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Optics Express

Optics Express

  • Editor: Andrew M. Weiner
  • Vol. 21, Iss. 3 — Feb. 11, 2013
  • pp: 2701–2706

Cantor dust zone plates

Vicente Ferrando, Arnau Calatayud, Fernando Giménez, Walter D. Furlan, and Juan A. Monsoriu  »View Author Affiliations

Optics Express, Vol. 21, Issue 3, pp. 2701-2706 (2013)

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In this paper we use the Cantor Dust to design zone plates based on a two-dimensional fractal for the first time. The pupil function that defines the coined Cantor Dust Zone Plates (CDZPs) can be written as a combination of rectangle functions. Thus CDZPs can be considered as photon sieves with rectangular holes. The axial irradiances produced by CDZPs of different fractal orders are obtained analitically and experimentally, analyzing the influence of the fractality. The transverse irradiance patterns generated by this kind of zone plates has been also investigated.

© 2013 OSA

OCIS Codes
(050.1940) Diffraction and gratings : Diffraction
(050.1970) Diffraction and gratings : Diffractive optics

ToC Category:
Diffraction and Gratings

Original Manuscript: December 5, 2012
Revised Manuscript: January 14, 2013
Manuscript Accepted: January 14, 2013
Published: January 28, 2013

Vicente Ferrando, Arnau Calatayud, Fernando Giménez, Walter D. Furlan, and Juan A. Monsoriu, "Cantor dust zone plates," Opt. Express 21, 2701-2706 (2013)

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  1. A. Siemion, A. Siemion, M. Makowski, J. Suszek, J. Bomba, A. Czerwiski, F. Garet, J.-L. Coutaz, and M. Sypek, “Diffractive paper lens for terahertz optics,” Opt. Lett.37, 4320–4322 (2012). [CrossRef] [PubMed]
  2. A. Sakdinawat and Y. Liu, “Soft-x-ray microscopy using spiral zone plates,” Opt. Lett.32, 2635–2637 (2007). [CrossRef] [PubMed]
  3. G. Saavedra, W. D. Furlan, and J. A. Monsoriu, “Fractal zone plates,” Opt. Lett.28, 971–973 (2003). [CrossRef] [PubMed]
  4. J. A. Davis, L. Ramirez, J. A. Rodrigo Martín-Romo, T. Alieva, and M. L. Calvo, “Focusing properties of fractal zone plates: experimental implementation with a liquid-crystal display,” Opt. Lett.29, 1321–1323 (2004). [CrossRef] [PubMed]
  5. J. A. Monsoriu, G. Saavedra, and W. D. Furlan, “Fractal zone plates with variable lacunarity,” Opt. Express12, 4227–4234 (2004). [CrossRef]
  6. D. Hai-Tao, W. Xin, and X. Ke-Shu, “Focusing properties of fractal zone plates with variable lacunarity: experimental studies based on liquid crystal on silicon,” Chinese Phys. Lett.22, 2851–2854 (2005). [CrossRef]
  7. W. D. Furlan, G. Saavedra, and J. A. Monsoriu, “White-light imaging with fractal zone plates,” Opt. Lett.32, 2109–2111 (2007). [CrossRef] [PubMed]
  8. X. Ge, Z. Wang, K. Gao, D. Wang, Z. Wu, J. Chen, Z. Pan, K. Zhang, Y. Hong, P. Zhu, and Z. Wu, “Use of fractal zone plates for transmission x-ray microscopy,” Anal. Bioanal. Chem.404, 1303–1309 (2012). [CrossRef] [PubMed]
  9. L. J. Janicijevic, “Diffraction characteristics of square zone plates,” J. Opt.13, 199–206 (1982). [CrossRef]
  10. J. Alda, J. M. Rico-García, F. J. Salgado-Remacha, and L. M. Sanchez-Brea, “Diffractive performance of square Fresnel zone plates,” Opt. Commun.282, 3402–3407 (2009). [CrossRef]
  11. A. Calatayud, V. Ferrando, F. Giménez, W. Furlan, G. Saavedra, and J. Monsoriu, “Fractal square zone plates,” Opt. Commun.286, 42–45 (2013). [CrossRef]
  12. 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 (London)414, 184–188 (2001). [CrossRef]
  13. Q. Cao and J. Jahns, “Focusing analysis of the pinhole photon sieve: individual far-field model,” J. Opt. Soc. Am. A19, 2387–2393 (2002). [CrossRef]
  14. C. Xie, X. Zhu, H. Li, L. Shi, and Y. Wang, “Feasibility study of hard-x-ray nanofocusing above 20 keV using compound photon sieves,” Opt. Lett.35, 4048–4050 (2010). [CrossRef] [PubMed]
  15. C. Xie, X. Zhu, H. Li, L. Shi, Y. Hua, and M. Liu, “Toward two-dimensional nanometer resolution hard X-ray differential-interference-contrast imaging using modified photon sieves,” Opt. Lett.37, 749–751 (2012). [CrossRef] [PubMed]
  16. G. Andersen, “Membrane photon sieve telescopes,” Appl. Phys.49, 63916394 (2010).
  17. F. Giménez, J. A. Monsoriu, W. D. Furlan, and A. Pons, “Fractal photon sieve,” Opt. Express14, 11958–11963 (2006), http://www.opticsinfobase.org/oe/abstract.cfm?uri=oe-14-25-11958 . [CrossRef] [PubMed]
  18. F. Giménez, W. D. Furlan, and J. A. Monsoriu, “Lacunar fractal photon sieves,” Opt. Commun.277, 1–4 (2007). [CrossRef]
  19. B. Zhang and D. Zhao, “Square Fresnel zone plate with spiral phase for generating zero axial irradiance,” Opt. Lett.35, 1488–1490 (2010). [CrossRef] [PubMed]
  20. F. J. González, J. Alda, B. Ilic, and G. D. Boreman, “Infrared antennas coupled to lithographic Fresnel zone plate lenses,” Appl. Opt.43, 6067–6073 (2004). [CrossRef] [PubMed]
  21. L. Kelemen, S. Valkai, and P. Ormos, “Parallel photopolymerisation with complex light patterns generated by diffractive optical elements,” Opt. Express15, 14488–14497 (2007), http://www.opticsinfobase.org/oe/abstract.cfm?uri=oe-15-22-14488 . [CrossRef] [PubMed]

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