Abstract

A modified Fresnel zone plate that can produce an approximate Gaussian focal spot is proposed for the focusing and imaging of soft x rays and extreme ultraviolet radiation. The selection conditions for the positions and the widths of the concentric open rings are analytically presented. The focal spot size can be much smaller than the width of the narrowest open ring, and the sidelobes and the higher orders can be effectively suppressed. Through numerical experiments, we confirm that a Gaussian focal spot with a beam width of 7.7 nm can be produced by a modified Fresnel zone plate with a minimum structure size of 30 nm.

© 2003 Optical Society of America

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References

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  1. G. Schmahl, D. Rudolph, P. Guttmann, O. Christ, “Zone plates for x-ray microscopy,” in X-Ray Microscopy, G. Schmahl, D. Rudolph, eds. (Springer-Verlag, Berlin, 1984), Vol. 43, pp. 63–74.
  2. H. Arsenault, “Diffraction theory of Fresnel zone plates,” J. Opt. Soc. Am. 58, 1536 (1968).
    [CrossRef]
  3. D. J. Stigliani, R. Mittra, R. G. Semonin, “Resolving power of a zone plate,” J. Opt. Soc. Am. 57, 610–613 (1967).
    [CrossRef]
  4. J. A. Sun, A. Cai, “Archaic focusing properties of Fresnel zone plates,” J. Opt. Soc. Am. A 8, 33–35 (1991).
    [CrossRef]
  5. E. H. Anderson, V. Boegli, 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]
  6. E. H. Anderson, D. L. Olynick, B. Harteneck, E. Veklerov, G. Denbeaux, W. Chao, A. Lucero, L. Johnson, D. Attwood, “Nanofabrication and diffractive optics for high-resolution x-ray applications,” J. Vac. Sci. Technol. B 18, 2970–2975 (2000).
    [CrossRef]
  7. L. Kipp, M. Skibowski, R. L. Johnson, R. Berndt, R. Adelung, S. Harm, R. Seemann, “Sharper images by focusing soft X-rays with photon sieves,” Nature 414, 184–188 (2001).
    [CrossRef] [PubMed]
  8. Q. Cao, J. Jahns, “Focusing analysis of the pinhole photon sieve: individual far-field model,” J. Opt. Soc. Am. A 19, 2387–2393 (2002).
    [CrossRef]
  9. G. E. Artzner, J. P. Delaboudinière, X. Y. Song, “Photon sieves as EUV telescopes for solar orbiter,” in Innovative Telescopes and Instrumentation for Solar Astrophysics, S. L. Keil, S. V. Avakyan, S. I. Vavilov, eds., Proc. SPIE4853, 158–161 (2003).
    [CrossRef]
  10. M. Howells, http://www-esg.lbl.gov/esg/personnel/howells/Xraysieves.pdf . The opinion that the suppression of higher orders results not from the random distribution of pinholes but from the use of different ratios d/wfor different pinholes is presented in this reference, where dis the diameter of an individual pinhole and wis the width of the corresponding local half-zone of the underlying TFZP.
  11. Q. Cao, J. Jahns, “Nonparaxial model for the focusing of high-numerical-aperture photon sieves,” J. Opt. Soc. Am. A 20, 1005–1012 (2003).
    [CrossRef]
  12. A. E. Siegman, “New developments in laser resonators,” in Optical Resonators, D. A. Holmes, ed., Proc. SPIE1224, 2–14 (1990).
    [CrossRef]
  13. J. E. Harvey, “Fourier treatment of near-field scalar diffraction theory,” Am. J. Phys. 47, 974–980 (1979).
    [CrossRef]
  14. W. H. Southwell, “Validity of the Fresnel approximation in the near field,” J. Opt. Soc. Am. 71, 7–14 (1981).
    [CrossRef]
  15. C. J. R. Sheppard, M. Hrynevych, “Diffraction by a circular aperture: a generalization of Fresnel diffraction theory,” J. Opt. Soc. Am. A 9, 274–281 (1992).
    [CrossRef]

2003 (1)

2002 (1)

2001 (1)

L. Kipp, M. Skibowski, R. L. Johnson, R. Berndt, R. Adelung, S. Harm, R. 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, D. Attwood, “Nanofabrication and diffractive optics for high-resolution x-ray applications,” J. Vac. Sci. Technol. B 18, 2970–2975 (2000).
[CrossRef]

1995 (1)

E. H. Anderson, V. Boegli, 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)

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)

1967 (1)

Adelung, R.

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

Anderson, E. H.

E. H. Anderson, D. L. Olynick, B. Harteneck, E. Veklerov, G. Denbeaux, W. Chao, A. Lucero, L. Johnson, 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, 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.

Artzner, G. E.

G. E. Artzner, J. P. Delaboudinière, X. Y. Song, “Photon sieves as EUV telescopes for solar orbiter,” in Innovative Telescopes and Instrumentation for Solar Astrophysics, S. L. Keil, S. V. Avakyan, S. I. Vavilov, eds., Proc. SPIE4853, 158–161 (2003).
[CrossRef]

Attwood, D.

E. H. Anderson, D. L. Olynick, B. Harteneck, E. Veklerov, G. Denbeaux, W. Chao, A. Lucero, L. Johnson, 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, R. 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, 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]

Cai, A.

Cao, Q.

Chao, W.

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

Christ, O.

G. Schmahl, D. Rudolph, P. Guttmann, O. Christ, “Zone plates for x-ray microscopy,” in X-Ray Microscopy, G. Schmahl, D. Rudolph, eds. (Springer-Verlag, Berlin, 1984), Vol. 43, pp. 63–74.

Delaboudinière, J. P.

G. E. Artzner, J. P. Delaboudinière, X. Y. Song, “Photon sieves as EUV telescopes for solar orbiter,” in Innovative Telescopes and Instrumentation for Solar Astrophysics, S. L. Keil, S. V. Avakyan, S. I. Vavilov, eds., Proc. SPIE4853, 158–161 (2003).
[CrossRef]

Denbeaux, G.

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

Guttmann, P.

G. Schmahl, D. Rudolph, P. Guttmann, O. Christ, “Zone plates for x-ray microscopy,” in X-Ray Microscopy, G. Schmahl, D. Rudolph, eds. (Springer-Verlag, Berlin, 1984), Vol. 43, pp. 63–74.

Harm, S.

L. Kipp, M. Skibowski, R. L. Johnson, R. Berndt, R. Adelung, S. Harm, R. 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, 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]

Hrynevych, M.

Jahns, J.

Johnson, L.

E. H. Anderson, D. L. Olynick, B. Harteneck, E. Veklerov, G. Denbeaux, W. Chao, A. Lucero, L. Johnson, 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, R. 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, R. Seemann, “Sharper images by focusing soft X-rays with photon sieves,” Nature 414, 184–188 (2001).
[CrossRef] [PubMed]

Lucero, A.

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

Mittra, R.

Muray, L. P.

E. H. Anderson, V. Boegli, 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, D. Attwood, “Nanofabrication and diffractive optics for high-resolution x-ray applications,” J. Vac. Sci. Technol. B 18, 2970–2975 (2000).
[CrossRef]

Rudolph, D.

G. Schmahl, D. Rudolph, P. Guttmann, O. Christ, “Zone plates for x-ray microscopy,” in X-Ray Microscopy, G. Schmahl, D. Rudolph, eds. (Springer-Verlag, Berlin, 1984), Vol. 43, pp. 63–74.

Schmahl, G.

G. Schmahl, D. Rudolph, P. Guttmann, O. Christ, “Zone plates for x-ray microscopy,” in X-Ray Microscopy, G. Schmahl, D. Rudolph, eds. (Springer-Verlag, Berlin, 1984), Vol. 43, pp. 63–74.

Seemann, R.

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

Semonin, R. G.

Sheppard, C. J. R.

Siegman, A. E.

A. E. Siegman, “New developments in laser resonators,” in Optical Resonators, D. A. Holmes, ed., Proc. SPIE1224, 2–14 (1990).
[CrossRef]

Skibowski, M.

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

Song, X. Y.

G. E. Artzner, J. P. Delaboudinière, X. Y. Song, “Photon sieves as EUV telescopes for solar orbiter,” in Innovative Telescopes and Instrumentation for Solar Astrophysics, S. L. Keil, S. V. Avakyan, S. I. Vavilov, eds., Proc. SPIE4853, 158–161 (2003).
[CrossRef]

Southwell, W. H.

Stigliani, D. J.

Sun, J. A.

Veklerov, E.

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

Am. J. Phys. (1)

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

J. Opt. Soc. Am. (3)

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

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

E. H. Anderson, V. Boegli, 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, 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, R. Seemann, “Sharper images by focusing soft X-rays with photon sieves,” Nature 414, 184–188 (2001).
[CrossRef] [PubMed]

Other (4)

G. Schmahl, D. Rudolph, P. Guttmann, O. Christ, “Zone plates for x-ray microscopy,” in X-Ray Microscopy, G. Schmahl, D. Rudolph, eds. (Springer-Verlag, Berlin, 1984), Vol. 43, pp. 63–74.

G. E. Artzner, J. P. Delaboudinière, X. Y. Song, “Photon sieves as EUV telescopes for solar orbiter,” in Innovative Telescopes and Instrumentation for Solar Astrophysics, S. L. Keil, S. V. Avakyan, S. I. Vavilov, eds., Proc. SPIE4853, 158–161 (2003).
[CrossRef]

M. Howells, http://www-esg.lbl.gov/esg/personnel/howells/Xraysieves.pdf . The opinion that the suppression of higher orders results not from the random distribution of pinholes but from the use of different ratios d/wfor different pinholes is presented in this reference, where dis the diameter of an individual pinhole and wis the width of the corresponding local half-zone of the underlying TFZP.

A. E. Siegman, “New developments in laser resonators,” in Optical Resonators, D. A. Holmes, ed., Proc. SPIE1224, 2–14 (1990).
[CrossRef]

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Figures (6)

Fig. 1
Fig. 1

Schematic view of a modified Fresnel zone plate. See text for the definitions of the parameters f, fn, and rn.

Fig. 2
Fig. 2

Transmittance (T) functions of a MFZP (lower graph) and of the underlying TFZP (upper graph) (a) in the transition zones between region 1 and region 2, (b) in the transition zones between region 2 and region 3. For clarity, the widths of all the half-zones of the underlying TFZP are drawn uniformly in the s coordinate.

Fig. 3
Fig. 3

(a) Change of the widths of the open rings with the increase of n, (b) Change of the widths of the opaque rings with the increase of n.

Fig. 4
Fig. 4

Normalized intensity distributions (to the peak intensity in each case) at the focal plane for an ideal MFZP and for the corresponding TFZP: (a) linear plots, (b) logarithmic plots. The solid curves are the intensity distributions of the ideal MFZP, the dashed curves are the desirable Gaussian distributions, and the dashed-dotted curves are the intensity distributions of the TFZP.

Fig. 5
Fig. 5

Normalized intensity distributions (to the peak intensity in each case) on the propagation axis: (a) the ideal MFZP, (b) the corresponding TFZP.

Fig. 6
Fig. 6

Normalized intensity distributions (to the peak intensity in each case) at the focal plane for a nonideal MFZP with errors: (a) linear plots, (b) logarithmic plots. The solid curves are the intensity distributions of the nonideal MFZP with errors, and the dashed curves are the intensity distributions of the ideal MFZP.

Tables (1)

Tables Icon

Table 1 Related Parameters in the Three Different Regions

Equations (14)

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Un(R)=1λAnfρ2exp(jkρ)rdrdθ,
ρfn+R2+(r2-rn2)-2Rr cos(θ-ϕ)2 fn,
Un(R)=kffn2expjkfn+R22 fn×anbnexpjk r2-rn22 fnJ0kRrfnrdr,
Un(R)=2 ffnexpjkfn+R22 fnJ0krnfn Rsinkdn2 fn.
Un(0)=2 ffnexp(jkfn)sinkdn2 fn.
fn=f+mnλsinkdn2 fn>0,
fn=f+mn+12λsinkdn2 fn<0,
Un(R)2 ffnexp[jk(fn-f )]sinkdn2 fnJ0krnF R.
2 ffnexp[jk(fn-f )]sinkdn2 fn=αDnexp-snσ2,
s=r2,ds=2rdr,
2α0exp(-r2/σ2)J0(kRr/F)rdr
=ασ2exp{-[σkR/(2F)]2},
U(R)ασ2exp-σkR2F2.
dn=2 fnkLπ-arcsinβ DnfnD1f1exp-sn-s1σ2,

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