Abstract

A type of square Fresnel zone plate with spiral phase for generating zero axial irradiance is proposed. Diffraction patterns of the zone plates with different generalized topological charges are given by numerical simulation, which also suggests their potential applications in generating hollow beams.

© 2010 Optical Society of America

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2009 (3)

J. Alda and F. J. Gonzalez, J. Opt. A 11, 085707 (2009).
[CrossRef]

W. D. Furlan, F. Gimenez, A. Calatayud, and J. A. Monsoriu, Opt. Express 17, 21891 (2009).
[CrossRef] [PubMed]

J. Alda, J. M. Rico-Garcia, F. J. Salgado-Remacha, and L. M. Sanchez-Brea, Opt. Commun. 282, 3402 (2009).
[CrossRef]

2007 (2)

2006 (2)

S. H. Tao, X. C. Yuan, J. Lin, and R. E. Burge, Appl. Phys. Lett. 89, 031105 (2006).
[CrossRef]

S. Wang, L. Hu, B. Zhang, J. Wang, and D. Zhao, Opt. Express 14, 932 (2006).
[CrossRef] [PubMed]

2005 (3)

2004 (1)

2003 (2)

2001 (1)

L. Kipp, M. Skibowski, R. L. Johnson, R. Berndt, R. Adelung, S. Harm, and R. Seemann, Nature 414, 184 (2001).
[CrossRef] [PubMed]

1999 (1)

I. E. Di. Fabrizio, F. Romanato, M. Gentili, S. Cabrini, B. Kaulich, J. Susini, and R. Barrett, Nature 401, 895 (1999).
[CrossRef]

1982 (1)

L. J. Janicijevic, J. Opt. (Paris) 13, 199 (1982).

1968 (1)

Adelung, R.

L. Kipp, M. Skibowski, R. L. Johnson, R. Berndt, R. Adelung, S. Harm, and R. Seemann, Nature 414, 184 (2001).
[CrossRef] [PubMed]

Alda, J.

J. Alda and F. J. Gonzalez, J. Opt. A 11, 085707 (2009).
[CrossRef]

J. Alda, J. M. Rico-Garcia, F. J. Salgado-Remacha, and L. M. Sanchez-Brea, Opt. Commun. 282, 3402 (2009).
[CrossRef]

Alieva, T.

Andersen, G.

Anderson, E. H.

W. Chao, B. D. Harteneck, J. A. Liddle, E. H. Anderson, and D. T. Attwood, Nature 435, 1210 (2005).
[CrossRef] [PubMed]

Attwood, D. T.

W. Chao, B. D. Harteneck, J. A. Liddle, E. H. Anderson, and D. T. Attwood, Nature 435, 1210 (2005).
[CrossRef] [PubMed]

Barrett, R.

I. E. Di. Fabrizio, F. Romanato, M. Gentili, S. Cabrini, B. Kaulich, J. Susini, and R. Barrett, Nature 401, 895 (1999).
[CrossRef]

Berndt, R.

L. Kipp, M. Skibowski, R. L. Johnson, R. Berndt, R. Adelung, S. Harm, and R. Seemann, Nature 414, 184 (2001).
[CrossRef] [PubMed]

Burge, R. E.

S. H. Tao, X. C. Yuan, J. Lin, and R. E. Burge, Appl. Phys. Lett. 89, 031105 (2006).
[CrossRef]

Cabrini, S.

I. E. Di. Fabrizio, F. Romanato, M. Gentili, S. Cabrini, B. Kaulich, J. Susini, and R. Barrett, Nature 401, 895 (1999).
[CrossRef]

Calatayud, A.

Calvo, M. L.

Chao, W.

W. Chao, B. D. Harteneck, J. A. Liddle, E. H. Anderson, and D. T. Attwood, Nature 435, 1210 (2005).
[CrossRef] [PubMed]

Davis, J. A.

Fabrizio, I. E. Di.

I. E. Di. Fabrizio, F. Romanato, M. Gentili, S. Cabrini, B. Kaulich, J. Susini, and R. Barrett, Nature 401, 895 (1999).
[CrossRef]

Furlan, W. D.

Gentili, M.

I. E. Di. Fabrizio, F. Romanato, M. Gentili, S. Cabrini, B. Kaulich, J. Susini, and R. Barrett, Nature 401, 895 (1999).
[CrossRef]

Gimenez, F.

Gonzalez, F. J.

J. Alda and F. J. Gonzalez, J. Opt. A 11, 085707 (2009).
[CrossRef]

Harm, S.

L. Kipp, M. Skibowski, R. L. Johnson, R. Berndt, R. Adelung, S. Harm, and R. Seemann, Nature 414, 184 (2001).
[CrossRef] [PubMed]

Harteneck, B. D.

W. Chao, B. D. Harteneck, J. A. Liddle, E. H. Anderson, and D. T. Attwood, Nature 435, 1210 (2005).
[CrossRef] [PubMed]

Herrmannsfeldt, W. B.

Hu, L.

Jacobsen, C.

Y. Wang, W. Yun, and C. Jacobsen, Nature 424, 50 (2003).
[CrossRef] [PubMed]

Janicijevic, L. J.

L. J. Janicijevic, J. Opt. (Paris) 13, 199 (1982).

Johnson, R. L.

L. Kipp, M. Skibowski, R. L. Johnson, R. Berndt, R. Adelung, S. Harm, and R. Seemann, Nature 414, 184 (2001).
[CrossRef] [PubMed]

Kaulich, B.

I. E. Di. Fabrizio, F. Romanato, M. Gentili, S. Cabrini, B. Kaulich, J. Susini, and R. Barrett, Nature 401, 895 (1999).
[CrossRef]

Kipp, L.

L. Kipp, M. Skibowski, R. L. Johnson, R. Berndt, R. Adelung, S. Harm, and R. Seemann, Nature 414, 184 (2001).
[CrossRef] [PubMed]

Lee, M. J.

Liddle, J. A.

W. Chao, B. D. Harteneck, J. A. Liddle, E. H. Anderson, and D. T. Attwood, Nature 435, 1210 (2005).
[CrossRef] [PubMed]

Lin, J.

S. H. Tao, X. C. Yuan, J. Lin, and R. E. Burge, Appl. Phys. Lett. 89, 031105 (2006).
[CrossRef]

Martin-Romo, J. A.

Monsoriu, J. A.

Ramires, L.

Rico-Garcia, J. M.

J. Alda, J. M. Rico-Garcia, F. J. Salgado-Remacha, and L. M. Sanchez-Brea, Opt. Commun. 282, 3402 (2009).
[CrossRef]

Romanato, F.

I. E. Di. Fabrizio, F. Romanato, M. Gentili, S. Cabrini, B. Kaulich, J. Susini, and R. Barrett, Nature 401, 895 (1999).
[CrossRef]

Saavedra, G.

Salgado-Remacha, F. J.

J. Alda, J. M. Rico-Garcia, F. J. Salgado-Remacha, and L. M. Sanchez-Brea, Opt. Commun. 282, 3402 (2009).
[CrossRef]

Sanchez-Brea, L. M.

J. Alda, J. M. Rico-Garcia, F. J. Salgado-Remacha, and L. M. Sanchez-Brea, Opt. Commun. 282, 3402 (2009).
[CrossRef]

Seemann, R.

L. Kipp, M. Skibowski, R. L. Johnson, R. Berndt, R. Adelung, S. Harm, and R. Seemann, Nature 414, 184 (2001).
[CrossRef] [PubMed]

Shum, P.

Skibowski, M.

L. Kipp, M. Skibowski, R. L. Johnson, R. Berndt, R. Adelung, S. Harm, and R. Seemann, Nature 414, 184 (2001).
[CrossRef] [PubMed]

Spranza, J. J.

Sun, X. W.

Susini, J.

I. E. Di. Fabrizio, F. Romanato, M. Gentili, S. Cabrini, B. Kaulich, J. Susini, and R. Barrett, Nature 401, 895 (1999).
[CrossRef]

Tao, S. H.

S. H. Tao, X. C. Yuan, J. Lin, and R. E. Burge, Appl. Phys. Lett. 89, 031105 (2006).
[CrossRef]

Trigger, K. R.

Wang, J.

Wang, Q.

Wang, S.

Wang, Y.

Y. Wang, W. Yun, and C. Jacobsen, Nature 424, 50 (2003).
[CrossRef] [PubMed]

Yin, X. J.

Yuan, X. C.

S. H. Tao, X. C. Yuan, J. Lin, and R. E. Burge, Appl. Phys. Lett. 89, 031105 (2006).
[CrossRef]

Yun, W.

Y. Wang, W. Yun, and C. Jacobsen, Nature 424, 50 (2003).
[CrossRef] [PubMed]

Zhang, B.

Zhao, D.

Appl. Opt. (1)

Appl. Phys. Lett. (2)

B. Zhang, D. Zhao, and S. Wang, Appl. Phys. Lett. 91, 021108 (2007).
[CrossRef]

S. H. Tao, X. C. Yuan, J. Lin, and R. E. Burge, Appl. Phys. Lett. 89, 031105 (2006).
[CrossRef]

J. Opt. (Paris) (1)

L. J. Janicijevic, J. Opt. (Paris) 13, 199 (1982).

J. Opt. A (1)

J. Alda and F. J. Gonzalez, J. Opt. A 11, 085707 (2009).
[CrossRef]

Nature (4)

L. Kipp, M. Skibowski, R. L. Johnson, R. Berndt, R. Adelung, S. Harm, and R. Seemann, Nature 414, 184 (2001).
[CrossRef] [PubMed]

I. E. Di. Fabrizio, F. Romanato, M. Gentili, S. Cabrini, B. Kaulich, J. Susini, and R. Barrett, Nature 401, 895 (1999).
[CrossRef]

Y. Wang, W. Yun, and C. Jacobsen, Nature 424, 50 (2003).
[CrossRef] [PubMed]

W. Chao, B. D. Harteneck, J. A. Liddle, E. H. Anderson, and D. T. Attwood, Nature 435, 1210 (2005).
[CrossRef] [PubMed]

Opt. Commun. (1)

J. Alda, J. M. Rico-Garcia, F. J. Salgado-Remacha, and L. M. Sanchez-Brea, Opt. Commun. 282, 3402 (2009).
[CrossRef]

Opt. Express (3)

Opt. Lett. (4)

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Figures (3)

Fig. 1
Fig. 1

Illustration of (a) the structure of a square FZP with spiral phase and (b) the scheme of the setup.

Fig. 2
Fig. 2

Square Fresnel zone plates and their diffraction patterns. (a) Normal square phase FZP. (b) Diffraction pattern in the focal plane of zone plate shown in (a). (c) Spiral phase FZP with generalized topological charge p = 1 . (d)–(f) are the corresponding diffraction patterns of (c) when z = 0.7092 m , 0.7042 m , and 0.7142 m , respectively. The upper-right parts of (b), (d), (e), and (f) are the enlargement of each figure’s central part.

Fig. 3
Fig. 3

Square spiral phase FZPs with different generalized topological charges and their diffraction patterns. (a), (c), and (e) Spiral phase FZPs with generalized topological charge p = 0.5 , 2, and 3; (b), (d), and (f) are the corresponding diffraction patterns of the zone plates shown in (a), (c), and (e) in the focal plane with z = 0.7092 m . The upper-right parts of (b), (d), and (f) are the enlargement of each figure’s central part.

Equations (7)

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I ( x , y , z ) = | i A λ r s t ( ξ , η ) exp ( i ψ ) exp ( i k r ) d ξ d η | 2 = | i A λ r s ( n transparent zones ) exp ( i k r + i ψ ) d ξ d η | 2 ,
r = [ ( x ξ ) 2 + ( y η ) 2 + z 2 ] 1 2 ,
ψ = ψ ( ξ , η ) = ψ ( l ) ,
I ( 0 , 0 , z ) = | i A λ r s ( n zones ) [ exp ( i k r P 1 + i ψ P 1 ) + exp ( i k r P 2 + i ψ P 2 ) ] d ξ d η | 2 .
r P 1 = r P 2 , ψ P 1 = ψ P 2 π ,
exp ( i k r P 1 + i ψ P 1 ) + exp ( i k r P 2 + i ψ P 2 ) = exp ( i k r P 1 + i ψ P 1 ) + exp ( i k r P 1 + i ψ P 1 + i π ) = 0 ,
I ( 0 , 0 , z ) = 0 .

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