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Journal of the Optical Society of America A

Journal of the Optical Society of America A


  • Vol. 21, Iss. 7 — Jul. 1, 2004
  • pp: 1251–1260

Second-order perturbation theory for scattering from heterogeneous rough surfaces

Charles-Antoine Guérin and Anne Sentenac  »View Author Affiliations

JOSA A, Vol. 21, Issue 7, pp. 1251-1260 (2004)

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We propose a model to calculate scattering from inhomogeneous three-dimensional, rough surfaces on top of a stratified medium. The roughness is made up of an ensemble of deposits with various shapes and permittivities whose heights remain small with respect to the wavelength of the incident light. This geometry is encountered in the remote sensing of soil surfaces, or in optics wherever there are contaminated planar components. Starting from a volume-integral equation involving the Green’s tensor of the stratified medium, we derive a height-perturbative expansion up to second order. Our formulation, which depends explicitly on the profiles of each deposit and on the Fresnel coefficients of the layered substrate, accounts for double-scattering events and permits an evaluation of depolarization in the plane of incidence. Comparisons with rigorous calculations in the simplified case of two-dimensional geometries are presented. It is shown that the second-order scattering term can be much more important for heterogeneous surfaces than for their homogeneous counterparts.

© 2004 Optical Society of America

OCIS Codes
(290.5880) Scattering : Scattering, rough surfaces

Original Manuscript: October 16, 2003
Revised Manuscript: February 20, 2004
Manuscript Accepted: February 20, 2004
Published: July 1, 2004

Charles-Antoine Guérin and Anne Sentenac, "Second-order perturbation theory for scattering from heterogeneous rough surfaces," J. Opt. Soc. Am. A 21, 1251-1260 (2004)

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  1. M. Saillard, A. Sentenac, “Rigorous solutions for electromagnetic scattering from rough surfaces,” Waves Random Media 11, R103–R137 (2001). [CrossRef]
  2. A. G. Voronovich, Wave Scattering from Rough Surfaces, Springer Series on Wave Phenomena (Springer, New York, 1994).
  3. T. Tsang, J. A. Kong, R. Shin, Theory of Microwave Remote Sensing (Wiley, New York, 1985).
  4. Rayleigh, The Theory of Sound, 3rd ed. (MacMillan, London, 1896).
  5. U. Fano, “The theory of anomalous diffraction gratings and of quasi-stationary waves on metallic surfaces (Sommerfeld’s waves),” J. Opt. Soc. Am. 31, 213–222 (1941). [CrossRef]
  6. S. O. Rice, “Reflection of electromagnetic waves from slightly rough surfaces.” Commun. Pure Appl. Math. 4, 351–378 (1951). [CrossRef]
  7. M. F. Chen, A. K. Fung, “A numerical study of the regions of validity of the Kirchhoff and small-perturbation rough surface scattering models,” Radio Sci. 23, 163–170 (1988). [CrossRef]
  8. J. M. Soto-Crespo, M. Nieto-Vesperinas, A. T. Friberg, “Scattering from slightly rough random surfaces: a detailed study on the validity of the small perturbation method,” J. Opt. Soc. Am. 7, 1185–1201 (1990). [CrossRef]
  9. J. A. Sanchez, A. A. Maradudin, E. R. Mendez, “Limits of validity of three perturbation theories of the specular scattering of light from one-dimensional, randomly rough, dielectric surfaces.” J. Opt. Soc. Am. 12, 1547–1557 (1995). [CrossRef]
  10. D. P. Winebrenner, A. Ishimaru, “Application of the phase perturbation technique to randomly rough surface,” J. Opt. Soc. Am. A 2, 2285–2294 (1985). [CrossRef]
  11. D. M. Milder, “An improved formalism for wave scattering from rough surfaces,” J. Acoust. Soc. Am. 89, 529–541 (1991). [CrossRef]
  12. S. Smith, “The operator expansion formalism for electromagnetic scattering from rough dielectric surfaces,” Radio Sci. 31, 1377–1385 (1996). [CrossRef]
  13. A. G. Voronovich, “Small-slope approximation for electromagnetic wave scattering at a rough interface of two dielectric half-spaces,” Waves Random Media 4, 337–367 (1994). [CrossRef]
  14. O. P. Bruno, F. Reitich, “Numerical solution of diffraction problems: a method of variation of boundaries,” J. Opt. Soc. Am. A 10, 1168–1175 (1993). [CrossRef]
  15. O. P. Bruno, F. Reitich, “Numerical solution of diffraction problems: a method of variation of boundaries. II. Finitely conducting gratings, Padé approximants, and singularities,” J. Opt. Soc. Am. A 10, 2307–2316 (1993). [CrossRef]
  16. O. P. Bruno, F. Reitich, “Numerical solution of diffraction problems: a method of variation of boundaries. III. Doubly periodic gratings,” J. Opt. Soc. Am. A 10, 2551–2562 (1993). [CrossRef]
  17. K. Sarabandi, O. Yisok, F. Ulaby, “A numerical simulation of scattering from one-dimensional, inhomogeneous, dielectric, random surfaces,” IEEE Trans. Geosci. Remote Sens. 34, 425–432 (1996). [CrossRef]
  18. L. Sung, G. Mulholland, T. Germer, “Polarized light-scattering measurements of dielectric spheres upon a silicon surface,” Opt. Lett. 24, 866–868 (1999). [CrossRef]
  19. R. Carminati, J.-J. Greffet, “Influence of dielectric contrast and topography on the near-field scattered by an inhomogeneous surface,” J. Opt. Soc. Am. A 12, 2716–2725 (1995). [CrossRef]
  20. S. Linden, J. Kuhl, H. Giessen, “Controlling the interaction between light and gold nanoparticles with selective suppression of extinction,” Phys. Rev. B 86, 4688–4691 (2001).
  21. L. J. Lévesque, B. E. Paton, “Detection of defects in multiple layer structures by using surface plasmon resonance,” Atmos. Ocean. 36, 7199–7203 (1997).
  22. I. Ohlidal, K. Navratil, “Scattering of light from multilayer systems with rough boundary,” Prog. Opt. 34, 251–334 (1995).
  23. H. Giovannini, M. Saillard, A. Sentenac, “Numerical study of scattering from rough inhomogeneous films,” J. Opt. Soc. Am. A 15, 1182–1191 (1998). [CrossRef]
  24. A. Sentenac, J.-J. Greffet, “Scattering by 2D particles deposited on a dielectric planar waveguide, a near-field and far-field study,” Waves Random Media 5, 145–155 (1995). [CrossRef]
  25. L. Li, “New formulation of the Fourier modal method for crossed surface-relief gratings,” J. Opt. Soc. Am. A 14, 2758–2767 (1997). [CrossRef]
  26. P. Chaumet, A. Rahmani, F. de Fornel, J. P. Dufour, “Evanescent light scattering: the validity of the dipole approximation,” Phys. Rev. B 58, 2310 (1998). [CrossRef]
  27. “Computational wave issues in remote sensing, imaging and target identification, propagation, and inverse scattering,” special issue, IEEE Trans. Geosci. Remote Sens. 38, (2000).
  28. A. Soubret, G. Berginc, C. Bourrely, “A new application of reduced Rayleigh equations to electromagnetic wave scattering by two-dimensional, randomly rough surfaces,” Phys. Rev. B 63, 245411 (2001). [CrossRef]
  29. P. Dinesen, J. Hesthaven, “Fast and accurate modeling of waveguide grating couplers, three-dimensional vectorial case,” J. Opt. Soc. Am. A 18, 2876–2885 (2001). [CrossRef]
  30. N. Zhuk, “Scattering of em waves from a slightly rough surface of a generally anisotropic plane-layered half space,” IEEE Trans. Antennas Propag. 45, 1774–1782 (1997). [CrossRef]
  31. A. Fuks, “Wave diffraction by a rough boundary of an arbitrary plane-layered medium,” IEEE Trans. Antennas Propag. 49, 630–639 (2001). [CrossRef]
  32. S. Dietrich, A. Haase, “Scattering of X-rays and neutrons at interfaces,” Phys. Rep. 260, (1995).
  33. P. Johansson, “Light scattering from disordered overlayers of metallic nanoparticles,” Phys. Rev. B 64, 165405 (2001). [CrossRef]
  34. T. Sondergaard, S. Boshelvonyi, “Vectorial model for multiple scattering by surface nanoparticles via surface polariton–polariton interactions,” Phys. Rev. B 67, 165405 (2003). [CrossRef]
  35. F. Pincemin, A. Sentenac, J. J. Greffet, “Near field scattered by a dielectric rod below a metallic surface,” J. Acoust. Soc. Am. 11, 1117–1127 (1994).
  36. X-Ray and Neutron Reflectivity: Principles and Applications, J. Daillant, A. Gibaud, eds. (Springer, New York, 1999).
  37. J. Lekner, Theory of Reflection of Electromagnetic and Particle Waves (Martinus Nijhoff, Dordrecht, The Netherlands, 1987).
  38. L. Tsang, J. A. Kong, K. H. Ding, Scattering of electromagnetic waves, first volume of three in Wiley Series in Remote Sensing (Wiley-Interscience, New York, 2001).

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