Abstract

A photon sieve can be composed of a large number of square pinholes. By taking the related coordinate transform into account, we present here an individual far-field model for a photon sieve composed of many square pinholes whose edges are symmetrically vertical or parallel to the polar coordinate. In particular, a simple analytical expression for the diffracted far field of an individual square pinhole is given, and the focusing contribution from an individual square pinhole is further discussed. The obtained results can be used for the analysis, design, and simulation of a high numerical aperture photon sieve composed of the above-mentioned square pinholes.

© 2010 Optical Society of America

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References

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  1. G. Schmahl, D. Rudolph, P. Guttmann, and O. Christ, in X-Ray Microscopy, G.Schmahl and D.Rudolph, eds. (Springer-Verlag, 1984), Vol. 43, pp. 63–74.
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    [CrossRef]
  3. E. H. Anderson, D. L. Olynick, B. Harteneck, E. Veklerov, G. Denbeaux, W. Chao, A. Lucero, L. Johnson, and D. Attwood, “Nanofabrication and diffractive optics for high-resolution x-ray applications,” J. Vac. Sci. Technol. B 18, 2970–2975 (2000).
    [CrossRef]
  4. H. Arsenault, “Diffraction theory of Fresnel zone plates,” J. Opt. Soc. Am. 58, 1536 (1968).
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  5. J. A. Sun and A. Cai, “Archaic focusing properties of Fresnel zone plates,” J. Opt. Soc. Am. A 8, 33–35 (1991).
    [CrossRef]
  6. R. Chmelík, “Analytical description of wave fields in focal regions of diffractive lenses,” J. Mod. Opt. 43, 1463–1471 (1996).
    [CrossRef]
  7. L. Kipp, M. Skibowski, R. L. Johnson, R. Berndt, R. Adelung, S. Harm, and T. Seemann, “Sharper images by focusing soft X-rays with photon sieves,” Nature 414, 184–188 (2001).
    [CrossRef] [PubMed]
  8. Q. Cao and J. Jahns, “Focusing analysis of the pinhole photon sieve: individual far-field model,” J. Opt. Soc. Am. A 19, 2387–2393 (2002).
    [CrossRef]
  9. Q. Cao and J. Jahns, “Nonparaxial model for the focusing of high numerical aperture photon sieves,” J. Opt. Soc. Am. A 20, 1005–1012 (2003).
    [CrossRef]
  10. G. Cheng, T. Xing, Y. Yang, and J. Ma, “Experimental characterization of optical properties of photon sieve,” Proc. SPIE 6724, 1–6 (2007).
  11. Z. Gao, X. Luo, J. Ma, Y. Fu, and C. Du, “Imaging properties of the photon sieve with a large aperture,” Opt. Laser Technol. 40, 614–618 (2008).
    [CrossRef]
  12. J. Zhang, Q. Cao, X. Lu, and Z. Lin, “Focusing contribution of individual pinholes of a photon sieve: dependence on the order of local ring of underlying traditional Fresnel zone plate,” Chin. Opt. Lett. 8, 256–258 (2010).
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  14. G. Andersen and D. Tullson, “Broadband antihole photon sieve telescope,” Appl. Opt. 46, 3706–3708 (2007).
    [CrossRef] [PubMed]
  15. G. E. Arzner, J. P. Delaboudinière, and X. Y. Song, “Photon sieves as EUV telescopes for solar orbiter,” Proc. SPIE 4853, 158–161 (2003).
    [CrossRef]
  16. J. Jia, J. Jiang, C. Xie, and M. Liu, “Photon sieve for reduction of the far-field diffraction spot size in the laser free-space communication system,” Opt. Commun. 281, 4536–4539 (2008).
    [CrossRef]
  17. F. Giménez, J. A. Monsoriu, W. D. Furlan, and A. Pons, “Fractal photon sieve,” Opt. Express 14, 11958–11963 (2006).
    [CrossRef] [PubMed]
  18. F. Giménez, W. D. Furlan, and J. A. Monsoriu, “Lacunar fractal photon sieves,” Opt. Commun. 277, 1–4 (2007).
    [CrossRef]
  19. H.-H. Chung, N. M. Bradman, M. R. Davidson, and P. H. Holloway, “Dual wavelength photon sieves,” Opt. Eng. (Bellingham) 47, 118001 (2008).
    [CrossRef]
  20. Y. Liu, H. Dai, X. Sun, and T. J. Huang, “Electrically switchable phase-type fractal zone plates and fractal photon sieves,” Opt. Express 17, 12418–12423 (2009).
    [CrossRef] [PubMed]
  21. C. Zhou, X. Dong, L. Shi, C. Wang, and C. Du, “Experimental study of a multiwavelength photon sieve designed by random-area-divided approach,” Appl. Opt. 48, 1619–1623 (2009).
    [CrossRef] [PubMed]
  22. J. Jia and C. Xie, “Phase zone photon sieve,” Chin. Phys. B 18, 183–188 (2009).
    [CrossRef]
  23. J. E. Harvey, “Fourier treatment of near-field scalar diffraction theory,” Am. J. Phys. 47, 974–980 (1979).
    [CrossRef]
  24. W. H. Southwell, “Validity of the Fresnel approximation in the near field,” J. Opt. Soc. Am. 71, 7–14 (1981).
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    [CrossRef]

2010 (1)

2009 (3)

2008 (3)

J. Jia, J. Jiang, C. Xie, and M. Liu, “Photon sieve for reduction of the far-field diffraction spot size in the laser free-space communication system,” Opt. Commun. 281, 4536–4539 (2008).
[CrossRef]

H.-H. Chung, N. M. Bradman, M. R. Davidson, and P. H. Holloway, “Dual wavelength photon sieves,” Opt. Eng. (Bellingham) 47, 118001 (2008).
[CrossRef]

Z. Gao, X. Luo, J. Ma, Y. Fu, and C. Du, “Imaging properties of the photon sieve with a large aperture,” Opt. Laser Technol. 40, 614–618 (2008).
[CrossRef]

2007 (3)

G. Cheng, T. Xing, Y. Yang, and J. Ma, “Experimental characterization of optical properties of photon sieve,” Proc. SPIE 6724, 1–6 (2007).

F. Giménez, W. D. Furlan, and J. A. Monsoriu, “Lacunar fractal photon sieves,” Opt. Commun. 277, 1–4 (2007).
[CrossRef]

G. Andersen and D. Tullson, “Broadband antihole photon sieve telescope,” Appl. Opt. 46, 3706–3708 (2007).
[CrossRef] [PubMed]

2006 (1)

2005 (1)

2003 (2)

Q. Cao and J. Jahns, “Nonparaxial model for the focusing of high numerical aperture photon sieves,” J. Opt. Soc. Am. A 20, 1005–1012 (2003).
[CrossRef]

G. E. Arzner, J. P. Delaboudinière, and X. Y. Song, “Photon sieves as EUV telescopes for solar orbiter,” Proc. SPIE 4853, 158–161 (2003).
[CrossRef]

2002 (1)

2001 (1)

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

2000 (1)

E. H. Anderson, D. L. Olynick, B. Harteneck, E. Veklerov, G. Denbeaux, W. Chao, A. Lucero, L. Johnson, and D. Attwood, “Nanofabrication and diffractive optics for high-resolution x-ray applications,” J. Vac. Sci. Technol. B 18, 2970–2975 (2000).
[CrossRef]

1996 (1)

R. Chmelík, “Analytical description of wave fields in focal regions of diffractive lenses,” J. Mod. Opt. 43, 1463–1471 (1996).
[CrossRef]

1995 (1)

E. H. Anderson, V. Boegli, and L. P. Muray, “Electron beam lithography digital pattern generator and electronics for generalized curvilinear structures,” J. Vac. Sci. Technol. B 13, 2529–2534 (1995).
[CrossRef]

1992 (1)

1991 (1)

1984 (1)

G. Schmahl, D. Rudolph, P. Guttmann, and O. Christ, in X-Ray Microscopy, G.Schmahl and D.Rudolph, eds. (Springer-Verlag, 1984), Vol. 43, pp. 63–74.

1981 (1)

1979 (1)

J. E. Harvey, “Fourier treatment of near-field scalar diffraction theory,” Am. J. Phys. 47, 974–980 (1979).
[CrossRef]

1968 (1)

Adelung, R.

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

Andersen, G.

Anderson, E. H.

E. H. Anderson, D. L. Olynick, B. Harteneck, E. Veklerov, G. Denbeaux, W. Chao, A. Lucero, L. Johnson, and D. Attwood, “Nanofabrication and diffractive optics for high-resolution x-ray applications,” J. Vac. Sci. Technol. B 18, 2970–2975 (2000).
[CrossRef]

E. H. Anderson, V. Boegli, and L. P. Muray, “Electron beam lithography digital pattern generator and electronics for generalized curvilinear structures,” J. Vac. Sci. Technol. B 13, 2529–2534 (1995).
[CrossRef]

Arsenault, H.

Arzner, G. E.

G. E. Arzner, J. P. Delaboudinière, and X. Y. Song, “Photon sieves as EUV telescopes for solar orbiter,” Proc. SPIE 4853, 158–161 (2003).
[CrossRef]

Attwood, D.

E. H. Anderson, D. L. Olynick, B. Harteneck, E. Veklerov, G. Denbeaux, W. Chao, A. Lucero, L. Johnson, and D. Attwood, “Nanofabrication and diffractive optics for high-resolution x-ray applications,” J. Vac. Sci. Technol. B 18, 2970–2975 (2000).
[CrossRef]

Berndt, R.

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

Boegli, V.

E. H. Anderson, V. Boegli, and L. P. Muray, “Electron beam lithography digital pattern generator and electronics for generalized curvilinear structures,” J. Vac. Sci. Technol. B 13, 2529–2534 (1995).
[CrossRef]

Bradman, N. M.

H.-H. Chung, N. M. Bradman, M. R. Davidson, and P. H. Holloway, “Dual wavelength photon sieves,” Opt. Eng. (Bellingham) 47, 118001 (2008).
[CrossRef]

Cai, A.

Cao, Q.

Chao, W.

E. H. Anderson, D. L. Olynick, B. Harteneck, E. Veklerov, G. Denbeaux, W. Chao, A. Lucero, L. Johnson, and D. Attwood, “Nanofabrication and diffractive optics for high-resolution x-ray applications,” J. Vac. Sci. Technol. B 18, 2970–2975 (2000).
[CrossRef]

Cheng, G.

G. Cheng, T. Xing, Y. Yang, and J. Ma, “Experimental characterization of optical properties of photon sieve,” Proc. SPIE 6724, 1–6 (2007).

Chmelík, R.

R. Chmelík, “Analytical description of wave fields in focal regions of diffractive lenses,” J. Mod. Opt. 43, 1463–1471 (1996).
[CrossRef]

Christ, O.

G. Schmahl, D. Rudolph, P. Guttmann, and O. Christ, in X-Ray Microscopy, G.Schmahl and D.Rudolph, eds. (Springer-Verlag, 1984), Vol. 43, pp. 63–74.

Chung, H. -H.

H.-H. Chung, N. M. Bradman, M. R. Davidson, and P. H. Holloway, “Dual wavelength photon sieves,” Opt. Eng. (Bellingham) 47, 118001 (2008).
[CrossRef]

Dai, H.

Davidson, M. R.

H.-H. Chung, N. M. Bradman, M. R. Davidson, and P. H. Holloway, “Dual wavelength photon sieves,” Opt. Eng. (Bellingham) 47, 118001 (2008).
[CrossRef]

Delaboudinière, J. P.

G. E. Arzner, J. P. Delaboudinière, and X. Y. Song, “Photon sieves as EUV telescopes for solar orbiter,” Proc. SPIE 4853, 158–161 (2003).
[CrossRef]

Denbeaux, G.

E. H. Anderson, D. L. Olynick, B. Harteneck, E. Veklerov, G. Denbeaux, W. Chao, A. Lucero, L. Johnson, and D. Attwood, “Nanofabrication and diffractive optics for high-resolution x-ray applications,” J. Vac. Sci. Technol. B 18, 2970–2975 (2000).
[CrossRef]

Dong, X.

Du, C.

C. Zhou, X. Dong, L. Shi, C. Wang, and C. Du, “Experimental study of a multiwavelength photon sieve designed by random-area-divided approach,” Appl. Opt. 48, 1619–1623 (2009).
[CrossRef] [PubMed]

Z. Gao, X. Luo, J. Ma, Y. Fu, and C. Du, “Imaging properties of the photon sieve with a large aperture,” Opt. Laser Technol. 40, 614–618 (2008).
[CrossRef]

Fu, Y.

Z. Gao, X. Luo, J. Ma, Y. Fu, and C. Du, “Imaging properties of the photon sieve with a large aperture,” Opt. Laser Technol. 40, 614–618 (2008).
[CrossRef]

Furlan, W. D.

F. Giménez, W. D. Furlan, and J. A. Monsoriu, “Lacunar fractal photon sieves,” Opt. Commun. 277, 1–4 (2007).
[CrossRef]

F. Giménez, J. A. Monsoriu, W. D. Furlan, and A. Pons, “Fractal photon sieve,” Opt. Express 14, 11958–11963 (2006).
[CrossRef] [PubMed]

Gao, Z.

Z. Gao, X. Luo, J. Ma, Y. Fu, and C. Du, “Imaging properties of the photon sieve with a large aperture,” Opt. Laser Technol. 40, 614–618 (2008).
[CrossRef]

Giménez, F.

F. Giménez, W. D. Furlan, and J. A. Monsoriu, “Lacunar fractal photon sieves,” Opt. Commun. 277, 1–4 (2007).
[CrossRef]

F. Giménez, J. A. Monsoriu, W. D. Furlan, and A. Pons, “Fractal photon sieve,” Opt. Express 14, 11958–11963 (2006).
[CrossRef] [PubMed]

Guttmann, P.

G. Schmahl, D. Rudolph, P. Guttmann, and O. Christ, in X-Ray Microscopy, G.Schmahl and D.Rudolph, eds. (Springer-Verlag, 1984), Vol. 43, pp. 63–74.

Harm, S.

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

Harteneck, B.

E. H. Anderson, D. L. Olynick, B. Harteneck, E. Veklerov, G. Denbeaux, W. Chao, A. Lucero, L. Johnson, and D. Attwood, “Nanofabrication and diffractive optics for high-resolution x-ray applications,” J. Vac. Sci. Technol. B 18, 2970–2975 (2000).
[CrossRef]

Harvey, J. E.

J. E. Harvey, “Fourier treatment of near-field scalar diffraction theory,” Am. J. Phys. 47, 974–980 (1979).
[CrossRef]

Holloway, P. H.

H.-H. Chung, N. M. Bradman, M. R. Davidson, and P. H. Holloway, “Dual wavelength photon sieves,” Opt. Eng. (Bellingham) 47, 118001 (2008).
[CrossRef]

Hrynevych, M.

Huang, T. J.

Jahns, J.

Jia, J.

J. Jia and C. Xie, “Phase zone photon sieve,” Chin. Phys. B 18, 183–188 (2009).
[CrossRef]

J. Jia, J. Jiang, C. Xie, and M. Liu, “Photon sieve for reduction of the far-field diffraction spot size in the laser free-space communication system,” Opt. Commun. 281, 4536–4539 (2008).
[CrossRef]

Jiang, J.

J. Jia, J. Jiang, C. Xie, and M. Liu, “Photon sieve for reduction of the far-field diffraction spot size in the laser free-space communication system,” Opt. Commun. 281, 4536–4539 (2008).
[CrossRef]

Johnson, L.

E. H. Anderson, D. L. Olynick, B. Harteneck, E. Veklerov, G. Denbeaux, W. Chao, A. Lucero, L. Johnson, and D. Attwood, “Nanofabrication and diffractive optics for high-resolution x-ray applications,” J. Vac. Sci. Technol. B 18, 2970–2975 (2000).
[CrossRef]

Johnson, R. L.

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

Kipp, L.

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

Lin, Z.

Liu, M.

J. Jia, J. Jiang, C. Xie, and M. Liu, “Photon sieve for reduction of the far-field diffraction spot size in the laser free-space communication system,” Opt. Commun. 281, 4536–4539 (2008).
[CrossRef]

Liu, Y.

Lu, X.

Lucero, A.

E. H. Anderson, D. L. Olynick, B. Harteneck, E. Veklerov, G. Denbeaux, W. Chao, A. Lucero, L. Johnson, and D. Attwood, “Nanofabrication and diffractive optics for high-resolution x-ray applications,” J. Vac. Sci. Technol. B 18, 2970–2975 (2000).
[CrossRef]

Luo, X.

Z. Gao, X. Luo, J. Ma, Y. Fu, and C. Du, “Imaging properties of the photon sieve with a large aperture,” Opt. Laser Technol. 40, 614–618 (2008).
[CrossRef]

Ma, J.

Z. Gao, X. Luo, J. Ma, Y. Fu, and C. Du, “Imaging properties of the photon sieve with a large aperture,” Opt. Laser Technol. 40, 614–618 (2008).
[CrossRef]

G. Cheng, T. Xing, Y. Yang, and J. Ma, “Experimental characterization of optical properties of photon sieve,” Proc. SPIE 6724, 1–6 (2007).

Monsoriu, J. A.

F. Giménez, W. D. Furlan, and J. A. Monsoriu, “Lacunar fractal photon sieves,” Opt. Commun. 277, 1–4 (2007).
[CrossRef]

F. Giménez, J. A. Monsoriu, W. D. Furlan, and A. Pons, “Fractal photon sieve,” Opt. Express 14, 11958–11963 (2006).
[CrossRef] [PubMed]

Muray, L. P.

E. H. Anderson, V. Boegli, and L. P. Muray, “Electron beam lithography digital pattern generator and electronics for generalized curvilinear structures,” J. Vac. Sci. Technol. B 13, 2529–2534 (1995).
[CrossRef]

Olynick, D. L.

E. H. Anderson, D. L. Olynick, B. Harteneck, E. Veklerov, G. Denbeaux, W. Chao, A. Lucero, L. Johnson, and D. Attwood, “Nanofabrication and diffractive optics for high-resolution x-ray applications,” J. Vac. Sci. Technol. B 18, 2970–2975 (2000).
[CrossRef]

Pons, A.

Rudolph, D.

G. Schmahl, D. Rudolph, P. Guttmann, and O. Christ, in X-Ray Microscopy, G.Schmahl and D.Rudolph, eds. (Springer-Verlag, 1984), Vol. 43, pp. 63–74.

Schmahl, G.

G. Schmahl, D. Rudolph, P. Guttmann, and O. Christ, in X-Ray Microscopy, G.Schmahl and D.Rudolph, eds. (Springer-Verlag, 1984), Vol. 43, pp. 63–74.

Seemann, T.

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

Sheppard, C. J. R.

Shi, L.

Skibowski, M.

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

Song, X. Y.

G. E. Arzner, J. P. Delaboudinière, and X. Y. Song, “Photon sieves as EUV telescopes for solar orbiter,” Proc. SPIE 4853, 158–161 (2003).
[CrossRef]

Southwell, W. H.

Sun, J. A.

Sun, X.

Tullson, D.

Veklerov, E.

E. H. Anderson, D. L. Olynick, B. Harteneck, E. Veklerov, G. Denbeaux, W. Chao, A. Lucero, L. Johnson, and D. Attwood, “Nanofabrication and diffractive optics for high-resolution x-ray applications,” J. Vac. Sci. Technol. B 18, 2970–2975 (2000).
[CrossRef]

Wang, C.

Xie, C.

J. Jia and C. Xie, “Phase zone photon sieve,” Chin. Phys. B 18, 183–188 (2009).
[CrossRef]

J. Jia, J. Jiang, C. Xie, and M. Liu, “Photon sieve for reduction of the far-field diffraction spot size in the laser free-space communication system,” Opt. Commun. 281, 4536–4539 (2008).
[CrossRef]

Xing, T.

G. Cheng, T. Xing, Y. Yang, and J. Ma, “Experimental characterization of optical properties of photon sieve,” Proc. SPIE 6724, 1–6 (2007).

Yang, Y.

G. Cheng, T. Xing, Y. Yang, and J. Ma, “Experimental characterization of optical properties of photon sieve,” Proc. SPIE 6724, 1–6 (2007).

Zhang, J.

Zhou, C.

Am. J. Phys. (1)

J. E. Harvey, “Fourier treatment of near-field scalar diffraction theory,” Am. J. Phys. 47, 974–980 (1979).
[CrossRef]

Appl. Opt. (2)

Chin. Opt. Lett. (1)

Chin. Phys. B (1)

J. Jia and C. Xie, “Phase zone photon sieve,” Chin. Phys. B 18, 183–188 (2009).
[CrossRef]

J. Mod. Opt. (1)

R. Chmelík, “Analytical description of wave fields in focal regions of diffractive lenses,” J. Mod. Opt. 43, 1463–1471 (1996).
[CrossRef]

J. Opt. Soc. Am. (2)

J. Opt. Soc. Am. A (4)

J. Vac. Sci. Technol. B (2)

E. H. Anderson, V. Boegli, and L. P. Muray, “Electron beam lithography digital pattern generator and electronics for generalized curvilinear structures,” J. Vac. Sci. Technol. B 13, 2529–2534 (1995).
[CrossRef]

E. H. Anderson, D. L. Olynick, B. Harteneck, E. Veklerov, G. Denbeaux, W. Chao, A. Lucero, L. Johnson, and D. Attwood, “Nanofabrication and diffractive optics for high-resolution x-ray applications,” J. Vac. Sci. Technol. B 18, 2970–2975 (2000).
[CrossRef]

Nature (1)

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

Opt. Commun. (2)

J. Jia, J. Jiang, C. Xie, and M. Liu, “Photon sieve for reduction of the far-field diffraction spot size in the laser free-space communication system,” Opt. Commun. 281, 4536–4539 (2008).
[CrossRef]

F. Giménez, W. D. Furlan, and J. A. Monsoriu, “Lacunar fractal photon sieves,” Opt. Commun. 277, 1–4 (2007).
[CrossRef]

Opt. Eng. (Bellingham) (1)

H.-H. Chung, N. M. Bradman, M. R. Davidson, and P. H. Holloway, “Dual wavelength photon sieves,” Opt. Eng. (Bellingham) 47, 118001 (2008).
[CrossRef]

Opt. Express (2)

Opt. Laser Technol. (1)

Z. Gao, X. Luo, J. Ma, Y. Fu, and C. Du, “Imaging properties of the photon sieve with a large aperture,” Opt. Laser Technol. 40, 614–618 (2008).
[CrossRef]

Opt. Lett. (1)

Proc. SPIE (2)

G. E. Arzner, J. P. Delaboudinière, and X. Y. Song, “Photon sieves as EUV telescopes for solar orbiter,” Proc. SPIE 4853, 158–161 (2003).
[CrossRef]

G. Cheng, T. Xing, Y. Yang, and J. Ma, “Experimental characterization of optical properties of photon sieve,” Proc. SPIE 6724, 1–6 (2007).

Other (1)

G. Schmahl, D. Rudolph, P. Guttmann, and O. Christ, in X-Ray Microscopy, G.Schmahl and D.Rudolph, eds. (Springer-Verlag, 1984), Vol. 43, pp. 63–74.

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Figures (4)

Fig. 1
Fig. 1

Schematic view of a photon sieve composed of many square pinholes.

Fig. 2
Fig. 2

Schematic drawing of the translation and rotation of coordinate relative to the initial coordinate for the n th square pinhole. The central coordinate of square pinhole is ( x n , y n ) in the initial x y coordinate system. The side length of square pinhole is b n . The tangent of θ is y n / x n .

Fig. 3
Fig. 3

Schematic view of a photon sieve for point-to-point imaging. (a) A photon sieve for point-to-point imaging. (b) Transverse plane of the considered photon sieve.

Fig. 4
Fig. 4

Field value U n ( 0 , 0 ) of a pinhole illustrated as a function of the ratio of the size of the pinhole to the width of the local Fresnel zone.

Equations (31)

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

U n ( X , Y ) = 1 2 π S n V n ( x , y ) exp ( j k r 01 ) r 01 ( j k + 1 r 01 ) q r 01 d x d y ,
U n ( X , Y ) = 1 λ S n V n ( x , y ) exp ( j k r 01 ) q r 01 2 d x d y ,
r 01 = [ ( X x ) 2 + ( Y y ) 2 + q 2 ] 1 / 2 = ( q 2 + X 2 + Y 2 2 X x 2 Y y + x 2 + y 2 ) 1 / 2 H + x 2 + y 2 2 X x 2 Y y 2 H ,
U n ( X , Y ) = 1 λ q H 2 exp ( j k H ) S n V n ( x , y ) exp ( j k x 2 + y 2 2 X x 2 Y y 2 H ) d x d y .
V n ( x , y ) = A n   exp ( j k L n ) exp { j k [ g n ( x x n ) + h n ( y y n ) ] } ,
U n ( X , Y ) = 1 λ q H 2 A n   exp [ j k ( H + L n ) ] S n exp ( j k x 2 + y 2 2 X x 2 Y y 2 H ) d x d y ,
( x y ) = ( cos   θ sin   θ sin   θ cos   θ ) ( x y ) = ( cos   θ sin   θ sin   θ cos   θ ) ( x x n y y n ) ,
U n ( X , Y ) = 1 λ q H 2 A n   exp [ j k ( H + L n ) ] b n / 2 b n / 2 b n / 2 b n / 2 exp ( j k 2 H r 2 ) exp { j k H [ X ( x   cos   θ y   sin   θ ) + Y ( x   sin   θ + y   cos   θ ) ] } d x d y ,
U n ( X , Y ) = λ q π 2 A n   exp [ j k ( H + L n ) ] 1 X Y sin ( k b n 2 H X ) sin ( k b n 2 H Y ) ,
U n ( 0 , 0 ) = λ q π 2 A n   exp [ j k ( Q n + L n ) ] 1 x y sin ( k b n 2 Q n x ) sin ( k b n 2 Q n y ) ,
k ( Q n + L n ) = 2 m π + const . ,
1 x y sin ( k b n 2 Q n x ) sin ( k b n 2 Q n y ) > 0 ,
k ( Q n + L n ) = ( 2 m + 1 ) π + const . ,
1 x y sin ( k b n 2 Q n x ) sin ( k b n 2 Q n y ) < 0 ,
U n ( 0 , 0 ) = q π b n f n r n Q n 2 A n   exp [ j k ( Q n + P n ) ] sin ( k b n 2 f n r n ) ,
r n λ f n 2 w ,
U n ( 0 , 0 ) = λ q 2 π f n 2 r n 2 Q n 2 A n   exp [ j k ( Q n + P n ) ] b n w sin ( π 2 b n w ) ,
U n ( 0 , 0 ) 2 π b n w sin ( π 2 b n w ) .
U n ( 0 , 0 ) d w J 1 ( π 2 d w ) ,
g = λ q f n 2 4 r n 2 Q n 2 A n   exp [ j k ( Q n + P n ) ] .
g ( m ) 1 m .
A n = A ( x n , y n ) ,
L n = L ( x n , y n ) = ( x n 2 + y n 2 + p 2 ) 1 / 2 = P n ,
g n = ( L / x ) ( x n , y n ) = x n P n ,
h n = ( L / y ) ( x n , y n ) = y n P n ,
cos   θ = x n / r n ,
sin   θ = y n / r n ,
x = r n ( 1 + Q n / P n ) = r n Q n / f n ,
y = 0.
lim y 0   sin ( k b n 2 Q n y ) / y = k b n 2 Q n .
U n ( 0 , 0 ) = q π b n f n r n Q n 2 A n   exp [ j k ( Q n + P n ) ] sin ( k b n 2 f n r n ) ,

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