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Optics Express

Optics Express

  • Editor: Andrew M. Weiner
  • Vol. 21, Iss. 7 — Apr. 8, 2013
  • pp: 7951–7956

Robustness of Cantor Diffractals

Rupesh Verma, Manoj Kumar Sharma, Varsha Banerjee, and Paramasivam Senthilkumaran  »View Author Affiliations

Optics Express, Vol. 21, Issue 7, pp. 7951-7956 (2013)

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Diffractals are electromagnetic waves diffracted by a fractal aperture. In an earlier paper, we reported an important property of Cantor diffractals, that of redundancy [R. Verma et. al., Opt. Express 20, 8250 (2012)]. In this paper, we report another important property, that of robustness. The question we address is: How much disorder in the Cantor grating can be accommodated by diffractals to continue to yield faithfully its fractal dimension and generator? This answer is of consequence in a number of physical problems involving fractal architecture.

© 2013 OSA

OCIS Codes
(050.0050) Diffraction and gratings : Diffraction and gratings
(050.1220) Diffraction and gratings : Apertures
(290.5880) Scattering : Scattering, rough surfaces

ToC Category:
Diffraction and Gratings

Original Manuscript: January 31, 2013
Revised Manuscript: March 12, 2013
Manuscript Accepted: March 14, 2013
Published: March 26, 2013

Rupesh Verma, Manoj Kumar Sharma, Varsha Banerjee, and Paramasivam Senthilkumaran, "Robustness of Cantor Diffractals," Opt. Express 21, 7951-7956 (2013)

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  1. R. Verma, V. Banerjee, and P. Senthilkumaran, “Redundancy in cantor diffractals,” Opt. Express20, 8250–8255 (2012). [CrossRef] [PubMed]
  2. B. B. Mandelbrot, The Fractal Geometry of Nature (W. H. Freeman, 1982).
  3. A. L. Barabasi and H. E. Stanley, Fractal Concepts in Surface Growth (Cambridge University, 1995). [CrossRef]
  4. Tamas Vicsek, Fractal Growth Phenomena (World Scientific, 1992). [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. Express12, 4227–4234 (2004). [CrossRef] [PubMed]
  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. F. Gimenez, J. A. Monsoriu, W. D. Furlan, and Amparo Pons, “Fractal photon sieve,” Opt. Express14, 11958–11963 (2006). [CrossRef] [PubMed]
  9. J. A. Monsoriu, C. J. Z. Rodriguez, and W. D. Furlan, “Fractal axicons,” Opt. Commun.263, 1–5 (2006). [CrossRef]
  10. K. Jarrendahl, M. Dulea, J. Birch, and J.-E. Sundgren, “X-ray diffraction from amorphous Ge/Si Cantor superlattices,” Phys. Rev. B51, 7621–7631 (1995). [CrossRef]
  11. A. D. Jaggard and D. L. Jaggard, “Scattering from fractal superlattices with variable lacunarity,” J. Opt. Soc. Am. A15, 1626–1635 (1998). [CrossRef]
  12. H. Aubert and D. L. Jaggard, “Wavelet analysis of transients in fractal superlattices,” IEEE Trans. Antennas Propag.50, 338–345 (2002). [CrossRef]
  13. G. H. C. New, M. A. Yates, J. P. Woerdman, and G. S. McDonald, “Diffractive origin of fractal resonator modes,” Opt. Commun.193, 261–266 (2001). [CrossRef]
  14. M. Berry, C. Storm, and W. van Saarloos, “Theory of unstable laser modes: edge waves and fractality,” Opt. Commun.197, 393–402 (2001). [CrossRef]
  15. M. V. Berry, “Diffractals,” J. Phys. A: Math. Gen.12, 781–797 (1979). [CrossRef]
  16. D. Bak, S. P. Kim, S. K. Kim, K. -S. Soh, and J. H. Yee, “Fractal diffraction grating,” 1–7 http://arxiv.org/abs/physics/9802007 .
  17. B. Hou, G. Xu, W. Wen, and G. K. L. Wong, “Diffraction by an optical fractal grating,” Appl. Phys. Lett.85, 6125–6127 (2004). [CrossRef]
  18. C. Allain and M. Cloitre, “Spatial spectrum of a general family of self-similar arrays,” Phys. Rev. A36, 5751–5757 (1987). [CrossRef] [PubMed]
  19. D. A. Hamburger-Lidar, “Elastic scattering by deterministic and random fractals: Self-affinity of the diffraction spectrum,” Phys. Rev. E54, 354–370 (1996). [CrossRef]
  20. C. Guerin and M. Holschneider, “Scattering on fractal measures,” J. Phys. A29, 7651–7667 (1996). [CrossRef]
  21. M. Lehman, “Fractal diffraction grating built through rectangular domains,” Opt. Commun.195, 11–26 (2001). [CrossRef]
  22. C. Allain and M. Cloitre, “Optical diffraction on fractals,” Phys. Rev. B33, 3566–3569 (1986). [CrossRef]
  23. B. Dubuc, J. F. Quiniou, C. R. Carmes, C. Tricot, and S. W. Zucker, “Evaluating the fractal dimensions of profiles,” Phys. Rev. A39, 1500–1512 (1989). [CrossRef] [PubMed]
  24. J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, 1996).

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