Abstract

A novel apodized photon sieve is presented in which random dense Gaussian distribution is implemented to modulate the pinhole density in each zone. The random distribution in dense Gaussian distribution causes intrazone discontinuities. Also, the dense Gaussian distribution generates a substantial number of pinholes in order to form a large degree of overlap between the holes in a few innermost zones of the photon sieve; thereby, clear zones are formed. The role of the discontinuities on the focusing properties of the photon sieve is examined as well. Analysis shows that secondary maxima have evidently been suppressed, transmission has increased enormously, and the central maxima width is approximately unchanged in comparison to the dense Gaussian distribution. Theoretical results have been completely verified by experiment.

© 2012 Optical Society of America

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References

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  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 (London) 414, 184–188 (2001).
    [CrossRef]
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  3. 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]
  4. F. Giménez, J. A. Monsoriu, W. D. Furlan, and A. Pons, “Fractal photon sieve,” Opt. Express 14, 11958–11963 (2006).
    [CrossRef]
  5. G. Andersen, “Large optical photon sieve,” Opt. Lett. 30, 2976–2978 (2005).
    [CrossRef]
  6. G. Anderson and D. Tullson, “Broadband antihole photon sieve telescope,” Appl. Opt. 46, 3706–3708 (2007).
    [CrossRef]
  7. G. Cheng, C. Hu, P. Xu, and T. Xing, “Zernike apodized photon sieves for high-resolution phase-contrast x-ray microscopy,” Opt. Lett. 35, (2010).
  8. A. Sabatyan and S. Mirzaie, “Efficiency-enhanced photon sieve using Gaussian/overlapped distribution of pinholes,” Appl. Opt. 50, 1517–1522 (2011).
    [CrossRef]
  9. J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, 1996).
  10. 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]

2011 (1)

2010 (1)

G. Cheng, C. Hu, P. Xu, and T. Xing, “Zernike apodized photon sieves for high-resolution phase-contrast x-ray microscopy,” Opt. Lett. 35, (2010).

2008 (1)

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]

2007 (1)

2006 (1)

2005 (1)

2003 (1)

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

Andersen, G.

Anderson, 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 (London) 414, 184–188 (2001).
[CrossRef]

Cao, Q.

Cheng, G.

G. Cheng, C. Hu, P. Xu, and T. Xing, “Zernike apodized photon sieves for high-resolution phase-contrast x-ray microscopy,” Opt. Lett. 35, (2010).

Furlan, W. D.

Giménez, F.

Goodman, J. W.

J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, 1996).

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 (London) 414, 184–188 (2001).
[CrossRef]

Hu, C.

G. Cheng, C. Hu, P. Xu, and T. Xing, “Zernike apodized photon sieves for high-resolution phase-contrast x-ray microscopy,” Opt. Lett. 35, (2010).

Jahns, J.

Jia, 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]

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, 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 (London) 414, 184–188 (2001).
[CrossRef]

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 (London) 414, 184–188 (2001).
[CrossRef]

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]

Mirzaie, S.

Monsoriu, J. A.

Pons, A.

Sabatyan, A.

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 (London) 414, 184–188 (2001).
[CrossRef]

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 (London) 414, 184–188 (2001).
[CrossRef]

Tullson, D.

Xie, C.

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, C. Hu, P. Xu, and T. Xing, “Zernike apodized photon sieves for high-resolution phase-contrast x-ray microscopy,” Opt. Lett. 35, (2010).

Xu, P.

G. Cheng, C. Hu, P. Xu, and T. Xing, “Zernike apodized photon sieves for high-resolution phase-contrast x-ray microscopy,” Opt. Lett. 35, (2010).

Appl. Opt. (2)

J. Opt. Soc. Am. A (2)

Nature (London) (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 (London) 414, 184–188 (2001).
[CrossRef]

Opt. Commun. (1)

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]

Opt. Express (1)

Opt. Lett. (2)

G. Andersen, “Large optical photon sieve,” Opt. Lett. 30, 2976–2978 (2005).
[CrossRef]

G. Cheng, C. Hu, P. Xu, and T. Xing, “Zernike apodized photon sieves for high-resolution phase-contrast x-ray microscopy,” Opt. Lett. 35, (2010).

Other (1)

J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, 1996).

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Figures (9)

Fig. 1.
Fig. 1.

Schematic view of a pupil function M(x,y) with arbitrary paraxial illumination.

Fig. 2.
Fig. 2.

Left and right PSs are generated by implementing regular and random dense Gaussian distribution, respectively, including (a) and (b) 4, (c) and (d) 11, and (e) and (f) 22 clear zones, which are made up of the fully overlapped holes. So, the corresponding PSs were constructed using the Gaussian parameters (α, β, γ) (a) (50, 44, 178); (b) (20, 7, 89); and (c) (100, 44, 178), respectively.

Fig. 3.
Fig. 3.

Comparison of the calculated transverse intensity distribution of PS with 4, 11, and 22 numbers of the clear zones indicated by solid, dotted, and dashed lines, respectively, in (a) linear scale and (b) log scale. So, the corresponding PSs were constructed using the Gaussian parameters (α, β, γ) (a) (50, 44, 178); (b) (20, 7, 89); and (c) (100, 44, 178), respectively.

Fig. 4.
Fig. 4.

Intensity distribution at the focal plane of a PS constructed using regular (dashed line) and random (solid line) dense Gaussian distribution, which has the least number of the clear zones by using the Gaussian parameters (α,β,γ)=(50,44,178) in two scales: (a) linear and (b) logarithmic.

Fig. 5.
Fig. 5.

Intensity distribution at the focal plane of a PS constructed using regular (dashed line) and random (solid line) dense Gaussian distribution, which has an intermediate number of the clear zones by using the Gaussian parameters (α,β,γ)=(20,7,89) in two scales: (a) linear and (b) logarithmic.

Fig. 6.
Fig. 6.

Intensity distribution at the focal plane of a PS constructed using regular (dashed line) and random (solid line) dense Gaussian distribution, which has the highest number of the clear zones by using the Gaussian parameters (α,β,γ)=(100,44,178) in two scales: (a) linear and (b) logarithmic.

Fig. 7.
Fig. 7.

CCD recorded transverse intensity distributions at the focal plane of PSs constructed using the regular (left figures) and random (right ones) distribution with the Gaussian parameters (α, β, γ) (a) (50, 44, 178); (b) (20, 7, 89); and (c) (100, 44, 178); using which 4, 11, and 22 clear zones are generated in the corresponding PS, respectively.

Fig. 8.
Fig. 8.

Experimental intensity distribution profiles across the focal plane of PS constructed using the regular (dashed line) and random (solid line) distribution with the Gaussian parameters (α, β, γ) for (a) (50, 44, 178); (b) (20, 7, 89); and (c) (100, 44, 178), using which 4, 11, and 22 clear zones are generated in the corresponding PS, respectively.

Fig. 9.
Fig. 9.

Experimental comparison of transmitted power between the generated DGPS including 4 (dotted line), 11 (dashed line), and 22 (solid line) clear zones.

Equations (3)

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U(x,y,z)=2πeikziλz[M(x,y)eik2z(x2+y2)],
f(m)=αe(mγ)2/β2,
M(x,y)={1,(xxmn)2+(yymn)2rm2,0,other,

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