Abstract

The reflectance of corrugated surfaces with a fractal distribution of grooves is investigated. Triadic and polyadic Cantor fractal distributions are considered, and the reflected intensity is compared with that of the corresponding periodic structure. The self-similarity property of the response is analyzed when varying the depth of the grooves and the lacunarity parameter. The results confirm that the response is self-similar for the whole range of depths considered, and this property is also maintained for all values of the lacunarity parameter.

© 2007 Optical Society of America

PDF Article

References

  • View by:
  • |
  • |

  1. R. Petit, "Diffraction gratings," C. r. hebd. Seanc. Acad. Sci., Paris,  260, 4454 (1965).
  2. R. C. Hollins and D. L. Jordan, "Measurments of 10.6 μm radiation scattered by a pseudo-random surface of rectangular grooves," Optica Acta,  30,1725-1734 (1983).
  3. J. R. Andrewartha, J. R. Fox and I. J. Wilson, "Resonance anomalies in the lamellar grating," Optica Acta,  26,69-89 (1977).
  4. A. Wirgin and A. A. Maradudin, "Resonant enhancement of the electric field in the grooves of bare metallic gratings exposed to S-polarized light," Phys. Rev. B,  31, 5573-5576 (1985).
    [CrossRef]
  5. E. G. Loewen, M. Nevière and D. Maystre, "Efficiency optimization of rectangular groove gratings for use in the visible and IR regions," Appl. Opt. 18,2262-2266 (1979).
  6. L. Li, "A modal analysis of lamellar diffraction gratings in conical mountings," J. Mod. Opt. 40,553-573 (1993).
  7. T. J. Park, H. J. Eom and K. Yoshitomi, "Analysis of TM scattering from finite rectangular grooves in a conducting plane," J. Opt. Soc. Am. A 10,905-911 (1993).
  8. D. Maystre, "Rigorous theory of light scattering from rough surfaces," J. Opt. 5,43-51 (1984).
  9. Y. L. Kok, "A boundary value solution to electromagnetic scattering by a rectangular groove in a ground plane," J. Opt. Soc. Am. A 9,302-311 (1992).
  10. T.-M. Wang and H. Ling, "A connection algorithm on the problem of EM scattering from arbitrary cavities," J. EM Waves and Applics. 5,301-314 (1991).
  11. R. A. Depine and D. C. Skigin, "Scattering from metallic surfaces having a finite number of rectangular grooves," J. Opt. Soc. Am. A 11,2844-2850 (1994).
  12. D. C. Skigin, V. V. Veremey and R. Mittra, "Superdirective radiation from finite gratings of rectangular grooves," IEEE Trans. Antennas Propag. 47,376-383 (1999).
    [CrossRef]
  13. A. N. Fantino, S. I. Grosz and D. C. Skigin, "Resonant effect in periodic gratings comprising a finite number of grooves in each period," Phys. Rev. E 64,016605 (2001).
    [CrossRef]
  14. S. I. Grosz, D. C. Skigin and A. N. Fantino, "Resonant effects in compound diffraction gratings: influence of the geometrical parameters of the surface," Phys. Rev. E 65,056619 (2002).
    [CrossRef]
  15. D. C. Skigin and R. A. Depine, "Diffraction by dual-period gratings," Appl. Opt. 46,1385-1391 (2007).
    [CrossRef]
  16. B. Mandelbrot, The Fractal Geometry of Nature, Freeman, San Francisco, 1982.
  17. Y. Sakurada, J. Uozumi, and T Asakura, "Fresnel diffraction by 1-D regular fractals," Pure Appl. Opt. 1,29-40 (1992).
    [CrossRef]
  18. 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).
  19. A. Lakhtakia, N. S. Holter, V. K. Varadan and V. V. Varadan, "Self-similarity in diffraction by a self-similar fractal screen," IEEE Transactions on Antennas and Propagation 35, 236-239 (1987).
    [CrossRef]
  20. 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]
  21. S. A. Ledesma, C. C. Iemmi and V. L. Brudny, "Scaling properties of the scattered field produced by fractal gratings," Opt. Commun. 144,292-298 (1997).
    [CrossRef]
  22. A. D. Jaggard and D. L. Jaggard, "Scattering from fractal superlattices with variable lacunarity," J. Opt. Soc. Am. A 15,1626-1635 (1998).
    [CrossRef]
  23. R. E. Plotnick, R. H. Gardner, W. W. Hargrove, K. Prestegaard, and M. Perlmutter, "Lacunarity analysis: A general technique for the analysis of spatial patterns," Phys. Rev. E 53,5461-5468 (1996).
    [CrossRef]
  24. 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]

2007

2006

2004

2002

S. I. Grosz, D. C. Skigin and A. N. Fantino, "Resonant effects in compound diffraction gratings: influence of the geometrical parameters of the surface," Phys. Rev. E 65,056619 (2002).
[CrossRef]

2001

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).

A. N. Fantino, S. I. Grosz and D. C. Skigin, "Resonant effect in periodic gratings comprising a finite number of grooves in each period," Phys. Rev. E 64,016605 (2001).
[CrossRef]

1999

D. C. Skigin, V. V. Veremey and R. Mittra, "Superdirective radiation from finite gratings of rectangular grooves," IEEE Trans. Antennas Propag. 47,376-383 (1999).
[CrossRef]

1998

1997

S. A. Ledesma, C. C. Iemmi and V. L. Brudny, "Scaling properties of the scattered field produced by fractal gratings," Opt. Commun. 144,292-298 (1997).
[CrossRef]

1996

R. E. Plotnick, R. H. Gardner, W. W. Hargrove, K. Prestegaard, and M. Perlmutter, "Lacunarity analysis: A general technique for the analysis of spatial patterns," Phys. Rev. E 53,5461-5468 (1996).
[CrossRef]

1994

1993

L. Li, "A modal analysis of lamellar diffraction gratings in conical mountings," J. Mod. Opt. 40,553-573 (1993).

T. J. Park, H. J. Eom and K. Yoshitomi, "Analysis of TM scattering from finite rectangular grooves in a conducting plane," J. Opt. Soc. Am. A 10,905-911 (1993).

1992

Y. L. Kok, "A boundary value solution to electromagnetic scattering by a rectangular groove in a ground plane," J. Opt. Soc. Am. A 9,302-311 (1992).

Y. Sakurada, J. Uozumi, and T Asakura, "Fresnel diffraction by 1-D regular fractals," Pure Appl. Opt. 1,29-40 (1992).
[CrossRef]

1991

T.-M. Wang and H. Ling, "A connection algorithm on the problem of EM scattering from arbitrary cavities," J. EM Waves and Applics. 5,301-314 (1991).

1987

A. Lakhtakia, N. S. Holter, V. K. Varadan and V. V. Varadan, "Self-similarity in diffraction by a self-similar fractal screen," IEEE Transactions on Antennas and Propagation 35, 236-239 (1987).
[CrossRef]

1985

A. Wirgin and A. A. Maradudin, "Resonant enhancement of the electric field in the grooves of bare metallic gratings exposed to S-polarized light," Phys. Rev. B,  31, 5573-5576 (1985).
[CrossRef]

1984

D. Maystre, "Rigorous theory of light scattering from rough surfaces," J. Opt. 5,43-51 (1984).

1983

R. C. Hollins and D. L. Jordan, "Measurments of 10.6 μm radiation scattered by a pseudo-random surface of rectangular grooves," Optica Acta,  30,1725-1734 (1983).

1979

1977

J. R. Andrewartha, J. R. Fox and I. J. Wilson, "Resonance anomalies in the lamellar grating," Optica Acta,  26,69-89 (1977).

1965

R. Petit, "Diffraction gratings," C. r. hebd. Seanc. Acad. Sci., Paris,  260, 4454 (1965).

Appl. Opt.

C. r. hebd. Seanc. Acad. Sci.

R. Petit, "Diffraction gratings," C. r. hebd. Seanc. Acad. Sci., Paris,  260, 4454 (1965).

IEEE Trans. Antennas Propag.

D. C. Skigin, V. V. Veremey and R. Mittra, "Superdirective radiation from finite gratings of rectangular grooves," IEEE Trans. Antennas Propag. 47,376-383 (1999).
[CrossRef]

IEEE Transactions on Antennas and Propagation

A. Lakhtakia, N. S. Holter, V. K. Varadan and V. V. Varadan, "Self-similarity in diffraction by a self-similar fractal screen," IEEE Transactions on Antennas and Propagation 35, 236-239 (1987).
[CrossRef]

J. EM Waves and Applics.

T.-M. Wang and H. Ling, "A connection algorithm on the problem of EM scattering from arbitrary cavities," J. EM Waves and Applics. 5,301-314 (1991).

J. Mod. Opt.

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).

L. Li, "A modal analysis of lamellar diffraction gratings in conical mountings," J. Mod. Opt. 40,553-573 (1993).

J. Opt.

D. Maystre, "Rigorous theory of light scattering from rough surfaces," J. Opt. 5,43-51 (1984).

J. Opt. Soc. Am. A

Opt. Commun.

S. A. Ledesma, C. C. Iemmi and V. L. Brudny, "Scaling properties of the scattered field produced by fractal gratings," Opt. Commun. 144,292-298 (1997).
[CrossRef]

Opt. Express

Optica Acta

R. C. Hollins and D. L. Jordan, "Measurments of 10.6 μm radiation scattered by a pseudo-random surface of rectangular grooves," Optica Acta,  30,1725-1734 (1983).

J. R. Andrewartha, J. R. Fox and I. J. Wilson, "Resonance anomalies in the lamellar grating," Optica Acta,  26,69-89 (1977).

Phys. Rev. B

A. Wirgin and A. A. Maradudin, "Resonant enhancement of the electric field in the grooves of bare metallic gratings exposed to S-polarized light," Phys. Rev. B,  31, 5573-5576 (1985).
[CrossRef]

Phys. Rev. E

A. N. Fantino, S. I. Grosz and D. C. Skigin, "Resonant effect in periodic gratings comprising a finite number of grooves in each period," Phys. Rev. E 64,016605 (2001).
[CrossRef]

S. I. Grosz, D. C. Skigin and A. N. Fantino, "Resonant effects in compound diffraction gratings: influence of the geometrical parameters of the surface," Phys. Rev. E 65,056619 (2002).
[CrossRef]

R. E. Plotnick, R. H. Gardner, W. W. Hargrove, K. Prestegaard, and M. Perlmutter, "Lacunarity analysis: A general technique for the analysis of spatial patterns," Phys. Rev. E 53,5461-5468 (1996).
[CrossRef]

Pure Appl. Opt.

Y. Sakurada, J. Uozumi, and T Asakura, "Fresnel diffraction by 1-D regular fractals," Pure Appl. Opt. 1,29-40 (1992).
[CrossRef]

Other

B. Mandelbrot, The Fractal Geometry of Nature, Freeman, San Francisco, 1982.

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Metrics