed]

Pas'ko, V.

Reicherter, M.

Rocca, F.

P. Coullet, L. Gil, and F. Rocca, Opt. Commun. 73, 403 (1989).

Rubinstein-Dunlop, H.

H. He, M. E. J. Friese, N. R. Heckenberg, and H. Rubinstein-Dunlop, Phys. Rev. Lett. 75, 826 (1995).
[PubMed]

Skeldon, K.

J. Leach, J. Courtial, K. Skeldon, S. M. Barnett, S. Franke-Arnold, and M. J. Padgett, Phys. Rev. Lett. 92, 013601 (2004).
[PubMed]

Smith, C. P.

Swartzlander, G. A.

Tiziani, H. J.

Vasnetsov, M.

Vaziri, A.

A. Mair, A. Vaziri, G. Weihs, and A. Zeilinger, Nature 412, 313 (2001).
[PubMed]

Wagemann, E. U.

Weihs, G.

A. Mair, A. Vaziri, G. Weihs, and A. Zeilinger, Nature 412, 313 (2001).
[PubMed]

White, A. G.

Zeilinger, A.

A. Mair, A. Vaziri, G. Weihs, and A. Zeilinger, Nature 412, 313 (2001).
[PubMed]

Appl. Opt. (2)

J. Opt. A. (1)

M. V. Berry, J. Opt. A. 6, 259 (2004).

Nature (1)

A. Mair, A. Vaziri, G. Weihs, and A. Zeilinger, Nature 412, 313 (2001).
[PubMed]

Opt. Commun. (2)

P. Coullet, L. Gil, and F. Rocca, Opt. Commun. 73, 403 (1989).

A. Y. Bekshaev and A. I. Karamoch, Opt. Commun. 281, 1366 (2008).

Opt. Express (1)

Opt. Lett. (5)

Phys. Rev. Lett. (2)

H. He, M. E. J. Friese, N. R. Heckenberg, and H. Rubinstein-Dunlop, Phys. Rev. Lett. 75, 826 (1995).
[PubMed]

J. Leach, J. Courtial, K. Skeldon, S. M. Barnett, S. Franke-Arnold, and M. J. Padgett, Phys. Rev. Lett. 92, 013601 (2004).
[PubMed]

Proc. R. Soc. London Ser. A (2)

P. A. M. Dirac, Proc. R. Soc. London Ser. A 133, 60 (1931).

J. F. Nye and M. V. Berry, Proc. R. Soc. London Ser. A 336, 165 (1974).

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

Vortex diffraction gratings having a period of 32 pixels for (a) l = 0 , (b) l = 1.5 , (c) l = 3 . Here black represents a phase of 0 rad, while white represents a phase of π rad.

Fig. 2
Fig. 2

Experimental diffraction patterns generated by the vortex diffraction gratings for (a) l = 0 (standard grating), (b) l = 1 , (c) l = 1.5 , (d) l = 2 , (e) l = 3 .

Fig. 3
Fig. 3

Experimental diffraction patterns generated by the vortex diffraction grating with l = + 2 , when it is illuminated with a vortex beam with (a) m = 4 , (b) m = 2 , (c) m = 0 , (d) m = + 2 , and (e) m = + 4 .

Fig. 4
Fig. 4

Experimental diffraction patterns generated by the vortex diffraction grating with (a)–(c) l = + 1.5 , when it is illuminated with a vortex beam with (a) m = 1.5 , (b) m = 0 , and (c) m = + 1.5 . In (d), (e), and (f), we chose values of l = m = 2.87 , 3.36 , 8.86 , respectively.

Equations (1)

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

G l , γ ( x , y ) = n = c n exp ( i l n φ ) exp ( i n γ x ) .

Metrics