Abstract

We report a 2D static binary phase Dammann vortex grating that combines the features of a conventional vortex grating and a Dammann grating. This grating uniformly distributes energies among the diffraction orders, so the low-efficiency problem at higher diffraction orders of conventional vortex gratings is resolved and the detection range of the optical vortices (OVs) is greatly increased. Experimental results of OV detection using a fabricated 5×5 Dammann vortex grating are given, and the topological charge detection range from 12 to +12 is achieved. The potential applications of such gratings include transmitting, receiving, and multiplexing OV beams in optical communication systems.

© 2010 Optical Society of America

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2010 (2)

J. M. Hickmann, E. J. S. Fonseca, W. C. Soares, and S. Chávez-Cerda, Phys. Rev. Lett. 105, 053904 (2010).
[CrossRef] [PubMed]

I. Moreno, J. A. Davis, D. M. Cottrell, N. Zhang, and X. C. Yuan, Opt. Lett. 35, 1536 (2010).
[CrossRef] [PubMed]

2009 (1)

2008 (2)

S. Franke-Arnold, L. Allen, and M. Padgett, Laser & Photon. Rev. 2, 299 (2008).
[CrossRef]

G. C. G. Berkhout and M. W. Beijersbergen, Phys. Rev. Lett. 101, 100801 (2008).
[CrossRef] [PubMed]

2007 (2)

J. Lin, X. C. Yuan, S. H. Tao, and R. E. Burge, Appl. Opt. 46, 4680 (2007).
[CrossRef] [PubMed]

G. Molina-Terriza, J. P. Torres, and L. Torner, Nat. Phys. 3, 305 (2007).
[CrossRef]

2004 (3)

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

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

G. Gibson II, J. Courtial, M. Vasnetsov, S. Barnett, S. Franke-Arnold, and M. Padgett, Proc. SPIE , 5550, 367(2004).
[CrossRef]

2000 (1)

S. N. Khonina, V. V. Kotlyar, R. V. Skidanov, V. A. Soifer, P. Laakkonen, and J. Turunen, Opt. Commun. 175, 301 (2000).
[CrossRef]

1995 (1)

1989 (3)

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

U. Krackhardt and N. Streibl, Opt. Commun. 74, 31(1989).
[CrossRef]

N. Streibl, J. Mod. Opt. 36, 1559 (1989).
[CrossRef]

1986 (1)

1977 (1)

H. Dammann and E. Klotz, Opt. Acta 24, 505 (1977).
[CrossRef]

1974 (1)

J. F. Nye and M. V. Berry, Proc. Royal Soc. London Ser. A 336, 165 (1974).
[CrossRef]

1972 (1)

1971 (1)

H. Dammann and K. Görtler, Opt. Commun. 3, 312(1971).
[CrossRef]

Allen, L.

S. Franke-Arnold, L. Allen, and M. Padgett, Laser & Photon. Rev. 2, 299 (2008).
[CrossRef]

Barnett, S.

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

G. Gibson II, J. Courtial, M. Vasnetsov, S. Barnett, S. Franke-Arnold, and M. Padgett, Proc. SPIE , 5550, 367(2004).
[CrossRef]

Barnett, S. M.

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

Beijersbergen, M. W.

G. C. G. Berkhout and M. W. Beijersbergen, Phys. Rev. Lett. 101, 100801 (2008).
[CrossRef] [PubMed]

Berkhout, G. C. G.

G. C. G. Berkhout and M. W. Beijersbergen, Phys. Rev. Lett. 101, 100801 (2008).
[CrossRef] [PubMed]

Berry, M. V.

J. F. Nye and M. V. Berry, Proc. Royal Soc. London Ser. A 336, 165 (1974).
[CrossRef]

Boivin, L. P.

Burge, R. E.

Chávez-Cerda, S.

J. M. Hickmann, E. J. S. Fonseca, W. C. Soares, and S. Chávez-Cerda, Phys. Rev. Lett. 105, 053904 (2010).
[CrossRef] [PubMed]

Cottrell, D. M.

Coullet, P.

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

Courtial, J.

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

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

G. Gibson II, J. Courtial, M. Vasnetsov, S. Barnett, S. Franke-Arnold, and M. Padgett, Proc. SPIE , 5550, 367(2004).
[CrossRef]

Dammann, H.

H. Dammann and E. Klotz, Opt. Acta 24, 505 (1977).
[CrossRef]

H. Dammann and K. Görtler, Opt. Commun. 3, 312(1971).
[CrossRef]

Davis, J. A.

Fonseca, E. J. S.

J. M. Hickmann, E. J. S. Fonseca, W. C. Soares, and S. Chávez-Cerda, Phys. Rev. Lett. 105, 053904 (2010).
[CrossRef] [PubMed]

Franke-Arnold, S.

S. Franke-Arnold, L. Allen, and M. Padgett, Laser & Photon. Rev. 2, 299 (2008).
[CrossRef]

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

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

G. Gibson II, J. Courtial, M. Vasnetsov, S. Barnett, S. Franke-Arnold, and M. Padgett, Proc. SPIE , 5550, 367(2004).
[CrossRef]

Gibson, G.

G. Gibson II, J. Courtial, M. Vasnetsov, S. Barnett, S. Franke-Arnold, and M. Padgett, Proc. SPIE , 5550, 367(2004).
[CrossRef]

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

Gil, L.

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

Görtler, K.

H. Dammann and K. Görtler, Opt. Commun. 3, 312(1971).
[CrossRef]

Hickmann, J. M.

J. M. Hickmann, E. J. S. Fonseca, W. C. Soares, and S. Chávez-Cerda, Phys. Rev. Lett. 105, 053904 (2010).
[CrossRef] [PubMed]

Khonina, S. N.

S. N. Khonina, V. V. Kotlyar, R. V. Skidanov, V. A. Soifer, P. Laakkonen, and J. Turunen, Opt. Commun. 175, 301 (2000).
[CrossRef]

Klotz, E.

H. Dammann and E. Klotz, Opt. Acta 24, 505 (1977).
[CrossRef]

Kotlyar, V. V.

S. N. Khonina, V. V. Kotlyar, R. V. Skidanov, V. A. Soifer, P. Laakkonen, and J. Turunen, Opt. Commun. 175, 301 (2000).
[CrossRef]

Krackhardt, U.

U. Krackhardt and N. Streibl, Opt. Commun. 74, 31(1989).
[CrossRef]

L., B. M.

Laakkonen, P.

S. N. Khonina, V. V. Kotlyar, R. V. Skidanov, V. A. Soifer, P. Laakkonen, and J. Turunen, Opt. Commun. 175, 301 (2000).
[CrossRef]

Leach, J.

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

Leger, J. R.

Lin, J.

Liu, L.

Mitry, M. J.

Molina-Terriza, G.

G. Molina-Terriza, J. P. Torres, and L. Torner, Nat. Phys. 3, 305 (2007).
[CrossRef]

Moreno, I.

Nye, J. F.

J. F. Nye and M. V. Berry, Proc. Royal Soc. London Ser. A 336, 165 (1974).
[CrossRef]

Padgett, M.

S. Franke-Arnold, L. Allen, and M. Padgett, Laser & Photon. Rev. 2, 299 (2008).
[CrossRef]

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

G. Gibson II, J. Courtial, M. Vasnetsov, S. Barnett, S. Franke-Arnold, and M. Padgett, Proc. SPIE , 5550, 367(2004).
[CrossRef]

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).
[CrossRef] [PubMed]

Pas’ko, V.

Rocca, F.

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

Skeldon, K.

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

Skidanov, R. V.

S. N. Khonina, V. V. Kotlyar, R. V. Skidanov, V. A. Soifer, P. Laakkonen, and J. Turunen, Opt. Commun. 175, 301 (2000).
[CrossRef]

Soares, W. C.

J. M. Hickmann, E. J. S. Fonseca, W. C. Soares, and S. Chávez-Cerda, Phys. Rev. Lett. 105, 053904 (2010).
[CrossRef] [PubMed]

Soifer, V. A.

S. N. Khonina, V. V. Kotlyar, R. V. Skidanov, V. A. Soifer, P. Laakkonen, and J. Turunen, Opt. Commun. 175, 301 (2000).
[CrossRef]

Streibl, N.

U. Krackhardt and N. Streibl, Opt. Commun. 74, 31(1989).
[CrossRef]

N. Streibl, J. Mod. Opt. 36, 1559 (1989).
[CrossRef]

Swanson, G. J.

Tao, S. H.

Torner, L.

G. Molina-Terriza, J. P. Torres, and L. Torner, Nat. Phys. 3, 305 (2007).
[CrossRef]

Torres, J. P.

G. Molina-Terriza, J. P. Torres, and L. Torner, Nat. Phys. 3, 305 (2007).
[CrossRef]

Turunen, J.

S. N. Khonina, V. V. Kotlyar, R. V. Skidanov, V. A. Soifer, P. Laakkonen, and J. Turunen, Opt. Commun. 175, 301 (2000).
[CrossRef]

Vasnetsov, M.

G. Gibson II, J. Courtial, M. Vasnetsov, S. Barnett, S. Franke-Arnold, and M. Padgett, Proc. SPIE , 5550, 367(2004).
[CrossRef]

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

Veldkamp, W. B.

Yuan, X. C.

Zhang, N.

Zhou, C.

Appl. Opt. (3)

J. Mod. Opt. (1)

N. Streibl, J. Mod. Opt. 36, 1559 (1989).
[CrossRef]

Laser & Photon. Rev. (1)

S. Franke-Arnold, L. Allen, and M. Padgett, Laser & Photon. Rev. 2, 299 (2008).
[CrossRef]

Nat. Phys. (1)

G. Molina-Terriza, J. P. Torres, and L. Torner, Nat. Phys. 3, 305 (2007).
[CrossRef]

Opt. Acta (1)

H. Dammann and E. Klotz, Opt. Acta 24, 505 (1977).
[CrossRef]

Opt. Commun. (4)

U. Krackhardt and N. Streibl, Opt. Commun. 74, 31(1989).
[CrossRef]

H. Dammann and K. Görtler, Opt. Commun. 3, 312(1971).
[CrossRef]

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

S. N. Khonina, V. V. Kotlyar, R. V. Skidanov, V. A. Soifer, P. Laakkonen, and J. Turunen, Opt. Commun. 175, 301 (2000).
[CrossRef]

Opt. Express (1)

Opt. Lett. (3)

Phys. Rev. Lett. (3)

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

G. C. G. Berkhout and M. W. Beijersbergen, Phys. Rev. Lett. 101, 100801 (2008).
[CrossRef] [PubMed]

J. M. Hickmann, E. J. S. Fonseca, W. C. Soares, and S. Chávez-Cerda, Phys. Rev. Lett. 105, 053904 (2010).
[CrossRef] [PubMed]

Proc. Royal Soc. London Ser. A (1)

J. F. Nye and M. V. Berry, Proc. Royal Soc. London Ser. A 336, 165 (1974).
[CrossRef]

Proc. SPIE (1)

G. Gibson II, J. Courtial, M. Vasnetsov, S. Barnett, S. Franke-Arnold, and M. Padgett, Proc. SPIE , 5550, 367(2004).
[CrossRef]

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Figures (3)

Fig. 1
Fig. 1

(a) Phase structure (black for 0 and white for π) of conventional 2D binary vortex grating with filling factor of 1 / 4 and (b) the respective far-field diffraction patterns.

Fig. 2
Fig. 2

(a) 2D 5 × 5 Dammann vortex phase pattern (black for 0 and white for π), (b) central bifurcation area of the fabricated phase mask, and (c) and (d) center portion and typical outer areas of the fabricated Dammann vortex grating.

Fig. 3
Fig. 3

OV detection results using the fabricated Dammann vortex grating. The topological charges of the input OV are (a) 0, (b) 2 , (c) 7 , and (d) + 12 , and the labels show the detection orders.

Equations (2)

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t ( x ) = n = 0 N ( 1 ) n rect [ x ( x n + 1 + x n ) / 2 x n + 1 x n ] ,
T m = { 2 n = 0 N ( x n + 1 x n ) , m = 0 1 m π n = 0 N ( 1 ) n [ sin ( 2 π m x n + 1 ) sin ( 2 π m x n ) ] , m 0 .

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