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Small-Amplitude Perturbation Theory for One-Dimensionally Rough Surfaces

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Part of the book series: Nanostructure Science and Technology ((NST))

Abstract

There has been considerable interest in the scattering of light from rough surfaces having surface height fluctuations small compared to the illumination wavelength. This case of weak roughness is important in practical applications such as scattering from the residual roughness of polished optical surfaces.1 There has also been interest in scattering from weakly rough metal surfaces when the excitation of surface plasmon polaritons is significant.2,3 Under appropriate conditions, a vertical roughness of only a few nanometers can produce remarkably strong scattering effects arising from polariton excitation. This line of research has been driven more by fundamental interest, and studies have often addressed the unusual features such as backscattering enhancement that appear in the diffuse scattering distributions.

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References

  1. J.M. Bennett and L. Mattsson, Introduction to Surface Roughness and Scattering (Optical Society of America, Washington, D.C., 1989) and references therein.

    Google Scholar 

  2. A.R. McGurn, A.A. Maradudin, and V. Celli, “Localization effects in the scattering of light from a randomly rough grating,” Phys. Rev. B 31, 4866–4871 (1985).

    Article  ADS  Google Scholar 

  3. 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).

    Article  ADS  Google Scholar 

  4. A.A. Maradudin and E.R. Méndez, “Enhanced backscattering of light from weakly rough, random metal surfaces,” Appl. Opt. 32, 3335–3343 (1993).

    Article  ADS  Google Scholar 

  5. A.R. McGurn and 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).

    Article  MATH  ADS  Google Scholar 

  6. 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).

    Article  ADS  Google Scholar 

  7. C.S. West and K.A. O’Donnell, “Observations of backscattering enhancement from polaritons on a rough metal surface,” J. Opt. Soc. Am. A 12, 390–397 (1995).

    Article  ADS  Google Scholar 

  8. C.S. West and K.A. O’Donnell, “Scattering by plasmon polaritons on a metal surface with a detuned roughness spectrum,” Opt. Lett. 21, 1–3 (1996).

    Article  ADS  Google Scholar 

  9. J.W. Goodman, Statistical Optics (Wiley, New York, 1985).

    Google Scholar 

  10. A.C. Genz and A.A. Malik, “An adaptive algorithm for numerical integration over an N-dimensional rectangular region,” J. Comput. Appl. Math. 6, 295–302 (1980).

    Article  MATH  Google Scholar 

  11. T.R. Michel, “Resonant light scattering from weakly rough random surfaces and imperfect gratings,” J. Opt. Soc. Am. A 11, 1874–1885 (1994).

    Article  ADS  Google Scholar 

  12. K.A. O’Donnell and E. R. Méndez, “Enhanced specular peaks in diffuse light scattering from weakly rough metal surfaces,” J. Opt. Soc. Am. A 20, 2338–2346 (2003).

    Article  ADS  Google Scholar 

  13. K.A. O’Donnell, C.S. West, and E.R. Méndez, “Backscattering enhancement from polariton-polariton coupling on a rough metal surface,” Phys. Rev. B 57, 13209–13219 (1998).

    Article  ADS  Google Scholar 

  14. A.A. Maradudin, A.R. McGurn, and E.R. Méndez, “Surface plasmon polariton mechanism for enhanced backscattering of light from one-dimensional randomly rough metal surfaces,” J. Opt. Soc. Am. A 12, 2500–2506 (1995).

    Article  ADS  Google Scholar 

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O’Donnell, K.A. (2007). Small-Amplitude Perturbation Theory for One-Dimensionally Rough Surfaces. In: Maradudin, A.A. (eds) Light Scattering and Nanoscale Surface Roughness. Nanostructure Science and Technology. Springer, Boston, MA. https://doi.org/10.1007/978-0-387-35659-4_5

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