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Journal of the Optical Society of America A

Journal of the Optical Society of America A


  • Vol. 18, Iss. 7 — Jul. 1, 2001
  • pp: 1507–1518

High-order perturbation theory for light scattering from a rough metal surface

K. A. O’Donnell  »View Author Affiliations

JOSA A, Vol. 18, Issue 7, pp. 1507-1518 (2001)

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The angular distribution of the mean diffuse intensity scattered from a metal surface with one-dimensional roughness is studied with perturbation theory. From an approach based on the reduced Rayleigh equations in p polarization, exact perturbation terms up to eighth order in the height parameter are developed for surface roughness consistent with a stationary Gaussian process. The theory is evaluated for a number of cases in which surface plasmon polariton excitation is significant and produces effects such as backscattering enhancement. For surface roughness having a wide Gaussian power spectrum, it is found that the high-order terms lead to roughness-induced broadening of the backscattering peak. For rectangular spectra, two cases are studied in which backscattering effects are due to sixth- and eighth-order terms; both cases provide good comparisons with previously unexplained experimental results. Further, because of an eighth-order term, the diffuse intensity is shown to contain a specular peak that also relies on polariton excitation. This new effect is studied in detail and is found to arise from the constructive interference of contributions produced by multiple-scattering processes, although the time-reversed paths that produce backscattering enhancement are not essential to the specular effect.

© 2001 Optical Society of America

OCIS Codes
(240.5770) Optics at surfaces : Roughness
(240.6680) Optics at surfaces : Surface plasmons
(290.5880) Scattering : Scattering, rough surfaces

Original Manuscript: October 17, 2000
Manuscript Accepted: December 20, 2000
Published: July 1, 2001

K. A. O’Donnell, "High-order perturbation theory for light scattering from a rough metal surface," J. Opt. Soc. Am. A 18, 1507-1518 (2001)

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  1. A. R. McGurn, A. A. Maradudin, V. Celli, “Localization effects in the scattering of light from a randomly rough grating,” Phys. Rev. B 31, 4866–4871 (1985). [CrossRef]
  2. V. Celli, A. A. Maradudin, A. M. Marvin, A. R. McGurn, “Some aspects of light scattering from a randomly rough metal surface,” J. Opt. Soc. Am. A 2, 2225–2239 (1985). [CrossRef]
  3. C. S. West, K. A. O’Donnell, “Observations of backscattering enhancement from polaritons on a rough metal surface,” J. Opt. Soc. Am. A 12, 390–397 (1995). [CrossRef]
  4. C. S. West, K. A. O’Donnell, “Scattering by plasmon polaritons on a metal surface with a detuned roughness spectrum,” Opt. Lett. 21, 1–3 (1996). [CrossRef] [PubMed]
  5. A. Arsenieva, S. Feng, “Correspondence between correlation functions and enhanced backscattering peak for scattering from smooth random surfaces,” Phys. Rev. B 47, 13047–13050 (1993). [CrossRef]
  6. V. Malyshkin, A. R. McGurn, T. A. Leskova, A. A. Maradudin, M. Nieto-Vesperinas, “Speckle correlations in the light scattered from weakly rough random metal surfaces,” Waves Random Media 7, 479–520 (1997). [CrossRef]
  7. C. S. West, K. A. O’Donnell, “Angular correlation functions of light scattered from weakly rough metal surfaces,” Phys. Rev. B 59, 2393–2406 (1999). [CrossRef]
  8. P. Tran, V. Celli, “Monte Carlo calculation of backscattering enhancement for a randomly rough grating,” J. Opt. Soc. Am. A 5, 1635–1637 (1988). [CrossRef]
  9. T. R. Michel, “Resonant light scattering from weakly rough random surfaces and imperfect gratings,” J. Opt. Soc. Am. A 11, 1874–1885 (1994). [CrossRef]
  10. A. A. Maradudin, E. R. Méndez, “Enhanced backscattering of light from weakly rough, random metal surfaces,” Appl. Opt. 32, 3335–3343 (1993). [CrossRef] [PubMed]
  11. V. Freilikher, I. Yurkevich, “Backscattering enhancement from surfaces with random impedance,” Phys. Lett. A 183, 247–252 (1993). [CrossRef]
  12. A. R. McGurn, A. A. Maradudin, “Perturbation theory results for the diffuse scattering of light from two-dimensional randomly rough metal surfaces,” Waves Random Media 6, 251–267 (1996). [CrossRef]
  13. H. Hanato, H. Ogura, Z. L. Wang, “Scattering from a slightly random, one-dimensional metal surface: 45° linearly polarized incidence, backscattering enhancement and degree of polarization,” Waves Random Media 7, 11–34 (1997). [CrossRef]
  14. J. W. Goodman, Statistical Optics (Wiley, New York, 1985), p. 82.
  15. M. Arnold, M. Otto, “Notes on localization of surface plasmon polaritons,” Opt. Commun. 125, 122–136 (1996). [CrossRef]
  16. D. S. Wiersma, M. P. van Albada, B. A. van Tiggelen, A. Lagendijk, “Experimental evidence for recurrent multiple scattering events of light in disordered media,” Phys. Rev. Lett. 74, 4193–4196 (1995). [CrossRef] [PubMed]
  17. K. A. O’Donnell, C. S. West, E. R. Méndez, “Backscattering enhancement from polariton–polariton coupling on a rough metal surface,” Phys. Rev. B 57, 13209–13219 (1998). [CrossRef]
  18. C. S. West, “Backscattering enhancement from plasmon polaritons on rough metal surfaces,” Ph.D. dissertation (Georgia Institute of Technology, Atlanta, Georgia, 1997), p. 152.
  19. M. Nieto-Vesperinas, J. M. Soto-Crespo, “Connection between blazes from gratings and enhancements from random rough surfaces,” Phys. Rev. B 39, 8193–8197 (1989). [CrossRef]
  20. E. R. Méndez, M. A. Ponce, V. Ruiz-Cortés, Z. Gu, “Coherent effects in the scattering of light from random surfaces with symmetry,” Opt. Lett. 16, 123–125 (1991). [CrossRef]

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