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Optics Express

Optics Express

  • Editor: C. Martijn de Sterke
  • Vol. 15, Iss. 21 — Oct. 17, 2007
  • pp: 13858–13864

Devil’s lenses

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

Optics Express, Vol. 15, Issue 21, pp. 13858-13864 (2007)

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In this paper we present a new kind of kinoform lenses in which the phase distribution is characterized by the “devil’s staircase” function. The focusing properties of these fractal DOEs coined devil’s lenses (DLs) are analytically studied and compared with conventional Fresnel kinoform lenses. It is shown that under monochromatic illumination a DL give rise a single fractal focus that axially replicates the self-similarity of the lens. Under broadband illumination the superposition of the different monochromatic foci produces an increase in the depth of focus and also a strong reduction in the chromaticity variation along the optical axis.

© 2007 Optical Society of America

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

ToC Category:
Fiber Optics and Optical Communications

Original Manuscript: June 13, 2007
Revised Manuscript: September 13, 2007
Manuscript Accepted: September 17, 2007
Published: October 5, 2007

Juan A. Monsoriu, Walter D. Furlan, Genaro Saavedra, and Fernando Giménez, "Devil’s lenses," Opt. Express 15, 13858-13864 (2007)

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  1. J. Courtial and M. J. Padgett, "Monitor-outside-a-monitor effect and self-similar fractal structure in the eigenmodes of unstable optical resonators," Phys. Rev. Lett. 85, 5320-5323 (2000). [CrossRef]
  2. O. Trabocchi, S. Granieri, and W. D. Furlan, "Optical propagation of fractal fields. Experimental analysis in a single display," J. Mod. Opt. 48, 1247-1253 (2001).
  3. M. Lehman, "Fractal diffraction gratings built through rectangular domains," Opt. Commun. 195, 11-26 (2001). [CrossRef]
  4. J. G. Huang, J. M. Christian, and G. S. McDonald "Fresnel diffraction and fractal patterns from polygonal apertures," J. Opt. Soc. Am. A 23, 2768-2774 (2006). [CrossRef]
  5. G. Saavedra, W. D. Furlan, and J. A. Monsoriu, "Fractal zone plates," Opt. Lett. 28, 971-973 (2003). [CrossRef] [PubMed]
  6. J.A. Monsoriu, G. Saavedra, and W.D. Furlan, "Fractal zone plates with variable lacunarity," Opt. Express 12, 4227-4234 (2004). http://www.opticsinfobase.org/abstract.cfm?URI=oe-12-18-4227> [CrossRef] [PubMed]
  7. 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]
  8. H.-T. Dai, X. Wang, K.-S. Xu, "Focusing properties of fractal zone plates with variable lacunarity: experimental studies based on liquid crystal on silicon," Chin. Phys. Lett. 22, 2851-2854 (2005). [CrossRef]
  9. S. H. Tao, X.-C. Yuan, J. Lin, and R. Burge, "Sequence of focused optical vortices generated by a spiral fractal zone plates," Appl. Phys. Lett. 89, 031105 (2006). [CrossRef]
  10. C. Martelli and J. Canning, "Fresnel Fibres with Omnidirectional Zone Cross-sections," Opt. Express 15, 4281-4286 (2007). [CrossRef] [PubMed]
  11. F. Giménez, J. A. Monsoriu, W. D. Furlan, and A. Pons, "Fractal Photon Sieves," Opt. Express 14, 11958-11963 (2006). http://www.opticsinfobase.org/abstract.cfm?URI=oe-14-25-11958> [CrossRef] [PubMed]
  12. J. A. Jordan, P. M. Hirsch, L. B. Lesem, and D. L. Van Rooy, "Kinoform lenses," Appl. Opt. 9, 1883-1887 (1970) [PubMed]
  13. D. R. Chalice, "A characterizationof the Cantor function," Amer. Math. Monthly 98, 255-258 (1991). [CrossRef]
  14. F. Doveil, A. Macor, and Y. Elskens, "Direct observation of a devil’s staircase in wave-particle interaction," Chaos 16, 033130 (2006). [CrossRef]
  15. M. Hupalo, J. Schamalian, and M. C. Tringides, "Devil’s staircase in Pb/Si(111) ordered phases," Phys. Rev. Lett. 90, 216106 (2003). [CrossRef] [PubMed]
  16. Y. F. Chen, T. H. Lu, K. W. Su, and K. F. Huang, "Devil’s staircase in three-dimensional coherent waves localized on Lissajous parametric surfaces," Phys. Rev. Lett. 96, 213902 (2006). [CrossRef] [PubMed]
  17. Y. Han, L. N. Hazra, and C. A. Delisle, "Exact surface-relief profile of a kinoform lens from its phase function," J. Opt. Soc. Am. A 12, 524-529 (1995). [CrossRef]
  18. M. J. Yzuel and J. Santamaria, "Polychromatic Optical Image. Diffraction limited system and Influence of the Longitudinal Chromatic Aberration," Opt. Acta 22, 673-690 (1975). [CrossRef]

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