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Optics Express

Optics Express

  • Editor: Michael Duncan
  • Vol. 12, Iss. 18 — Sep. 6, 2004
  • pp: 4227–4234

Fractal zone plates with variable lacunarity

Juan A. Monsoriu, Genaro Saavedra, and Walter D. Furlan  »View Author Affiliations

Optics Express, Vol. 12, Issue 18, pp. 4227-4234 (2004)

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Fractal zone plates (FZPs), i.e., zone plates with fractal structure, have been recently introduced in optics. These zone plates are distinguished by the fractal focusing structure they provide along the optical axis. In this paper we study the effects on this axial response of an important descriptor of fractals: the lacunarity. It is shown that this parameter drastically affects the profile of the irradiance response along the optical axis. In spite of this fact, the axial behavior always has the self-similarity characteristics of the FZP itself.

© 2004 Optical Society of America

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

ToC Category:
Research Papers

Original Manuscript: August 4, 2004
Revised Manuscript: August 24, 2004
Published: September 6, 2004

Juan Monsoriu, Genaro Saavedra, and Walter Furlan, "Fractal zone plates with variable lacunarity," Opt. Express 12, 4227-4234 (2004)

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  1. J. Ojeda-Castañeda and C. Gómez-Reino, Eds., Selected papers on zone plates (SPIE Optical Engineering Press, Washington, 1996).
  2. S. Wang, X. Zhang, �??Terahertz tomographic imaging with a Fresnel lens,�?? Opt. Photon. News 13, 59 (2002). [CrossRef]
  3. Y Wang, W. Yun, and C. Jacobsen, �??Achromatic Fresnel optics for wideband extreme-ultraviolet and X-ray imaging,�?? Nature 424, 50-53 (2003). [CrossRef] [PubMed]
  4. 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 414, 184-188 (2001). [CrossRef] [PubMed]
  5. Q. Cao and J. Jahns, �??Modified Fresnel zone plates that produce sharp Gaussian focal spots,�?? J. Opt. Soc. Am. A 20, 1576-1581 (2003). [CrossRef]
  6. Q. Cao and J. Jahns, �??Comprehensive focusing analysis of various Fresnel zone plates,�?? J. Opt. Soc. Am. A 21, 561-571 (2004). [CrossRef]
  7. G. Saavedra, W.D. Furlan, and J.A. Monsoriu, �??Fractal zone plates,�?? Opt. Lett. 28, 971-973 (2003). [CrossRef] [PubMed]
  8. W.D. Furlan, G. Saavedra, and J.A. Monsoriu, �??Fractal zone plates produce axial irradiance with fractal profile,�?? Opt.& Photon. News 28, 971-973 (2003).
  9. 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]
  10. B. Mandelbrot, The Fractal Geometry of Nature (Freeman, San Francisco, 1982).
  11. A.D. Jaggard and D.L. Jaggard, �??Cantor ring diffractals,�?? Opt. Commun. 158, 141�??148 (1998). [CrossRef]
  12. L. Zunino and M. Garavaglia, �??Fraunhofer diffraction by Cantor fractals with variable lacunarity,�?? J. Mod. Opt. 50, 717-727 (2003). [CrossRef]
  13. Y. Sakurada, J. Uozumi, and T Asakura, �??Fresnel diffraction by 1-D regular fractals,�?? Pure Appl. Opt. 1, 29�??40 (1992). [CrossRef]
  14. H. Melville and G. F. Milne, �??Optical trapping of three-dimensional structures using dynamic holograms,�?? Opt. Express 11, 3562-3567 (2003) <a href="http://www.opticsexpress.org/abstract.cfm?URI=OPEX-11-26-3562">http://www.opticsexpress.org/abstract.cfm?URI=OPEX-11-26-3562</a>. [CrossRef] [PubMed]

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