OSA's Digital Library

Journal of the Optical Society of America A

Journal of the Optical Society of America A

| OPTICS, IMAGE SCIENCE, AND VISION

  • Vol. 18, Iss. 5 — May. 1, 2001
  • pp: 1101–1111

Electromagnetic wave scattering from conducting self-affine surfaces: an analytic and numerical study

Ingve Simonsen, Damien Vandembroucq, and Stéphane Roux  »View Author Affiliations


JOSA A, Vol. 18, Issue 5, pp. 1101-1111 (2001)
http://dx.doi.org/10.1364/JOSAA.18.001101


View Full Text Article

Enhanced HTML    Acrobat PDF (279 KB)





Browse Journals / Lookup Meetings

Browse by Journal and Year


   


Lookup Conference Papers

Close Browse Journals / Lookup Meetings

Article Tools

Share
Citations

Abstract

We derive an analytical expression for the scattering of an s-polarized plane wave from a perfectly conducting self-affine one-dimensional surface in the framework of the Kirchhoff approximation. We show that most of the results can be recovered by means of a scaling analysis. We identify the typical slope taken over one wavelength as the relevant parameter controlling the scattering process. We compare our predictions with direct numerical simulations performed on surfaces of varying roughness parameters and confirm the broad range of applicability of our description up to very large roughness. Finally we verify that a nonzero electrical resistivity, provided that it is small, does not invalidate our results.

© 2001 Optical Society of America

OCIS Codes
(240.5770) Optics at surfaces : Roughness
(290.5880) Scattering : Scattering, rough surfaces

History
Original Manuscript: May 26, 2000
Revised Manuscript: October 19, 2000
Manuscript Accepted: September 20, 2000
Published: May 1, 2001

Citation
Ingve Simonsen, Damien Vandembroucq, and Stéphane Roux, "Electromagnetic wave scattering from conducting self-affine surfaces: an analytic and numerical study," J. Opt. Soc. Am. A 18, 1101-1111 (2001)
http://www.opticsinfobase.org/josaa/abstract.cfm?URI=josaa-18-5-1101


Sort:  Author  |  Year  |  Journal  |  Reset  

References

  1. J. W. S. Rayleigh, The Theory of Sound (Dover, New York, 1945).
  2. M. Nieto-Vesperinas, J. M. Soto-Crespo, “Monte Carlo simulations for scattering of electromagnetic waves from perfectly conductive random rough surfaces,” Opt. Lett. 12, 979–981 (1987). [CrossRef] [PubMed]
  3. E. R. Méndez, K. A. O’Donnell, “Observation of depolarization and backscattering enhancement in light scattering from Gaussian random rough surfaces,” Opt. Commun. 61, 91–95 (1987). [CrossRef]
  4. A. A. Maradudin, E. R. Méndez, T. Michel, “Backscattering effects in the elastic scattering of p-polarized light from a large-amplitude random metallic grating,” Opt. Lett. 14, 151–153 (1989). [CrossRef] [PubMed]
  5. J. A. Sanchez-Gil, “Coupling, resonance transmission, and tunneling of surface-plasmon polaritons through metallic gratings of finite length,” Phys. Rev. B 53, 10317–10327 (1996). [CrossRef]
  6. S. C. Kitson, W. L. Barnes, J. L. Sambles, “Full photonic band gap for surface modes in the visible,” Phys. Rev. Lett. 77, 2670–2673 (1996). [CrossRef] [PubMed]
  7. F. Pincemin, J. J. Greffet, “Propagation and localization of a surface plasmon polariton on a finite grating,” J. Opt. Soc. Am. B 13, 1499–1509 (1996). [CrossRef]
  8. J. A. Sanchez-Gil, A. A. Maradudin, “Competition between Anderson localization and leakage of surface-plasmon polaritons on randomly rough periodic metal surfaces,” Phys. Rev. B 56, 1103–1106 (1997). [CrossRef]
  9. C. S. West, K. A. O’Donnell, “Observation of backscattering enhancement from polaritons on a rough metal surface,” J. Opt. Soc. Am. A 12, 390–397 (1995). [CrossRef]
  10. A. Sentenac, J. J. Greffet, “Mean-field theory of light scattering by one-dimensional rough surfaces,” J. Opt. Soc. Am. A 15, 528–532 (1998). [CrossRef]
  11. S. L. Broschat, E. I. Thorsos, “An investigation of the small slope approximation for scattering from rough surfaces. i: theory,” J. Acoust. Soc. Am. 97, 2082–2093 (1995). [CrossRef]
  12. J. A. Ogilvy, Theory of Wave Scattering from Random Rough Surfaces (IOP, Bristol, UK, 1991).
  13. P. Beckmann, A. Spizzichino, The Scattering of Electromagnetic Waves from Rough Surfaces (Artech House, Norwood, Mass., 1963).
  14. B. B. Mandelbrot, The Fractal Geometry of Nature (Freeman, New York, 1975).
  15. E. Bouchaud, “Scaling properties of cracks,” J. Phys. Condens. Matter 9, 4319–4344 (1997). [CrossRef]
  16. P. Meakin, Fractals, Scaling and Growth Far from Equilibrium (Cambridge U. Press, Cambridge, UK, 1998).
  17. F. Plouraboué, M. Boehm, “Multi-scale roughness transfer in cold metal rolling,” Tribol. Int. 32, 45–57 (1999). [CrossRef]
  18. M. V. Berry, “Diffractals,” J. Phys. A 12, 781–797 (1979). [CrossRef]
  19. D. L. Jaggard, X. Sun, “Fractal surface scattering: a generalized Rayleigh solution,” J. Appl. Phys. 68(11), 5456–5462 (1990). [CrossRef]
  20. M. K. Shepard, R. A. Brackett, R. E. Arvidson, “Self-affine (fractal) topography: surface parametrization and radar scattering,” J. Geophys. Res. 100, E6, 11709–11718 (1995). [CrossRef]
  21. P. E. McSharry, P. J. Cullen, D. Moroney, “Wave scattering by a two-dimensional band limited fractal surface based on a perturbation of the Green’s function,” J. Appl. Phys. 78(12), 6940–6948 (1995). [CrossRef]
  22. N. Lin, H. P. Lee, S. P. Lim, K. S. Lee, “Wave scattering from fractal surfaces,” J. Mod. Opt. 42, 225–235 (1995). [CrossRef]
  23. J. Chen, T. K. Y. Lo, H. Leung, J. Litva, “The use of fractals for modeling EM waves scattering from rough sea surface,” IEEE Trans. Geosci. 34(4), 966–972 (1996). [CrossRef]
  24. C. J. R. Sheppard, “Scattering by fractal surfaces with an outer-scale,” Opt. Commun. 122, 178–188 (1996). [CrossRef]
  25. J. A. Sánchez-Gil, J. V. Garcı́a-Ramos, “Far field intensity of electromagnetic waves scattered from random, self-affine fractal metal surfaces,” Waves Random Media 7, 285–293 (1997). [CrossRef]
  26. J. A. Sánchez-Gil, J. V. Garcı́a-Ramos, “Calculations of the direct electromagnetic enhancement in surface enhanced raman scattering on random self-affine fractal metal surfaces,” J. Chem. Phys. 108, 1317–1325 (1998).
  27. Y-P Zhao, C. F. Cheng, G. C. Wang, T. M. Lu, “Power law behavior in diffraction from fractal surfaces,” Surf. Sci. 409, L703–L708 (1998). [CrossRef]
  28. E. Jakeman, “Scattering by fractals” in Fractals in Physics, L. Pietronero, E. Tossati, eds. (Elsevier, Amsterdam, 1986), pp. 55–60.
  29. D. L. Jordan, R. C. Hollins, E. Jakeman, A. Prewett, “Visible and infra-red scattering from well-characterized surfaces,” Surf. Topog. 1, 27–36 (1988).
  30. H. N. Yang, T. M. Lu, G. C. Wang, “Diffraction from surface growth fronts,” Phys. Rev. B 47, 3911–3922 (1993). [CrossRef]
  31. Y. P. Zhao, G. C. Wang, T. M. Lu, “Diffraction from non-Gaussian rough surfaces,” Phys. Rev. B 55, 13938–13952 (1997). [CrossRef]
  32. Y. P. Zhao, I. Wu, C. F. Cheng, U. Block, G. C. Wang, T. M. Lu, “Characterization of random rough surfaces by in-plane light scattering,” J. Appl. Phys. 84, 2571–2582 (1998). [CrossRef]
  33. I. Simonsen, D. Vandembroucq, S. Roux, “Wave scattering from self-affine surfaces,” Phys. Rev. E 61, 5914–5917 (2000). [CrossRef]
  34. J. Schmittbuhl, J. P. Vilotte, S. Roux, “Reliability of self-affine measurements,” Phys. Rev. E 51, 131–147 (1995). [CrossRef]
  35. I. Simonsen, A. Hansen, O. M. Nes, “Determination of Hurst exponents by use of the wavelet transform,” Phys. Rev. E 58, 2779–2787 (1998). [CrossRef]
  36. A. A. Maradudin, T. Michel, A. R. McGurn, E. R. Méndez, “Enhanced backscattering of light from a random grating,” Ann. Phys. (New York) 203, 255–307 (1990). [CrossRef]
  37. P. Lévy, Théorie de l’Addition des Variables Aléatoires (Gauthier-Villars, Paris, 1937).
  38. B. V. Gnedenko, A. N. Kolmogorov, Limit Distributions for Sum of Independent Random Variables (Addison Wesley, Reading, Mass., 1954).
  39. E. I. Thorsos, “The validity of the Kirchhoff approximation for rough surface scattering using a Gaussian roughness spectrum,” J. Acoust. Soc. Am. 83, 78–82 (1988). [CrossRef]
  40. E. I. Thorsos, D. R. Jackson, “Studies of scattering theory using numerical methods,” Waves Random Media 3, S165–S190 (1991). [CrossRef]
  41. M. Abramowitz, I. A. Stegun, Handbook of Mathematical Functions (Dover, New York, 1964).
  42. W. H. Press, S. A. Teukolsky, W. T. Vetterling, B. P. Flannery, Numerical Recipes, 2nd ed. (Cambridge U. Press, Cambridge, UK, 1992).
  43. J. Feder, Fractals (Plenum, New York, 1988).
  44. E. D. Palik, Handbook of Optical Constants of Solids (Academic, New York, 1985).

Cited By

Alert me when this paper is cited

OSA is able to provide readers links to articles that cite this paper by participating in CrossRef's Cited-By Linking service. CrossRef includes content from more than 3000 publishers and societies. In addition to listing OSA journal articles that cite this paper, citing articles from other participating publishers will also be listed.


« Previous Article  |  Next Article »

OSA is a member of CrossRef.

CrossCheck Deposited