Abstract

We study modified optical vortices for encoding topological charges based on radius ratios between principal and the modified first sidelobe rings. The method is immune to harassments from alignment and phase matching between the beams and optical elements. Moreover, it is demonstrated that the radius ratios and their corresponding modulation parameters are independent to wavelength and size of the spiral phase mask.

© 2010 Optical Society of America

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2009 (4)

2008 (2)

Y. D. Liu, C. Q. Gao, M. W. Gao, X. Q. Qi, and H. Weber, Opt. Commun. 281, 3636 (2008).
[CrossRef]

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

2007 (2)

2006 (3)

2005 (1)

2004 (3)

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

Z. Bouchal and R. Čelechovský, New J. Phys. 6, 131 (2004).
[CrossRef]

2002 (1)

J. Leach, M. J. Padgett, S. M. Barnett, S. F. Arnold, and J. Courtial, Phys. Rev. Lett. 88, 257901 (2002).
[CrossRef] [PubMed]

2001 (1)

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

1999 (1)

Alfano, R. R.

Arnold, S. F.

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

J. Leach, M. J. Padgett, S. M. Barnett, S. F. Arnold, and J. Courtial, Phys. Rev. Lett. 88, 257901 (2002).
[CrossRef] [PubMed]

Barnett, S. M.

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

J. Leach, M. J. Padgett, S. M. Barnett, S. F. Arnold, and J. Courtial, Phys. Rev. Lett. 88, 257901 (2002).
[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]

Bouchal, Z.

R. Čelechovský and Z. Bouchal, New J. Phys. 9, 328 (2007).
[CrossRef]

Z. Bouchal and R. Čelechovský, New J. Phys. 6, 131 (2004).
[CrossRef]

Burge, R. E.

Campos, J.

Celechovský, R.

R. Čelechovský and Z. Bouchal, New J. Phys. 9, 328 (2007).
[CrossRef]

Z. Bouchal and R. Čelechovský, New J. Phys. 6, 131 (2004).
[CrossRef]

Chen, J.

J. Chen, D. F. Kuang, and Z. L. Fang, Chin. Phys. Lett. 26, 094210 (2009).
[CrossRef]

Cottrell, D. M.

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).
[CrossRef] [PubMed]

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

J. Leach, M. J. Padgett, S. M. Barnett, S. F. Arnold, and J. Courtial, Phys. Rev. Lett. 88, 257901 (2002).
[CrossRef] [PubMed]

Davis, J. A.

Elfstrom, H.

Fang, Z. L.

J. Chen, D. F. Kuang, and Z. L. Fang, Chin. Phys. Lett. 26, 094210 (2009).
[CrossRef]

Franke-Arnold, S.

Gao, C. Q.

Y. D. Liu, C. Q. Gao, M. W. Gao, X. Q. Qi, and H. Weber, Opt. Commun. 281, 3636 (2008).
[CrossRef]

Gao, M. W.

Y. D. Liu, C. Q. Gao, M. W. Gao, X. Q. Qi, and H. Weber, Opt. Commun. 281, 3636 (2008).
[CrossRef]

Gibson, G.

Guo, C. S.

C. S. Guo, S. J. Yue, and G. X. Wei, Appl. Phys. Lett. 94, 231104 (2009).
[CrossRef]

C. S. Guo, L. L. Lu, and H. T. Wang, Opt. Lett. 34, 3686 (2009).
[CrossRef] [PubMed]

Khonina, S. N.

Kotlyar, V. V.

Kovalev, A. A.

Kuang, D. F.

J. Chen, D. F. Kuang, and Z. L. Fang, Chin. Phys. Lett. 26, 094210 (2009).
[CrossRef]

Leach, J.

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

J. Leach, M. J. Padgett, S. M. Barnett, S. F. Arnold, and J. Courtial, Phys. Rev. Lett. 88, 257901 (2002).
[CrossRef] [PubMed]

Lin, J.

Liu, Y. D.

Y. D. Liu, C. Q. Gao, M. W. Gao, X. Q. Qi, and H. Weber, Opt. Commun. 281, 3636 (2008).
[CrossRef]

Lu, L. L.

Mair, A.

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

Mitry, M. J.

Moreno, I.

Padgett, M. 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).
[CrossRef] [PubMed]

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

J. Leach, M. J. Padgett, S. M. Barnett, S. F. Arnold, and J. Courtial, Phys. Rev. Lett. 88, 257901 (2002).
[CrossRef] [PubMed]

Pas’ko, V.

Pascoguin, B. M. L.

Qi, X. Q.

Y. D. Liu, C. Q. Gao, M. W. Gao, X. Q. Qi, and H. Weber, Opt. Commun. 281, 3636 (2008).
[CrossRef]

Skeldon, K.

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

Soifer, V. A.

Sztul, H. I.

Tao, S. H.

Turunen, J.

Vasnetsov, M.

Vaziri, A.

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

Wang, H. T.

Weber, H.

Y. D. Liu, C. Q. Gao, M. W. Gao, X. Q. Qi, and H. Weber, Opt. Commun. 281, 3636 (2008).
[CrossRef]

Wei, G. X.

C. S. Guo, S. J. Yue, and G. X. Wei, Appl. Phys. Lett. 94, 231104 (2009).
[CrossRef]

Weihs, G.

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

Yuan, X. C.

Yue, S. J.

C. S. Guo, S. J. Yue, and G. X. Wei, Appl. Phys. Lett. 94, 231104 (2009).
[CrossRef]

Yzuel, M. J.

Zeilinger, A.

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

Appl. Opt. (2)

Appl. Phys. Lett. (1)

C. S. Guo, S. J. Yue, and G. X. Wei, Appl. Phys. Lett. 94, 231104 (2009).
[CrossRef]

Chin. Phys. Lett. (1)

J. Chen, D. F. Kuang, and Z. L. Fang, Chin. Phys. Lett. 26, 094210 (2009).
[CrossRef]

Nature (1)

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

New J. Phys. (2)

R. Čelechovský and Z. Bouchal, New J. Phys. 9, 328 (2007).
[CrossRef]

Z. Bouchal and R. Čelechovský, New J. Phys. 6, 131 (2004).
[CrossRef]

Opt. Commun. (1)

Y. D. Liu, C. Q. Gao, M. W. Gao, X. Q. Qi, and H. Weber, Opt. Commun. 281, 3636 (2008).
[CrossRef]

Opt. Express (1)

Opt. Lett. (6)

Phys. Rev. Lett. (3)

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

J. Leach, M. J. Padgett, S. M. Barnett, S. F. Arnold, and J. Courtial, Phys. Rev. Lett. 88, 257901 (2002).
[CrossRef] [PubMed]

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

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Figures (3)

Fig. 1
Fig. 1

(a) Radial intensity distribution of Fraunhofer diffraction pattern generated by a conventional annular spiral phase mask (dashed curve) and composite spiral phase mask (solid curve). (b) Corresponding composite spiral phase mask with n = 45 . The designed parameters are according to Table 1.

Fig. 2
Fig. 2

Experimental intensity distribution of modified principal-sidelobe rings for topological charge n = 42 , 45, 48, and 50 as shown in (a)–(d), and corresponding radius ratios 0.3415, 0.4910, 0.6422, and 0.7402, respectively; (e) comparison of the theoretical and experimental radius ratios of modified principal-sidelobe rings with topological charge from 41 to 50.

Fig. 3
Fig. 3

Radius of the principal ring ρ 1 and outer ring ρ 2 calculated numerically using Eq. (2) with radial modulation parameters in Table 1 at (A) R = 3 mm , λ = 532 nm ; (B) R = 3 mm , λ = 633 nm ; (C) R = 3 mm , λ = 1064 nm ; and (D) R = 5 mm , λ = 633 nm .

Tables (1)

Tables Icon

Table 1 Design Parameters in Radial Modulation for Each Annular Aperture

Equations (3)

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τ n ( r , φ ) = m = 0 N [ circl ( r β m R ) circl ( r β m + 1 R ) ] exp ( i n φ + i α m ω r ) , n = ± 1 , ± 2 , , m = 0 , 1 , 2 N ,
E n ( ρ , θ ) = ( i ) n + 1 f exp ( i n θ ) m = 0 N β m + 1 R β m R exp ( i α m ω r ) J n ( k f ρ r ) r d r ,
ρ 1 γ n 1 , 1 λ f 2 π R , ρ 2 γ n 1 , 1 λ f 2 π σ R ,

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