Abstract

Focusing properties of Fresnel zone plates with spiral phase with integer and fractional topological charges illuminated by plane wave are studied. Numerical results show that hollow beams can be generated and can also be controlled by the number of the zones and the topological charge, which implies the potential applications of such kind of zone plate in trapping and manipulating particles.

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References

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  1. M. Wieland, R. Frueke, T. Wilhein, C. Spielmann, M. Pohl, and U. Kleineberg, “Submicron extreme ultraviolet imaging using high-harmonic radiation,” Appl. Phys. Lett. 81(14), 2520–2522 (2002).
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    [CrossRef]
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2009 (4)

2007 (2)

A. Sakdinawat and Y. W. Liu, “Soft-X-ray microscopy using spiral zone plates,” Opt. Lett. 32(18), 2635–2637 (2007).
[CrossRef] [PubMed]

B. Z. Zhang, D. M. Zhao, and S. M. Wang, “Demonstrations of the diffraction and dispersion phenomena of part Fresnel phase zone plates,” Appl. Phys. Lett. 91(2), 021108 (2007).
[CrossRef]

2006 (2)

S. H. Tao, X. C. Yuan, J. Lin, and R. E. Burge, “Sequence of focused optical vortices generated by a spiral fractal zone plate,” Appl. Phys. Lett. 89(3), 031105 (2006).
[CrossRef]

G. C. Yin, Y. F. Song, M. T. Tang, F. R. Chen, K. S. Liang, F. W. Duewer, M. Feser, W. B. Yun, and H. P. D. Shieh, “30 nm resolution x-ray imaging at 8 keV using third order diffraction of a zone plate lens objective in a transmission microscope,” Appl. Phys. Lett. 89(22), 221122 (2006).
[CrossRef]

2005 (2)

2003 (1)

2002 (1)

M. Wieland, R. Frueke, T. Wilhein, C. Spielmann, M. Pohl, and U. Kleineberg, “Submicron extreme ultraviolet imaging using high-harmonic radiation,” Appl. Phys. Lett. 81(14), 2520–2522 (2002).
[CrossRef]

2001 (2)

M. Peuker, “High-efficiency nickel phase zone plates with 20 nm minimum outermost zone width,” Appl. Phys. Lett. 78(15), 2208–2210 (2001).
[CrossRef]

L. Kipp, M. Skibowski, R. L. Johnson, R. Berndt, R. Adelung, S. Harm, and R. Seemann, “Sharper images by focusing soft X-rays with photon sieves,” Nature 414(6860), 184–188 (2001).
[CrossRef] [PubMed]

2000 (1)

1999 (1)

E. Di Fabrizio, F. Romanato, M. Gentili, S. Cabrini, B. Kaulich, J. Susini, and R. Barrett, “High-efficiency multilevel zone plates for keV X-rays,” Nature 401(6756), 895–898 (1999).
[CrossRef]

Adelung, R.

L. Kipp, M. Skibowski, R. L. Johnson, R. Berndt, R. Adelung, S. Harm, and R. Seemann, “Sharper images by focusing soft X-rays with photon sieves,” Nature 414(6860), 184–188 (2001).
[CrossRef] [PubMed]

Anderson, E. H.

Attwood, D. T.

W. L. Chao, B. D. Harteneck, J. A. Liddle, E. H. Anderson, and D. T. Attwood, “Soft X-ray microscopy at a spatial resolution better than 15 nm,” Nature 435(7046), 1210–1213 (2005).
[CrossRef] [PubMed]

Barrett, R.

E. Di Fabrizio, F. Romanato, M. Gentili, S. Cabrini, B. Kaulich, J. Susini, and R. Barrett, “High-efficiency multilevel zone plates for keV X-rays,” Nature 401(6756), 895–898 (1999).
[CrossRef]

Berndt, R.

L. Kipp, M. Skibowski, R. L. Johnson, R. Berndt, R. Adelung, S. Harm, and R. Seemann, “Sharper images by focusing soft X-rays with photon sieves,” Nature 414(6860), 184–188 (2001).
[CrossRef] [PubMed]

Bertilson, M.

Burge, R. E.

S. H. Tao, X. C. Yuan, J. Lin, and R. E. Burge, “Sequence of focused optical vortices generated by a spiral fractal zone plate,” Appl. Phys. Lett. 89(3), 031105 (2006).
[CrossRef]

Cabrini, S.

E. Di Fabrizio, F. Romanato, M. Gentili, S. Cabrini, B. Kaulich, J. Susini, and R. Barrett, “High-efficiency multilevel zone plates for keV X-rays,” Nature 401(6756), 895–898 (1999).
[CrossRef]

Campos, J.

Chao, W. L.

Chen, F. R.

G. C. Yin, Y. F. Song, M. T. Tang, F. R. Chen, K. S. Liang, F. W. Duewer, M. Feser, W. B. Yun, and H. P. D. Shieh, “30 nm resolution x-ray imaging at 8 keV using third order diffraction of a zone plate lens objective in a transmission microscope,” Appl. Phys. Lett. 89(22), 221122 (2006).
[CrossRef]

Cottrell, D. M.

Davis, J. A.

Di Fabrizio, E.

E. Di Fabrizio, F. Romanato, M. Gentili, S. Cabrini, B. Kaulich, J. Susini, and R. Barrett, “High-efficiency multilevel zone plates for keV X-rays,” Nature 401(6756), 895–898 (1999).
[CrossRef]

Duewer, F. W.

G. C. Yin, Y. F. Song, M. T. Tang, F. R. Chen, K. S. Liang, F. W. Duewer, M. Feser, W. B. Yun, and H. P. D. Shieh, “30 nm resolution x-ray imaging at 8 keV using third order diffraction of a zone plate lens objective in a transmission microscope,” Appl. Phys. Lett. 89(22), 221122 (2006).
[CrossRef]

Feser, M.

G. C. Yin, Y. F. Song, M. T. Tang, F. R. Chen, K. S. Liang, F. W. Duewer, M. Feser, W. B. Yun, and H. P. D. Shieh, “30 nm resolution x-ray imaging at 8 keV using third order diffraction of a zone plate lens objective in a transmission microscope,” Appl. Phys. Lett. 89(22), 221122 (2006).
[CrossRef]

Fischer, P.

Frueke, R.

M. Wieland, R. Frueke, T. Wilhein, C. Spielmann, M. Pohl, and U. Kleineberg, “Submicron extreme ultraviolet imaging using high-harmonic radiation,” Appl. Phys. Lett. 81(14), 2520–2522 (2002).
[CrossRef]

Furlan, W. D.

Gentili, M.

E. Di Fabrizio, F. Romanato, M. Gentili, S. Cabrini, B. Kaulich, J. Susini, and R. Barrett, “High-efficiency multilevel zone plates for keV X-rays,” Nature 401(6756), 895–898 (1999).
[CrossRef]

Guttmann, P.

S. Rehbein, S. Heim, P. Guttmann, S. Werner, and G. Schneider, “Ultrahigh-resolution soft-x-ray microscopy with zone plates in high orders of diffraction,” Phys. Rev. Lett. 103(11), 110801 (2009).
[CrossRef] [PubMed]

Harm, S.

L. Kipp, M. Skibowski, R. L. Johnson, R. Berndt, R. Adelung, S. Harm, and R. Seemann, “Sharper images by focusing soft X-rays with photon sieves,” Nature 414(6860), 184–188 (2001).
[CrossRef] [PubMed]

Harteneck, B. D.

W. L. Chao, B. D. Harteneck, J. A. Liddle, E. H. Anderson, and D. T. Attwood, “Soft X-ray microscopy at a spatial resolution better than 15 nm,” Nature 435(7046), 1210–1213 (2005).
[CrossRef] [PubMed]

Heim, S.

S. Rehbein, S. Heim, P. Guttmann, S. Werner, and G. Schneider, “Ultrahigh-resolution soft-x-ray microscopy with zone plates in high orders of diffraction,” Phys. Rev. Lett. 103(11), 110801 (2009).
[CrossRef] [PubMed]

Hertz, H. M.

Holmberg, A.

Johnson, R. L.

L. Kipp, M. Skibowski, R. L. Johnson, R. Berndt, R. Adelung, S. Harm, and R. Seemann, “Sharper images by focusing soft X-rays with photon sieves,” Nature 414(6860), 184–188 (2001).
[CrossRef] [PubMed]

Kaulich, B.

E. Di Fabrizio, F. Romanato, M. Gentili, S. Cabrini, B. Kaulich, J. Susini, and R. Barrett, “High-efficiency multilevel zone plates for keV X-rays,” Nature 401(6756), 895–898 (1999).
[CrossRef]

Kim, J.

Kipp, L.

L. Kipp, M. Skibowski, R. L. Johnson, R. Berndt, R. Adelung, S. Harm, and R. Seemann, “Sharper images by focusing soft X-rays with photon sieves,” Nature 414(6860), 184–188 (2001).
[CrossRef] [PubMed]

Kleineberg, U.

M. Wieland, R. Frueke, T. Wilhein, C. Spielmann, M. Pohl, and U. Kleineberg, “Submicron extreme ultraviolet imaging using high-harmonic radiation,” Appl. Phys. Lett. 81(14), 2520–2522 (2002).
[CrossRef]

Liang, K. S.

G. C. Yin, Y. F. Song, M. T. Tang, F. R. Chen, K. S. Liang, F. W. Duewer, M. Feser, W. B. Yun, and H. P. D. Shieh, “30 nm resolution x-ray imaging at 8 keV using third order diffraction of a zone plate lens objective in a transmission microscope,” Appl. Phys. Lett. 89(22), 221122 (2006).
[CrossRef]

Liddle, J. A.

W. L. Chao, B. D. Harteneck, J. A. Liddle, E. H. Anderson, and D. T. Attwood, “Soft X-ray microscopy at a spatial resolution better than 15 nm,” Nature 435(7046), 1210–1213 (2005).
[CrossRef] [PubMed]

Lin, J.

S. H. Tao, X. C. Yuan, J. Lin, and R. E. Burge, “Sequence of focused optical vortices generated by a spiral fractal zone plate,” Appl. Phys. Lett. 89(3), 031105 (2006).
[CrossRef]

Liu, Y. W.

McNamara, D. E.

Monsoriu, J. A.

Osten, W.

Pedrini, G.

Peuker, M.

M. Peuker, “High-efficiency nickel phase zone plates with 20 nm minimum outermost zone width,” Appl. Phys. Lett. 78(15), 2208–2210 (2001).
[CrossRef]

Pohl, M.

M. Wieland, R. Frueke, T. Wilhein, C. Spielmann, M. Pohl, and U. Kleineberg, “Submicron extreme ultraviolet imaging using high-harmonic radiation,” Appl. Phys. Lett. 81(14), 2520–2522 (2002).
[CrossRef]

Rehbein, S.

S. Rehbein, S. Heim, P. Guttmann, S. Werner, and G. Schneider, “Ultrahigh-resolution soft-x-ray microscopy with zone plates in high orders of diffraction,” Phys. Rev. Lett. 103(11), 110801 (2009).
[CrossRef] [PubMed]

Reinspach, J.

Rekawa, S.

Romanato, F.

E. Di Fabrizio, F. Romanato, M. Gentili, S. Cabrini, B. Kaulich, J. Susini, and R. Barrett, “High-efficiency multilevel zone plates for keV X-rays,” Nature 401(6756), 895–898 (1999).
[CrossRef]

Saavedra, G.

Sakdinawat, A.

Schneider, G.

S. Rehbein, S. Heim, P. Guttmann, S. Werner, and G. Schneider, “Ultrahigh-resolution soft-x-ray microscopy with zone plates in high orders of diffraction,” Phys. Rev. Lett. 103(11), 110801 (2009).
[CrossRef] [PubMed]

Seemann, R.

L. Kipp, M. Skibowski, R. L. Johnson, R. Berndt, R. Adelung, S. Harm, and R. Seemann, “Sharper images by focusing soft X-rays with photon sieves,” Nature 414(6860), 184–188 (2001).
[CrossRef] [PubMed]

Shieh, H. P. D.

G. C. Yin, Y. F. Song, M. T. Tang, F. R. Chen, K. S. Liang, F. W. Duewer, M. Feser, W. B. Yun, and H. P. D. Shieh, “30 nm resolution x-ray imaging at 8 keV using third order diffraction of a zone plate lens objective in a transmission microscope,” Appl. Phys. Lett. 89(22), 221122 (2006).
[CrossRef]

Shum, P.

Situ, G. H.

Skibowski, M.

L. Kipp, M. Skibowski, R. L. Johnson, R. Berndt, R. Adelung, S. Harm, and R. Seemann, “Sharper images by focusing soft X-rays with photon sieves,” Nature 414(6860), 184–188 (2001).
[CrossRef] [PubMed]

Song, Y. F.

G. C. Yin, Y. F. Song, M. T. Tang, F. R. Chen, K. S. Liang, F. W. Duewer, M. Feser, W. B. Yun, and H. P. D. Shieh, “30 nm resolution x-ray imaging at 8 keV using third order diffraction of a zone plate lens objective in a transmission microscope,” Appl. Phys. Lett. 89(22), 221122 (2006).
[CrossRef]

Spielmann, C.

M. Wieland, R. Frueke, T. Wilhein, C. Spielmann, M. Pohl, and U. Kleineberg, “Submicron extreme ultraviolet imaging using high-harmonic radiation,” Appl. Phys. Lett. 81(14), 2520–2522 (2002).
[CrossRef]

Sun, X. W.

Susini, J.

E. Di Fabrizio, F. Romanato, M. Gentili, S. Cabrini, B. Kaulich, J. Susini, and R. Barrett, “High-efficiency multilevel zone plates for keV X-rays,” Nature 401(6756), 895–898 (1999).
[CrossRef]

Tang, M. T.

G. C. Yin, Y. F. Song, M. T. Tang, F. R. Chen, K. S. Liang, F. W. Duewer, M. Feser, W. B. Yun, and H. P. D. Shieh, “30 nm resolution x-ray imaging at 8 keV using third order diffraction of a zone plate lens objective in a transmission microscope,” Appl. Phys. Lett. 89(22), 221122 (2006).
[CrossRef]

Tao, S. H.

S. H. Tao, X. C. Yuan, J. Lin, and R. E. Burge, “Sequence of focused optical vortices generated by a spiral fractal zone plate,” Appl. Phys. Lett. 89(3), 031105 (2006).
[CrossRef]

Vogt, U.

von Hofsten, O.

Wang, Q.

Wang, S. M.

B. Z. Zhang, D. M. Zhao, and S. M. Wang, “Demonstrations of the diffraction and dispersion phenomena of part Fresnel phase zone plates,” Appl. Phys. Lett. 91(2), 021108 (2007).
[CrossRef]

Werner, S.

S. Rehbein, S. Heim, P. Guttmann, S. Werner, and G. Schneider, “Ultrahigh-resolution soft-x-ray microscopy with zone plates in high orders of diffraction,” Phys. Rev. Lett. 103(11), 110801 (2009).
[CrossRef] [PubMed]

Wieland, M.

M. Wieland, R. Frueke, T. Wilhein, C. Spielmann, M. Pohl, and U. Kleineberg, “Submicron extreme ultraviolet imaging using high-harmonic radiation,” Appl. Phys. Lett. 81(14), 2520–2522 (2002).
[CrossRef]

Wilhein, T.

M. Wieland, R. Frueke, T. Wilhein, C. Spielmann, M. Pohl, and U. Kleineberg, “Submicron extreme ultraviolet imaging using high-harmonic radiation,” Appl. Phys. Lett. 81(14), 2520–2522 (2002).
[CrossRef]

Yin, G. C.

G. C. Yin, Y. F. Song, M. T. Tang, F. R. Chen, K. S. Liang, F. W. Duewer, M. Feser, W. B. Yun, and H. P. D. Shieh, “30 nm resolution x-ray imaging at 8 keV using third order diffraction of a zone plate lens objective in a transmission microscope,” Appl. Phys. Lett. 89(22), 221122 (2006).
[CrossRef]

Yin, X. J.

Yuan, X. C.

S. H. Tao, X. C. Yuan, J. Lin, and R. E. Burge, “Sequence of focused optical vortices generated by a spiral fractal zone plate,” Appl. Phys. Lett. 89(3), 031105 (2006).
[CrossRef]

Yun, W. B.

G. C. Yin, Y. F. Song, M. T. Tang, F. R. Chen, K. S. Liang, F. W. Duewer, M. Feser, W. B. Yun, and H. P. D. Shieh, “30 nm resolution x-ray imaging at 8 keV using third order diffraction of a zone plate lens objective in a transmission microscope,” Appl. Phys. Lett. 89(22), 221122 (2006).
[CrossRef]

Zhang, B. Z.

B. Z. Zhang, D. M. Zhao, and S. M. Wang, “Demonstrations of the diffraction and dispersion phenomena of part Fresnel phase zone plates,” Appl. Phys. Lett. 91(2), 021108 (2007).
[CrossRef]

Zhao, D. M.

B. Z. Zhang, D. M. Zhao, and S. M. Wang, “Demonstrations of the diffraction and dispersion phenomena of part Fresnel phase zone plates,” Appl. Phys. Lett. 91(2), 021108 (2007).
[CrossRef]

Appl. Phys. Lett. (5)

M. Wieland, R. Frueke, T. Wilhein, C. Spielmann, M. Pohl, and U. Kleineberg, “Submicron extreme ultraviolet imaging using high-harmonic radiation,” Appl. Phys. Lett. 81(14), 2520–2522 (2002).
[CrossRef]

G. C. Yin, Y. F. Song, M. T. Tang, F. R. Chen, K. S. Liang, F. W. Duewer, M. Feser, W. B. Yun, and H. P. D. Shieh, “30 nm resolution x-ray imaging at 8 keV using third order diffraction of a zone plate lens objective in a transmission microscope,” Appl. Phys. Lett. 89(22), 221122 (2006).
[CrossRef]

M. Peuker, “High-efficiency nickel phase zone plates with 20 nm minimum outermost zone width,” Appl. Phys. Lett. 78(15), 2208–2210 (2001).
[CrossRef]

B. Z. Zhang, D. M. Zhao, and S. M. Wang, “Demonstrations of the diffraction and dispersion phenomena of part Fresnel phase zone plates,” Appl. Phys. Lett. 91(2), 021108 (2007).
[CrossRef]

S. H. Tao, X. C. Yuan, J. Lin, and R. E. Burge, “Sequence of focused optical vortices generated by a spiral fractal zone plate,” Appl. Phys. Lett. 89(3), 031105 (2006).
[CrossRef]

J. Opt. Soc. Am. A (1)

Nature (3)

L. Kipp, M. Skibowski, R. L. Johnson, R. Berndt, R. Adelung, S. Harm, and R. Seemann, “Sharper images by focusing soft X-rays with photon sieves,” Nature 414(6860), 184–188 (2001).
[CrossRef] [PubMed]

E. Di Fabrizio, F. Romanato, M. Gentili, S. Cabrini, B. Kaulich, J. Susini, and R. Barrett, “High-efficiency multilevel zone plates for keV X-rays,” Nature 401(6756), 895–898 (1999).
[CrossRef]

W. L. Chao, B. D. Harteneck, J. A. Liddle, E. H. Anderson, and D. T. Attwood, “Soft X-ray microscopy at a spatial resolution better than 15 nm,” Nature 435(7046), 1210–1213 (2005).
[CrossRef] [PubMed]

Opt. Express (2)

Opt. Lett. (4)

Phys. Rev. Lett. (1)

S. Rehbein, S. Heim, P. Guttmann, S. Werner, and G. Schneider, “Ultrahigh-resolution soft-x-ray microscopy with zone plates in high orders of diffraction,” Phys. Rev. Lett. 103(11), 110801 (2009).
[CrossRef] [PubMed]

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Figures (4)

Fig. 1
Fig. 1

The illustration of the (a) structure of Fresnel zone plate with spiral phase and (b) scheme of the setup.

Fig. 2
Fig. 2

Intensity distribution and diffraction patterns of spiral phase Fresnel zone plate with topological charge p = 1 with 60 zones. (a) Intensity distribution of the zone plate along optical axis z; (b), (c) diffraction patterns of the zone plate at z = f/3 = 0.2364m, z = f = 0.7092m; (d), (e) the corresponding intensity distributions.

Fig. 3
Fig. 3

Spiral phase Fresnel zone plates with integer topological charges and their diffraction patterns. (a), (b) Diffraction patterns of spiral phase FZP with topological charge p = 1 with 120 and 240 zones; (c), (e) spiral phase FZPs with topological charge p = 2 and 3 with 60 zones; (d), (f) the corresponding diffraction patterns of zone plates shown in (c), (e) in focal plane when z = 0.7092m.

Fig. 4
Fig. 4

Spiral phase Fresnel zone plates with fractional topological charges and their diffraction patterns. (a), (c), (e) Spiral phase FZPs with topological charge p = 0.25, 0.5, and 0.75 with 60 zones; (b), (d), (f) the corresponding diffraction patterns of the zone plates shown in (a), (c), (e) in focal plane when z = 0.7092m.

Tables (1)

Tables Icon

Table 1 Parameters of doughnut patterns generated by zone plates with different parameters

Equations (2)

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I ( ρ , θ , z ) = | i A λ R s ( n ​   zones ) exp ( i k R + i p θ ) r d r d φ | 2 ,
R = [ ( ρ cos θ r cos φ ) 2 + ( ρ sin θ r sin φ ) 2 + z 2 ] 1 / 2 ,

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