Abstract

A class of photon sieve is introduced whose structure is based on the overlapping pinholes in the innermost zones. This kind of distribution is produced by, for example, a particular form of Gaussian function. The focusing property of the proposed model was examined theoretically and experimentally. It is shown that under He-Ne laser and white light illumination, the focal spot size of this novel structure has considerably smaller FWHM than a photon sieve with randomly distributed pinholes and a Fresnel zone plate. In addition, secondary maxima have been suppressed effectively.

© 2011 Optical Society of America

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References

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  1. G. Schmahl, D. Rudolph, P. Guttmann, and O. Christ, “Zone plates for x-ray microscopy,” in X-Ray Microscopy, G.Schmahl and D.Rudolph, eds. (Springer-Verlag, 1984), Vol.  43, pp. 63–74.
  2. 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 sieve,” Nature 414, 184–188(2001).
    [CrossRef] [PubMed]
  3. 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]
  4. F. Giménez, J. A. Monsoriu, W. D. Furlan, and A. Pons, “Fractal photon sieve,” Opt. Express 14, 11958–11963(2006).
    [CrossRef] [PubMed]
  5. F. Giménez, W. D. Furlan, and J. A. Monsoriu, “Lacunar fractal photon sieves,” Opt. Commun. 277, 1–4 (2007).
    [CrossRef]
  6. J. Jia and X. Chang-Qing, “Phase zone photon sieve,” Chinese Physics B 18, 183–188 (2009).
    [CrossRef]
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    [CrossRef] [PubMed]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]

2009 (1)

J. Jia and X. Chang-Qing, “Phase zone photon sieve,” Chinese Physics B 18, 183–188 (2009).
[CrossRef]

2008 (1)

J. Jia, J. Jiang, C. Xie, and M. Li, “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]

2007 (1)

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

2006 (1)

2005 (1)

2003 (2)

2002 (1)

2001 (1)

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 sieve,” Nature 414, 184–188(2001).
[CrossRef] [PubMed]

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 sieve,” Nature 414, 184–188(2001).
[CrossRef] [PubMed]

Andersen, G.

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 sieve,” Nature 414, 184–188(2001).
[CrossRef] [PubMed]

Born, M.

M. Born and E. Wolf, Principles of Optics, 5th ed. (Pergamon, 1975), p. 378.

Cao, Q.

Chang-Qing, X.

J. Jia and X. Chang-Qing, “Phase zone photon sieve,” Chinese Physics B 18, 183–188 (2009).
[CrossRef]

Christ, O.

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

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]

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, “Zone plates for x-ray microscopy,” 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 R. Seemann, “Sharper images by focusing soft x-rays with photon sieve,” Nature 414, 184–188(2001).
[CrossRef] [PubMed]

Jahns, J.

Jia, J.

J. Jia and X. Chang-Qing, “Phase zone photon sieve,” Chinese Physics B 18, 183–188 (2009).
[CrossRef]

J. Jia, J. Jiang, C. Xie, and M. Li, “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. Li, “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, 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 sieve,” Nature 414, 184–188(2001).
[CrossRef] [PubMed]

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 sieve,” Nature 414, 184–188(2001).
[CrossRef] [PubMed]

Li, M.

J. Jia, J. Jiang, C. Xie, and M. Li, “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]

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]

Pons, A.

Rudolph, D.

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

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 sieve,” Nature 414, 184–188(2001).
[CrossRef] [PubMed]

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 sieve,” Nature 414, 184–188(2001).
[CrossRef] [PubMed]

Wolf, E.

M. Born and E. Wolf, Principles of Optics, 5th ed. (Pergamon, 1975), p. 378.

Xie, C.

J. Jia, J. Jiang, C. Xie, and M. Li, “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]

Chinese Physics B (1)

J. Jia and X. Chang-Qing, “Phase zone photon sieve,” Chinese Physics B 18, 183–188 (2009).
[CrossRef]

J. Opt. Soc. Am. A (3)

Nature (1)

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 sieve,” Nature 414, 184–188(2001).
[CrossRef] [PubMed]

Opt. Commun. (2)

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

J. Jia, J. Jiang, C. Xie, and M. Li, “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]

Opt. Express (1)

Opt. Lett. (1)

Other (2)

M. Born and E. Wolf, Principles of Optics, 5th ed. (Pergamon, 1975), p. 378.

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

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Figures (6)

Fig. 1
Fig. 1

Schematic view of imaging by a PS (after [2]). Details are described in the text.

Fig. 2
Fig. 2

Three types of diffractive lens: (a) FZP, (b) PS with quasi-random pinhole distribution, (c) DGPS.

Fig. 3
Fig. 3

Comparison of calculated transverse intensity distribution in focal plane of FZP (dashed curve), PS with quasi-random pinhole distribution (dotted curve), and DGPS (solid curve). (a) Linear scale, (b) log scale.

Fig. 4
Fig. 4

Comparison of FWHM for two photon sieves with the same focal lengths and different number of zones; dotted curve, 44 zones; solid curve, 88 zones. (a) Log scale, (b) linear scale.

Fig. 5
Fig. 5

CCD-recorded transverse intensity distribution of parallel white light beam diffracted by (a) FZP, (b) PS with quasi-random pinhole distribution, (c) DGPS, at their focal planes, as well as (d) normalized intensity of the samples.

Fig. 6
Fig. 6

CCD-recorded transverse intensity distribution of a paralleled He-Ne laser light beam diffracted by (a) FZP, (b) PS with a quasi-random pinhole distribution, (c) DGPS, at their focal planes, as well as (d) normalized intensity of the samples.

Equations (6)

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u n = i A 2 λ pinholes e i k ( r + s ) r s ( cos θ r + cos θ s ) d S ,
u n = A 0 a n exp ( i k ρ 2 2 q ) J 0 ( k | Δ ρ | q ρ ) ρ d ρ .
U n = n = 1 N W n u n ,
I ( ρ ) = | U n | 2 .
W n = n 0 exp ( ( r n r 0 ) 2 α 2 ) ,
r n = R 2 2 n f λ ,

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