Diffraction by Cantor fractal zone plates

Thumbnail Image
Full text at PDC
Publication Date
Rodrigo Martín-Romo, José Augusto
Alieva, Tatiana Krasheninnikova
Davis, Jeffrey A.
Advisors (or tutors)
Journal Title
Journal ISSN
Volume Title
Taylor and Francis Ltd.
Google Scholar
Research Projects
Organizational Units
Journal Issue
The paper reports studies, both experimental and using numerical simulation, of the Fresnel diffraction by recently introduced fractal zone plates associated with triadic and quintic Cantor sets. The evolution of the intensity patterns at planes transversal to the propagation direction is presented. A series of conventional and doughnut-like foci are observed around the principal focus. The position, depth and size of the foci depend on similarity dimensions and the fractal level of the encoded fractal structures, both directly related to the number of the corresponding Fresnel zones.
© 2005 Taylor & Francis. Research supported by projects TIC2002-1846 and TIC2002-11581-E Ministerio de Educación y Ciencia, Spain. T. Alieva acknowledges receipt of a ‘‘Ramón y Cajal’’ grant from Ministerio de Educación y Ciencia, Spain. The authors acknowledge the technical support of Hamamatsu (R. Díaz) in providing the CCD camera for these experiments.
1. Mandelbrot, BB. 1982. The Fractal Geometry of Nature, San Francisco, CA: Freeman. 2. Berry, MV. 1979. J. Phys. A: Math. Gen., 12: 781. 3. Allian, C and Cloitre, M. 1986. Phys. Rev. B, 33: 3563. 4. Uozumi, J and Asakura, T. 1994. Current Trends in Optics, Edited by: Dainty, JC. 83–94. Cambridge, MA: Academic Press. 5. Jaggard, DL and Sun, X. 1990. J. Opt. Soc. A., 7: 1131. 6. Sakurada, Y, Uozumi, J and Asakura, T. 1994. Pure Appl. Opt., 3: 371. 7. Alieva, T and Agullo-Lopez, F. 1996. Opt. Commun., 125: 267. 8. Lehman, M. 2001. Opt. Commun., 195: 11. 9. Rodriguez Merlo, D, Rodrigo Martín-Romo, JA, Alieva, T and Calvo, ML. 2003. Opt. Spectrosc., 95: 131. 10. Alieva, T and Calvo, ML. 2003. J. Opt. A: Pure. Appl. Opt., 5: S324. 11. Zunino, L and Garavaglia, M. 2003. J. Mod. Opt., 50: 717. 12. Karman, GP and Woerdman, JP. 2001. Opt. Lett., 23: 1909. 13. Berry, MV and Klein, S. 1996. J. Mod. Opt., 43: 2139. 14. Calva Méndez, D and Lehman, M. 2002. SPIE Proc., 4829: 309. 15. Saavedra, G, Furlan, WD and Monsoriu, JA. 2003. Opt. Lett., 28: 971. 16. Monsoriu, JA, Saavedra, G and Furlan, WD. 2004. Opt. Express, 12: 4227. 17. Davis, JA, Ramirez, L, Rodrigo, JA, Alieva, T and Calvo, ML. 2004. Opt. Lett., 29: 1321. 18. Rodrigo, JA, Alieva, T, Calvo, ML and Davis, JA. 2004. “Integrated Optical Devices, Nanostructures, and Displays”. In Proc. SPIE Edited by: Lewis, KL. Vol. 5622, 1474Venezuela. 19. Calvo, ML, Rodrigo, J and Alieva, T. Proc. ICO-20. Proc. SPIE on CD-ROM, Vol. 6027 (paper 0403-028). 20. Peitgen, H, Jürgens, H and Saupe, D. 1992. Chaos and Fractals, 205New York: Springer. 21. Ojeda-Catañeda, J and Gómez-Reino, C, eds. 1996. Selected Papers on Zone Plates, Washington: SPIE Optical Engineering Press. 22. Mendlovic, D, Zalevsky, Z and Konforti, N. 1997. J. Mod. Opt., 44: 407. 23. Mas, D, Garcia, J, Ferreira, C, Bernardo, LM and Marinho, F. 1999. Opt. Commun., 164: 233 .