Abstract

A nonperturbative, purely numerical, solution of the reduced Rayleigh equation for the scattering of p- and s-polarized light from a dielectric film with a two-dimensional randomly rough surface deposited on a planar metallic substrate, has been carried out. It is found that satellite peaks are present in the angular dependence of the elements of the mean differential reflection coefficient in addition to an enhanced backscattering peak. This result resolves a conflict between the results of earlier approximate theoretical studies of scattering from this system.

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  1. 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).
    [CrossRef]
  2. M. Nieto-Vesperinas and 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. A. A. Maradudin, E. R. Méndez, and 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]
  4. I. Simonsen, “Optics of surface disordered systems,” Eur. Phys. J.–Spec. Top. 181, 1–103 (2010).
    [CrossRef]
  5. A. McGurn and A. Maradudin, “An analogue of enhanced backscattering in the transmission of light through a thin film with a randomly rough surface,” Opt. Commun. 72, 279–285 (1989).
    [CrossRef]
  6. V. Freilikher, E. Kanzieper, and A. Maradudin, “Coherent scattering enhancement in systems bounded by rough surfaces,” Phys. Rep. 288, 127–204 (1997).
    [CrossRef]
  7. V. Freilikher, M. Pustilnik, and I. Yurkevich, “Wave scattering from a bounded medium with disorder,” Phys. Lett. A 193, 467–470 (1994).
    [CrossRef]
  8. A. McGurn and A. Maradudin, “Perturbation theory results for the diffuse scattering of light from two-dimensional randomly rough metal surfaces,” Wave. Random Media 6, 251–267 (1996).
    [CrossRef]
  9. J. T. Johnson, “Third-order small-perturbation method for scattering from dielectric rough surfaces,” J. Opt. Soc. Am. A 16, 2720–2736 (1999).
    [CrossRef]
  10. A. Soubret, G. Berginc, and C. Bourrely, “Application of reduced Rayleigh equations to electromagnetic wave scattering by two-dimensional randomly rough surfaces,” Phys. Rev. B 63, 245411 (2001).
    [CrossRef]
  11. I. Simonsen, A. A. Maradudin, and T. A. Leskova, “Scattering of electromagnetic waves from two-dimensional randomly rough perfectly conducting surfaces: The full angular intensity distribution,” Phys. Rev. A 81, 013806 (2010).
    [CrossRef]
  12. I. Simonsen, A. A. Maradudin, and T. A. Leskova, “Scattering of electromagnetic waves from two-dimensional randomly rough penetrable surfaces,” Phys. Rev. Lett. 104, 223904 (2010).
    [CrossRef] [PubMed]
  13. I. Simonsen, J. B. Kryvi, A. A. Maradudin, and T. A. Leskova, “Light scattering from anisotropic, randomly rough, perfectly conducting surfaces,” Comput. Phys. Commun. 182, 1904–1908 (2011).
    [CrossRef]
  14. T. Kawanishi, H. Ogura, and Z. L. Wang, “Scattering of an electromagnetic wave from a slightly random dielectric surface: Yoneda peak and Brewster angle in incoherent scattering,” Wave. Random Media 7, 351–384 (1997).
    [CrossRef]
  15. A. Soubret, G. Berginc, and C. Bourrely, “Backscattering enhancement of an electromagnetic wave scattered by two-dimensional rough layers,” J. Opt. Soc. Am. A 18, 2778–2788 (2001).
    [CrossRef]
  16. E. R. Méndez, E. I. Chaikina, and H. M. Escamilla, “Observation of satellite peaks and dips in the scattering of light in a double-pass geometry,” Opt. Lett. 24, 705–707 (1999).
    [CrossRef]
  17. T. Nordam, P. A. Letnes, and I. Simonsen, “Numerical simulations of scattering of light from two-dimensional surfaces using the reduced Rayleigh equation,” http://arxiv.org/abs/1204.4984 .
  18. T. A. Leskova, P. A. Letnes, A. A. Maradudin, T. Nordam, and I. Simonsen, “The scattering of light from two-dimensional randomly rough surfaces,” Proc. SPIE 8172, 817209 (2011).
    [CrossRef]
  19. T. A. Leskova, Department of Physics and Astronomy, University of California, Irvine CA 92697, U.S.A. (personal communication, 2010).
  20. J. T. Johnson, “Third-order small-perturbation method for scattering from dielectric rough surfaces,” J. Opt. Soc. Am. A 16, 2720–2736 (1999).
    [CrossRef]
  21. A. Maradudin, T. Michel, A. McGurn, and E. Méndez, “Enhanced backscattering of light from a random grating,” Ann. Phys. 203, 255–307 (1990).
    [CrossRef]
  22. W. Press, B. Flannery, S. Teukolsky, and W. Vetterling, Numerical recipes, 3rd ed. (Cambridge Univ Press, 2007).
  23. P. B. Johnson, “Optical constants of the noble metals,” Phys. Rev. 6, 4370–4379 (1972).
    [CrossRef]
  24. 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).
    [CrossRef]
  25. A. Madrazo and A. Maradudin, “Numerical solutions of the reduced Rayleigh equation for the scattering of electromagnetic waves from rough dielectric films on perfectly conducting substrates,” Opt. Commun. 134, 251–263 (1997).
    [CrossRef]
  26. I. Simonsen and A. Maradudin, “Numerical simulation of electromagnetic wave scattering from planar dielectric films deposited on rough perfectly conducting substrates,” Opt. Commun. 162, 99–111 (1999).
    [CrossRef]

2011 (2)

I. Simonsen, J. B. Kryvi, A. A. Maradudin, and T. A. Leskova, “Light scattering from anisotropic, randomly rough, perfectly conducting surfaces,” Comput. Phys. Commun. 182, 1904–1908 (2011).
[CrossRef]

T. A. Leskova, P. A. Letnes, A. A. Maradudin, T. Nordam, and I. Simonsen, “The scattering of light from two-dimensional randomly rough surfaces,” Proc. SPIE 8172, 817209 (2011).
[CrossRef]

2010 (3)

I. Simonsen, A. A. Maradudin, and T. A. Leskova, “Scattering of electromagnetic waves from two-dimensional randomly rough perfectly conducting surfaces: The full angular intensity distribution,” Phys. Rev. A 81, 013806 (2010).
[CrossRef]

I. Simonsen, A. A. Maradudin, and T. A. Leskova, “Scattering of electromagnetic waves from two-dimensional randomly rough penetrable surfaces,” Phys. Rev. Lett. 104, 223904 (2010).
[CrossRef] [PubMed]

I. Simonsen, “Optics of surface disordered systems,” Eur. Phys. J.–Spec. Top. 181, 1–103 (2010).
[CrossRef]

2001 (2)

A. Soubret, G. Berginc, and C. Bourrely, “Application of reduced Rayleigh equations to electromagnetic wave scattering by two-dimensional randomly rough surfaces,” Phys. Rev. B 63, 245411 (2001).
[CrossRef]

A. Soubret, G. Berginc, and C. Bourrely, “Backscattering enhancement of an electromagnetic wave scattered by two-dimensional rough layers,” J. Opt. Soc. Am. A 18, 2778–2788 (2001).
[CrossRef]

1999 (4)

1997 (3)

A. Madrazo and A. Maradudin, “Numerical solutions of the reduced Rayleigh equation for the scattering of electromagnetic waves from rough dielectric films on perfectly conducting substrates,” Opt. Commun. 134, 251–263 (1997).
[CrossRef]

T. Kawanishi, H. Ogura, and Z. L. Wang, “Scattering of an electromagnetic wave from a slightly random dielectric surface: Yoneda peak and Brewster angle in incoherent scattering,” Wave. Random Media 7, 351–384 (1997).
[CrossRef]

V. Freilikher, E. Kanzieper, and A. Maradudin, “Coherent scattering enhancement in systems bounded by rough surfaces,” Phys. Rep. 288, 127–204 (1997).
[CrossRef]

1996 (1)

A. McGurn and A. Maradudin, “Perturbation theory results for the diffuse scattering of light from two-dimensional randomly rough metal surfaces,” Wave. Random Media 6, 251–267 (1996).
[CrossRef]

1995 (1)

1994 (1)

V. Freilikher, M. Pustilnik, and I. Yurkevich, “Wave scattering from a bounded medium with disorder,” Phys. Lett. A 193, 467–470 (1994).
[CrossRef]

1990 (1)

A. Maradudin, T. Michel, A. McGurn, and E. Méndez, “Enhanced backscattering of light from a random grating,” Ann. Phys. 203, 255–307 (1990).
[CrossRef]

1989 (2)

A. A. Maradudin, E. R. Méndez, and 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]

A. McGurn and A. Maradudin, “An analogue of enhanced backscattering in the transmission of light through a thin film with a randomly rough surface,” Opt. Commun. 72, 279–285 (1989).
[CrossRef]

1987 (1)

1985 (1)

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).
[CrossRef]

1972 (1)

P. B. Johnson, “Optical constants of the noble metals,” Phys. Rev. 6, 4370–4379 (1972).
[CrossRef]

Berginc, G.

A. Soubret, G. Berginc, and C. Bourrely, “Application of reduced Rayleigh equations to electromagnetic wave scattering by two-dimensional randomly rough surfaces,” Phys. Rev. B 63, 245411 (2001).
[CrossRef]

A. Soubret, G. Berginc, and C. Bourrely, “Backscattering enhancement of an electromagnetic wave scattered by two-dimensional rough layers,” J. Opt. Soc. Am. A 18, 2778–2788 (2001).
[CrossRef]

Bourrely, C.

A. Soubret, G. Berginc, and C. Bourrely, “Backscattering enhancement of an electromagnetic wave scattered by two-dimensional rough layers,” J. Opt. Soc. Am. A 18, 2778–2788 (2001).
[CrossRef]

A. Soubret, G. Berginc, and C. Bourrely, “Application of reduced Rayleigh equations to electromagnetic wave scattering by two-dimensional randomly rough surfaces,” Phys. Rev. B 63, 245411 (2001).
[CrossRef]

Celli, V.

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).
[CrossRef]

Chaikina, E. I.

Escamilla, H. M.

Flannery, B.

W. Press, B. Flannery, S. Teukolsky, and W. Vetterling, Numerical recipes, 3rd ed. (Cambridge Univ Press, 2007).

Freilikher, V.

V. Freilikher, E. Kanzieper, and A. Maradudin, “Coherent scattering enhancement in systems bounded by rough surfaces,” Phys. Rep. 288, 127–204 (1997).
[CrossRef]

V. Freilikher, M. Pustilnik, and I. Yurkevich, “Wave scattering from a bounded medium with disorder,” Phys. Lett. A 193, 467–470 (1994).
[CrossRef]

Johnson, J. T.

Johnson, P. B.

P. B. Johnson, “Optical constants of the noble metals,” Phys. Rev. 6, 4370–4379 (1972).
[CrossRef]

Kanzieper, E.

V. Freilikher, E. Kanzieper, and A. Maradudin, “Coherent scattering enhancement in systems bounded by rough surfaces,” Phys. Rep. 288, 127–204 (1997).
[CrossRef]

Kawanishi, T.

T. Kawanishi, H. Ogura, and Z. L. Wang, “Scattering of an electromagnetic wave from a slightly random dielectric surface: Yoneda peak and Brewster angle in incoherent scattering,” Wave. Random Media 7, 351–384 (1997).
[CrossRef]

Kryvi, J. B.

I. Simonsen, J. B. Kryvi, A. A. Maradudin, and T. A. Leskova, “Light scattering from anisotropic, randomly rough, perfectly conducting surfaces,” Comput. Phys. Commun. 182, 1904–1908 (2011).
[CrossRef]

Leskova, T. A.

I. Simonsen, J. B. Kryvi, A. A. Maradudin, and T. A. Leskova, “Light scattering from anisotropic, randomly rough, perfectly conducting surfaces,” Comput. Phys. Commun. 182, 1904–1908 (2011).
[CrossRef]

T. A. Leskova, P. A. Letnes, A. A. Maradudin, T. Nordam, and I. Simonsen, “The scattering of light from two-dimensional randomly rough surfaces,” Proc. SPIE 8172, 817209 (2011).
[CrossRef]

I. Simonsen, A. A. Maradudin, and T. A. Leskova, “Scattering of electromagnetic waves from two-dimensional randomly rough penetrable surfaces,” Phys. Rev. Lett. 104, 223904 (2010).
[CrossRef] [PubMed]

I. Simonsen, A. A. Maradudin, and T. A. Leskova, “Scattering of electromagnetic waves from two-dimensional randomly rough perfectly conducting surfaces: The full angular intensity distribution,” Phys. Rev. A 81, 013806 (2010).
[CrossRef]

T. A. Leskova, Department of Physics and Astronomy, University of California, Irvine CA 92697, U.S.A. (personal communication, 2010).

Letnes, P. A.

T. A. Leskova, P. A. Letnes, A. A. Maradudin, T. Nordam, and I. Simonsen, “The scattering of light from two-dimensional randomly rough surfaces,” Proc. SPIE 8172, 817209 (2011).
[CrossRef]

Madrazo, A.

A. Madrazo and A. Maradudin, “Numerical solutions of the reduced Rayleigh equation for the scattering of electromagnetic waves from rough dielectric films on perfectly conducting substrates,” Opt. Commun. 134, 251–263 (1997).
[CrossRef]

Maradudin, A.

I. Simonsen and A. Maradudin, “Numerical simulation of electromagnetic wave scattering from planar dielectric films deposited on rough perfectly conducting substrates,” Opt. Commun. 162, 99–111 (1999).
[CrossRef]

A. Madrazo and A. Maradudin, “Numerical solutions of the reduced Rayleigh equation for the scattering of electromagnetic waves from rough dielectric films on perfectly conducting substrates,” Opt. Commun. 134, 251–263 (1997).
[CrossRef]

V. Freilikher, E. Kanzieper, and A. Maradudin, “Coherent scattering enhancement in systems bounded by rough surfaces,” Phys. Rep. 288, 127–204 (1997).
[CrossRef]

A. McGurn and A. Maradudin, “Perturbation theory results for the diffuse scattering of light from two-dimensional randomly rough metal surfaces,” Wave. Random Media 6, 251–267 (1996).
[CrossRef]

A. Maradudin, T. Michel, A. McGurn, and E. Méndez, “Enhanced backscattering of light from a random grating,” Ann. Phys. 203, 255–307 (1990).
[CrossRef]

A. McGurn and A. Maradudin, “An analogue of enhanced backscattering in the transmission of light through a thin film with a randomly rough surface,” Opt. Commun. 72, 279–285 (1989).
[CrossRef]

Maradudin, A. A.

I. Simonsen, J. B. Kryvi, A. A. Maradudin, and T. A. Leskova, “Light scattering from anisotropic, randomly rough, perfectly conducting surfaces,” Comput. Phys. Commun. 182, 1904–1908 (2011).
[CrossRef]

T. A. Leskova, P. A. Letnes, A. A. Maradudin, T. Nordam, and I. Simonsen, “The scattering of light from two-dimensional randomly rough surfaces,” Proc. SPIE 8172, 817209 (2011).
[CrossRef]

I. Simonsen, A. A. Maradudin, and T. A. Leskova, “Scattering of electromagnetic waves from two-dimensional randomly rough perfectly conducting surfaces: The full angular intensity distribution,” Phys. Rev. A 81, 013806 (2010).
[CrossRef]

I. Simonsen, A. A. Maradudin, and T. A. Leskova, “Scattering of electromagnetic waves from two-dimensional randomly rough penetrable surfaces,” Phys. Rev. Lett. 104, 223904 (2010).
[CrossRef] [PubMed]

A. A. Maradudin, E. R. Méndez, and 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]

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).
[CrossRef]

McGurn, A.

A. McGurn and A. Maradudin, “Perturbation theory results for the diffuse scattering of light from two-dimensional randomly rough metal surfaces,” Wave. Random Media 6, 251–267 (1996).
[CrossRef]

A. Maradudin, T. Michel, A. McGurn, and E. Méndez, “Enhanced backscattering of light from a random grating,” Ann. Phys. 203, 255–307 (1990).
[CrossRef]

A. McGurn and A. Maradudin, “An analogue of enhanced backscattering in the transmission of light through a thin film with a randomly rough surface,” Opt. Commun. 72, 279–285 (1989).
[CrossRef]

McGurn, A. R.

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).
[CrossRef]

Méndez, E.

A. Maradudin, T. Michel, A. McGurn, and E. Méndez, “Enhanced backscattering of light from a random grating,” Ann. Phys. 203, 255–307 (1990).
[CrossRef]

Méndez, E. R.

Michel, T.

Nieto-Vesperinas, M.

Nordam, T.

T. A. Leskova, P. A. Letnes, A. A. Maradudin, T. Nordam, and I. Simonsen, “The scattering of light from two-dimensional randomly rough surfaces,” Proc. SPIE 8172, 817209 (2011).
[CrossRef]

O’Donnell, K. A.

Ogura, H.

T. Kawanishi, H. Ogura, and Z. L. Wang, “Scattering of an electromagnetic wave from a slightly random dielectric surface: Yoneda peak and Brewster angle in incoherent scattering,” Wave. Random Media 7, 351–384 (1997).
[CrossRef]

Press, W.

W. Press, B. Flannery, S. Teukolsky, and W. Vetterling, Numerical recipes, 3rd ed. (Cambridge Univ Press, 2007).

Pustilnik, M.

V. Freilikher, M. Pustilnik, and I. Yurkevich, “Wave scattering from a bounded medium with disorder,” Phys. Lett. A 193, 467–470 (1994).
[CrossRef]

Simonsen, I.

I. Simonsen, J. B. Kryvi, A. A. Maradudin, and T. A. Leskova, “Light scattering from anisotropic, randomly rough, perfectly conducting surfaces,” Comput. Phys. Commun. 182, 1904–1908 (2011).
[CrossRef]

T. A. Leskova, P. A. Letnes, A. A. Maradudin, T. Nordam, and I. Simonsen, “The scattering of light from two-dimensional randomly rough surfaces,” Proc. SPIE 8172, 817209 (2011).
[CrossRef]

I. Simonsen, A. A. Maradudin, and T. A. Leskova, “Scattering of electromagnetic waves from two-dimensional randomly rough penetrable surfaces,” Phys. Rev. Lett. 104, 223904 (2010).
[CrossRef] [PubMed]

I. Simonsen, A. A. Maradudin, and T. A. Leskova, “Scattering of electromagnetic waves from two-dimensional randomly rough perfectly conducting surfaces: The full angular intensity distribution,” Phys. Rev. A 81, 013806 (2010).
[CrossRef]

I. Simonsen, “Optics of surface disordered systems,” Eur. Phys. J.–Spec. Top. 181, 1–103 (2010).
[CrossRef]

I. Simonsen and A. Maradudin, “Numerical simulation of electromagnetic wave scattering from planar dielectric films deposited on rough perfectly conducting substrates,” Opt. Commun. 162, 99–111 (1999).
[CrossRef]

Soto-Crespo, J. M.

Soubret, A.

A. Soubret, G. Berginc, and C. Bourrely, “Application of reduced Rayleigh equations to electromagnetic wave scattering by two-dimensional randomly rough surfaces,” Phys. Rev. B 63, 245411 (2001).
[CrossRef]

A. Soubret, G. Berginc, and C. Bourrely, “Backscattering enhancement of an electromagnetic wave scattered by two-dimensional rough layers,” J. Opt. Soc. Am. A 18, 2778–2788 (2001).
[CrossRef]

Teukolsky, S.

W. Press, B. Flannery, S. Teukolsky, and W. Vetterling, Numerical recipes, 3rd ed. (Cambridge Univ Press, 2007).

Vetterling, W.

W. Press, B. Flannery, S. Teukolsky, and W. Vetterling, Numerical recipes, 3rd ed. (Cambridge Univ Press, 2007).

Wang, Z. L.

T. Kawanishi, H. Ogura, and Z. L. Wang, “Scattering of an electromagnetic wave from a slightly random dielectric surface: Yoneda peak and Brewster angle in incoherent scattering,” Wave. Random Media 7, 351–384 (1997).
[CrossRef]

West, C. S.

Yurkevich, I.

V. Freilikher, M. Pustilnik, and I. Yurkevich, “Wave scattering from a bounded medium with disorder,” Phys. Lett. A 193, 467–470 (1994).
[CrossRef]

Ann. Phys. (1)

A. Maradudin, T. Michel, A. McGurn, and E. Méndez, “Enhanced backscattering of light from a random grating,” Ann. Phys. 203, 255–307 (1990).
[CrossRef]

Comput. Phys. Commun. (1)

I. Simonsen, J. B. Kryvi, A. A. Maradudin, and T. A. Leskova, “Light scattering from anisotropic, randomly rough, perfectly conducting surfaces,” Comput. Phys. Commun. 182, 1904–1908 (2011).
[CrossRef]

Eur. Phys. J.–Spec. Top. (1)

I. Simonsen, “Optics of surface disordered systems,” Eur. Phys. J.–Spec. Top. 181, 1–103 (2010).
[CrossRef]

J. Opt. Soc. Am. A (4)

Opt. Commun. (3)

A. Madrazo and A. Maradudin, “Numerical solutions of the reduced Rayleigh equation for the scattering of electromagnetic waves from rough dielectric films on perfectly conducting substrates,” Opt. Commun. 134, 251–263 (1997).
[CrossRef]

I. Simonsen and A. Maradudin, “Numerical simulation of electromagnetic wave scattering from planar dielectric films deposited on rough perfectly conducting substrates,” Opt. Commun. 162, 99–111 (1999).
[CrossRef]

A. McGurn and A. Maradudin, “An analogue of enhanced backscattering in the transmission of light through a thin film with a randomly rough surface,” Opt. Commun. 72, 279–285 (1989).
[CrossRef]

Opt. Lett. (3)

Phys. Lett. A (1)

V. Freilikher, M. Pustilnik, and I. Yurkevich, “Wave scattering from a bounded medium with disorder,” Phys. Lett. A 193, 467–470 (1994).
[CrossRef]

Phys. Rep. (1)

V. Freilikher, E. Kanzieper, and A. Maradudin, “Coherent scattering enhancement in systems bounded by rough surfaces,” Phys. Rep. 288, 127–204 (1997).
[CrossRef]

Phys. Rev. (1)

P. B. Johnson, “Optical constants of the noble metals,” Phys. Rev. 6, 4370–4379 (1972).
[CrossRef]

Phys. Rev. A (1)

I. Simonsen, A. A. Maradudin, and T. A. Leskova, “Scattering of electromagnetic waves from two-dimensional randomly rough perfectly conducting surfaces: The full angular intensity distribution,” Phys. Rev. A 81, 013806 (2010).
[CrossRef]

Phys. Rev. B (2)

A. Soubret, G. Berginc, and C. Bourrely, “Application of reduced Rayleigh equations to electromagnetic wave scattering by two-dimensional randomly rough surfaces,” Phys. Rev. B 63, 245411 (2001).
[CrossRef]

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).
[CrossRef]

Phys. Rev. Lett. (1)

I. Simonsen, A. A. Maradudin, and T. A. Leskova, “Scattering of electromagnetic waves from two-dimensional randomly rough penetrable surfaces,” Phys. Rev. Lett. 104, 223904 (2010).
[CrossRef] [PubMed]

Proc. SPIE (1)

T. A. Leskova, P. A. Letnes, A. A. Maradudin, T. Nordam, and I. Simonsen, “The scattering of light from two-dimensional randomly rough surfaces,” Proc. SPIE 8172, 817209 (2011).
[CrossRef]

Wave. Random Media (2)

T. Kawanishi, H. Ogura, and Z. L. Wang, “Scattering of an electromagnetic wave from a slightly random dielectric surface: Yoneda peak and Brewster angle in incoherent scattering,” Wave. Random Media 7, 351–384 (1997).
[CrossRef]

A. McGurn and A. Maradudin, “Perturbation theory results for the diffuse scattering of light from two-dimensional randomly rough metal surfaces,” Wave. Random Media 6, 251–267 (1996).
[CrossRef]

Other (3)

T. A. Leskova, Department of Physics and Astronomy, University of California, Irvine CA 92697, U.S.A. (personal communication, 2010).

T. Nordam, P. A. Letnes, and I. Simonsen, “Numerical simulations of scattering of light from two-dimensional surfaces using the reduced Rayleigh equation,” http://arxiv.org/abs/1204.4984 .

W. Press, B. Flannery, S. Teukolsky, and W. Vetterling, Numerical recipes, 3rd ed. (Cambridge Univ Press, 2007).

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Figures (4)

Fig. 1
Fig. 1

(a) The contributions to the mean differential reflection coefficient as functions of the polar scattering angle θs from the in-plane (ϕs = ϕ0) co-polarized (p→p, s→s) and cross-polarized (p→s, s→p) scattering of light incident on the two-dimensional randomly rough surface of a dielectric film deposited on the planar surface of silver, whose dielectric constant is ε3 = −18.28 + 0.481i. The wavelength of the incident light is λ = 633 nm, the angles of incidence are (θ0,ϕ0) = (0.74°, 45°). The dielectric constant of the film is ε2 = 2.6896+ 0.01i, and its mean thickness is d = 478.5 nm. The roughness of the surface is characterized by the power spectrum in Eq. (13), with k = 0.82(ω/c), k+ = 1.97(ω/c), and its rms height is δ = λ/40 = 15.82 nm. (b) The same as (a) for out-of-plane (ϕs = ϕ0 + 90°) scattering.

Fig. 2
Fig. 2

The complete angular distribution of the mean differential reflection coefficient 〈∂Rαβ/Ωsincoh for the light scattered incoherently from the film structure. The material and experimental parameters assumed here are those used in obtaining the plots presented in Fig. 1. Light of either p (left column) or s (right column) polarization is incident on the structure. In (a) and (d) all (diffusely) scattered light is recorded. In (b) and (e) only the p-polarized scattered light is recorded, while in (c) and (f) only the s-polarized scattered light is recorded. The dark dot in each panel indicates the enhanced backscattering peak. Note that the gray scale bar is cut at both ends in order to enhance the satellite rings. Also note that the contribution from single scattering is suppressed, i.e. the differential reflection coefficient is artificially set to 0 for | q k | > k .

Fig. 3
Fig. 3

The same as Fig. 1, but for angles of incidence given by (θ0,ϕ0) = (5.19°, 45°).

Fig. 4
Fig. 4

The same as Fig. 2, but for angles of incidence given by (θ0,ϕ0) = (5.19°, 45°). Note that the color bar is cut at both ends in order to enhance the satellite rings. Also note that the contribution from single scattering is suppressed, i.e. the differential reflection coefficient is artificially set to 0 for | q k | > k .

Equations (30)

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ζ ( x ) ζ ( x ) = δ 2 W ( | x x | ) .
E ( x | ω ) inc = { c ω [ k ^ α 1 ( k ) + x ^ 3 k ] B p ( k ) + ( x ^ 3 × k ^ ) B s ( k ) } × exp ( i k x i α 1 ( k ) x 3 )
E ( x | ω ) sc = d 2 q ( 2 π ) 2 { c ω [ q ^ α 1 ( q ) x ^ 3 q ] A p ( q ) + ( x ^ 3 × q ^ ) A s ( q ) } × exp ( i q x + i α 1 ( q ) x 3 ) ,
α i ( q ) = [ ɛ i ( ω c ) 2 q 2 ] 1 / 2 , Re α i ( q ) > 0 , Im α i ( q ) > 0 .
A α ( q ) = β R α β ( q | k ) B β ( k )
R ( q | k ) = ( R pp ( q | k ) R ps ( q | k ) R sp ( q | k ) R ss ( q | k ) ) .
d 2 q ( 2 π ) 2 M ( p | q ) R ( q | k ) = N ( p | k ) ,
M pp ( p | q ) = [ p q + α 2 ( p ) ( p ^ q ^ ) α 1 ( q ) ] × Γ p ( p ) exp ( i [ α 2 ( p ) α 1 ( q ) ] d ) I ( α 2 ( p ) α 1 ( q ) | p q ) α 2 ( p ) α 1 ( q ) + [ p q α 2 ( p ) ( p ^ q ^ ) α 1 ( q ) ] × Δ p ( p ) exp ( i [ α 2 ( p ) + α 1 ( q ) ] d ) I ( [ α 2 ( p ) + α 1 ( q ) ] | p q ) α 2 ( p ) + α 1 ( q )
M ps ( p | q ) = ω c α 2 ( p ) ( p ^ × q ^ ) 3 ( Γ p ( p ) exp ( i [ α 2 ( p ) α 1 ( q ) ] d ) I ( α 2 ( p ) α 1 ( q ) | p q ) α 2 ( p ) α 1 ( q ) Δ p ( p ) exp ( i [ α 2 ( p ) + α 1 ( q ) ] d ) I ( [ α 2 ( p ) + α 1 ( q ) ] | p q ) α 2 ( p ) + α 1 ( q ) )
M sp ( p | q ) = ω c ( p ^ × q ^ ) 3 α 1 ( q ) ( Γ s ( p ) exp ( i [ α 2 ( p ) α 1 ( q ) ] d ) I ( α 2 ( p ) α 1 ( q ) | p q ) α 2 ( p ) α 1 ( q ) + Δ s ( p ) exp ( i [ α 2 ( p ) + α 1 ( q ) ] d ) I ( [ α 2 ( p ) + α 1 ( q ) ] | p q ) α 2 ( p ) + α 1 ( q ) )
M ss ( p | q ) = ω 2 c 2 ( p ^ q ^ ) ( Γ s ( p ) exp ( i [ α 2 ( p ) α 1 ( q ) ] d ) I ( α 2 ( p ) α 1 ( q ) | p q ) α 2 ( p ) α 1 ( q ) + Δ s ( p ) exp ( i [ α 2 ( p ) + α 1 ( q ) ] d ) I ( [ α 2 ( p ) + α 1 ( q ) ] | p q ) α 2 ( p ) + α 1 ( q ) ) ,
N pp ( p | k ) = [ p k α 2 ( p ) ( p ^ k ^ ) α 1 ( k ) ] × Γ p ( p ) exp ( i [ α 2 ( p ) + α 1 ( k ) ] d ) I ( α 2 ( p ) + α 1 ( k ) | p k ) α 2 ( p ) + α 1 ( k ) [ p k + α 2 ( p ) ( p ^ k ^ ) α 1 ( k ) ] × Δ p ( p ) exp ( i [ α 2 ( p ) α 1 ( k ) ] d ) I ( [ α 2 ( p ) α 1 ( k ) ] | p k ) α 2 ( p ) α 1 ( k )
N ps ( p | k ) = ω c α 2 ( p ) ( p ^ × k ^ ) 3 × ( Γ p ( p ) exp ( i [ α 2 ( p ) + α 1 ( k ) ] d ) I ( α 2 ( p ) + α 1 ( k ) | p k ) α 2 ( p ) + α 1 ( k ) Δ p ( p ) exp ( i [ α 2 ( p ) α 1 ( k ) ] d ) I ( [ α 2 ( p ) α 1 ( k ) ] | p k ) α 2 ( p ) α 1 ( k ) )
N sp ( p | k ) = ω c ( p ^ × k ^ ) 3 α 1 ( k ) × ( Γ s ( p ) exp ( i [ α 2 ( p ) + α 1 ( k ) ] d ) I ( α 2 ( p ) + α 1 ( k ) | p k ) α 2 ( p ) + α 1 ( k ) + Δ s ( p ) exp ( i [ α 2 ( p ) α 1 ( k ) ] d ) I ( [ α 2 ( p ) α 1 ( k ) ] | p k ) α 2 ( p ) α 1 ( k ) )
N ss ( p | k ) = ω 2 c 2 ( p ^ k ^ ) × ( Γ s ( p ) exp ( i [ α 2 ( p ) + α 1 ( k ) ] d ) I ( α 2 ( p ) + α 1 ( k ) | p k ) α 2 ( p ) + α 1 ( k ) + Δ s ( p ) exp ( i [ α 2 ( p ) α 1 ( k ) ] d ) I ( [ α 2 ( p ) α 1 ( k ) ] | p k ) α 2 ( p ) α 1 ( k ) ) .
Γ p ( p ) = ɛ 2 α 3 ( p , ω ) + ɛ 3 α 2 ( p , ω )
Δ p ( p ) = ɛ 2 α 3 ( p , ω ) ɛ 3 α 2 ( p , ω )
Γ s ( p ) = α 3 ( p , ω ) + α 2 ( p , ω )
Δ s ( p ) = α 3 ( p , ω ) α 2 ( p , ω ) ,
I ( γ | Q ) = d 2 x exp ( i Q x ) exp [ i γ ζ ( x ) ] .
R pp Ω s incoh = 1 S ɛ 1 4 π 2 ω c α 1 2 ( q ) α 1 ( k ) [ | R pp ( q | k ) | 2 | R pp ( q | k ) | 2 ]
R ps Ω s incoh = 1 S ɛ 1 3 / 2 4 π 2 ω c α 1 2 ( q ) α 1 ( k ) [ | R ps ( q | k ) | 2 | R ps ( q | k ) | 2 ]
R sp Ω s incoh = 1 S 1 4 π 2 ɛ 1 ω c α 1 2 ( q ) α 1 ( k ) [ | R sp ( q | k ) | 2 | R sp ( q | k ) | 2 ]
R ss Ω s incoh = 1 S ɛ 1 4 π 2 ω c α 1 2 ( q ) α 1 ( k ) [ | R ss ( q | k ) | 2 | R ss ( q | k ) | 2 ] ,
g ( | k | ) = 4 π k + 2 k 2 θ ( | k | k ) θ ( k + | k | ) ,
sin θ s ( m , n ) = sin θ 0 ± c ω ɛ 1 [ q m ( ω ) q n ( ω ) ] .
α 2 ( q , ω ) = 1 2 ɛ 1 ɛ 3 ( ɛ 2 [ ɛ 1 β 3 ( q , ω ) + ɛ 3 β 1 ( q , ω ) ] cot [ α 2 ( q , ω ) d ] ± { ɛ 2 2 [ ɛ 1 β 3 ( q , ω ) + ɛ 3 β 1 ( q , ω ) ] 2 cot 2 [ α 2 ( q , ω ) d ] + 4 ɛ 1 ɛ 2 2 ɛ 3 β 1 ( q , ω ) β 3 ( q , ω ) } 1 / 2 )
α 2 ( q , ω ) = 1 2 ( [ β 1 ( q , ω ) + β 3 ( q , ω ) ] cot [ α 2 ( q , ω ) d ] ± { [ β 1 ( q , ω ) + β 3 ( q , ω ) ] 2 cot 2 [ α 2 ( q , ω ) d ] + 4 β 1 ( q , ω ) + β 3 ( q , ω ) } 1 / 2 )
q 1 ( ω ) = 1.4391 ( ω / c ) , q 2 ( ω ) = 1.0119 ( ω / c ) ,
q 1 ( ω ) = 1.5467 ( ω / c ) , q 2 ( ω ) = 1.2432 ( ω / c ) .

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