Abstract

We investigate numerically multiple light-scattering phenomena for two-dimensional randomly rough metallic surfaces, where surface plasmon polaritons (SPPs) mediate several surface scattering effects. The scattering problem is solved by numerical solution of the reduced Rayleigh equation for reflection. The multiple scattering phenomena of enhanced backscattering and enhanced forward scattering are observed in the same system, and their presence is due to the excitation of SPPs. The numerical results discussed are qualitatively different from previous results for one-dimensionally rough surfaces, as one-dimensional surfaces have a limited influence on the polarization of light.

© 2013 Optical Society of America

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  1. E. Ozbay, “Plasmonics: merging photonics and electronics at nanoscale dimensions,” Science 311, 189–193 (2006).
    [CrossRef]
  2. H. A. Atwater and A. Polman, “Plasmonics for improved photovoltaic devices,” Nat. Mater. 9, 205–213 (2010).
    [CrossRef]
  3. A. Savchenko, E. Kashuba, V. Kashuba, and B. Snopok, “Imaging technique for the screening of protein–protein interactions using scattered light under surface plasmon resonance conditions,” Anal. Chem. 79, 1349–1355 (2007).
    [CrossRef]
  4. A. Savchenko, E. Kashuba, V. Kashuba, and B. Snopok, “Imaging of plasmid DNA microarrays by scattering light under surface plasmon resonance conditions,” Sens. Lett. 6, 705–713 (2008).
    [CrossRef]
  5. 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]
  6. 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]
  7. 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).
    [CrossRef]
  8. We have chosen to use the term “enhanced forward scattering,” because it is an enhancement in the incoherently scattered light and because “specular scattering” is often understood to mean “coherent scattering.”
  9. K. A. O’Donnell and E. R. Mendéz, “Enhanced specular peaks in diffuse light scattering from weakly rough metal surfaces,” J. Opt. Soc. Am. A 20, 2338–2346 (2003).
    [CrossRef]
  10. I. Simonsen, “Enhanced back and forward scattering in the reflection of light from weakly rough random metal surfaces,” Phys. Status Solidi B 247, 2075–2083 (2010).
    [CrossRef]
  11. P. B. Johnson and R. W. Christy, “Optical constants of the noble metals,” Phys. Rev. 6, 4370–4379 (1972).
    [CrossRef]
  12. I. Simonsen, “Optics of surface disordered systems: a random walk through rough surface scattering phenomena,” Eur. Phys. J. Spec. Top. 181, 1–103 (2010).
    [CrossRef]
  13. 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).
    [CrossRef]
  14. G. C. Brown, V. Celli, M. Haller, and A. Marvin, “Vector theory of light scattering from a rough surface: unitary and reciprocal expansions,” Surf. Sci. 136, 381–397 (1984).
    [CrossRef]
  15. Lord Rayleigh, “On the dynamical theory of gratings,” Proc. R. Soc. London, Ser. A 79, 399–416 (1907).
    [CrossRef]
  16. A. G. Voronovich, Wave Scattering from Rough Surfaces, 2nd ed. (Springer-Verlag, 1999), pp. 54–63.
  17. 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]
  18. 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]
  19. A. A. Maradudin, T. Michel, A. R. McGurn, and E. R. Méndez, “Enhanced backscattering of light from a random grating,” Ann. Phys. 203, 255–307 (1990).
    [CrossRef]
  20. 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 (2011).
    [CrossRef]
  21. T. Nordam, P. A. Letnes, and I. Simonsen, “Numerical simulations of scattering of light from two-dimensional surfaces using the reduced Rayleigh equation,” ArXiv 1204.4984 (2012).
  22. P. A. Letnes, A. A. Maradudin, T. Nordam, and I. Simonsen, “Calculation of the Mueller matrix for scattering of light from two-dimensional rough surfaces,” Phys. Rev. A 86, 031803 (2012).
    [CrossRef]
  23. V. Agranovich and D. Mills, eds., Surface Polaritons: Electromagnetic Waves at Surfaces and Interfaces (North-Holland, 1982), pp. 93–145.
  24. A. A. Maradudin, ed., Light Scattering and Nanoscale Surface Roughness (Springer-Verlag, 2007), pp. 107–126.
  25. I. Simonsen, A. A. Maradudin, and T. A. Leskova, “The scattering of electromagnetic waves from two-dimensional randomly rough penetrable surfaces,” Phys. Rev. Lett. 104, 223904 (2010).
    [CrossRef]
  26. I. Simonsen, A. A. Maradudin, and T. A. Leskova, “The scattering of electromagnetic waves from two-dimensional randomly rough perfectly conducting surfaces: the full angular intensity distribution,” Phys. Rev. A 81, 013806 (2010).
    [CrossRef]
  27. T. Nordam, P. A. Letnes, I. Simonsen, and A. A. Maradudin, “Satellite peaks in the scattering of light from the two-dimensional randomly rough surface of a dielectric film on a planar metal surface,” Opt. Express 20, 11336–11350 (2012).
    [CrossRef]
  28. W. H. Press, S. A. Teukolsky, W. T. Vetterling, and B. P. Flannery, Numerical Recipes: The Art of Scientific Computing, 3rd ed. (Cambridge University, 2007), pp. 605–608.

2012

P. A. Letnes, A. A. Maradudin, T. Nordam, and I. Simonsen, “Calculation of the Mueller matrix for scattering of light from two-dimensional rough surfaces,” Phys. Rev. A 86, 031803 (2012).
[CrossRef]

T. Nordam, P. A. Letnes, I. Simonsen, and A. A. Maradudin, “Satellite peaks in the scattering of light from the two-dimensional randomly rough surface of a dielectric film on a planar metal surface,” Opt. Express 20, 11336–11350 (2012).
[CrossRef]

2011

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 (2011).
[CrossRef]

2010

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

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

H. A. Atwater and A. Polman, “Plasmonics for improved photovoltaic devices,” Nat. Mater. 9, 205–213 (2010).
[CrossRef]

I. Simonsen, “Optics of surface disordered systems: a random walk through rough surface scattering phenomena,” Eur. Phys. J. Spec. Top. 181, 1–103 (2010).
[CrossRef]

I. Simonsen, “Enhanced back and forward scattering in the reflection of light from weakly rough random metal surfaces,” Phys. Status Solidi B 247, 2075–2083 (2010).
[CrossRef]

2008

A. Savchenko, E. Kashuba, V. Kashuba, and B. Snopok, “Imaging of plasmid DNA microarrays by scattering light under surface plasmon resonance conditions,” Sens. Lett. 6, 705–713 (2008).
[CrossRef]

2007

A. Savchenko, E. Kashuba, V. Kashuba, and B. Snopok, “Imaging technique for the screening of protein–protein interactions using scattered light under surface plasmon resonance conditions,” Anal. Chem. 79, 1349–1355 (2007).
[CrossRef]

2006

E. Ozbay, “Plasmonics: merging photonics and electronics at nanoscale dimensions,” Science 311, 189–193 (2006).
[CrossRef]

2003

2001

1996

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).
[CrossRef]

1995

1990

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

1985

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]

1984

G. C. Brown, V. Celli, M. Haller, and A. Marvin, “Vector theory of light scattering from a rough surface: unitary and reciprocal expansions,” Surf. Sci. 136, 381–397 (1984).
[CrossRef]

1972

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

1907

Lord Rayleigh, “On the dynamical theory of gratings,” Proc. R. Soc. London, Ser. A 79, 399–416 (1907).
[CrossRef]

Atwater, H. A.

H. A. Atwater and A. Polman, “Plasmonics for improved photovoltaic devices,” Nat. Mater. 9, 205–213 (2010).
[CrossRef]

Berginc, G.

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]

Bourrely, C.

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]

Brown, G. C.

G. C. Brown, V. Celli, M. Haller, and A. Marvin, “Vector theory of light scattering from a rough surface: unitary and reciprocal expansions,” Surf. Sci. 136, 381–397 (1984).
[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]

G. C. Brown, V. Celli, M. Haller, and A. Marvin, “Vector theory of light scattering from a rough surface: unitary and reciprocal expansions,” Surf. Sci. 136, 381–397 (1984).
[CrossRef]

Christy, R. W.

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

Flannery, B. P.

W. H. Press, S. A. Teukolsky, W. T. Vetterling, and B. P. Flannery, Numerical Recipes: The Art of Scientific Computing, 3rd ed. (Cambridge University, 2007), pp. 605–608.

Haller, M.

G. C. Brown, V. Celli, M. Haller, and A. Marvin, “Vector theory of light scattering from a rough surface: unitary and reciprocal expansions,” Surf. Sci. 136, 381–397 (1984).
[CrossRef]

Johnson, P. B.

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

Kashuba, E.

A. Savchenko, E. Kashuba, V. Kashuba, and B. Snopok, “Imaging of plasmid DNA microarrays by scattering light under surface plasmon resonance conditions,” Sens. Lett. 6, 705–713 (2008).
[CrossRef]

A. Savchenko, E. Kashuba, V. Kashuba, and B. Snopok, “Imaging technique for the screening of protein–protein interactions using scattered light under surface plasmon resonance conditions,” Anal. Chem. 79, 1349–1355 (2007).
[CrossRef]

Kashuba, V.

A. Savchenko, E. Kashuba, V. Kashuba, and B. Snopok, “Imaging of plasmid DNA microarrays by scattering light under surface plasmon resonance conditions,” Sens. Lett. 6, 705–713 (2008).
[CrossRef]

A. Savchenko, E. Kashuba, V. Kashuba, and B. Snopok, “Imaging technique for the screening of protein–protein interactions using scattered light under surface plasmon resonance conditions,” Anal. Chem. 79, 1349–1355 (2007).
[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 (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 (2011).
[CrossRef]

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

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

Letnes, P. A.

T. Nordam, P. A. Letnes, I. Simonsen, and A. A. Maradudin, “Satellite peaks in the scattering of light from the two-dimensional randomly rough surface of a dielectric film on a planar metal surface,” Opt. Express 20, 11336–11350 (2012).
[CrossRef]

P. A. Letnes, A. A. Maradudin, T. Nordam, and I. Simonsen, “Calculation of the Mueller matrix for scattering of light from two-dimensional rough surfaces,” Phys. Rev. A 86, 031803 (2012).
[CrossRef]

T. Nordam, P. A. Letnes, and I. Simonsen, “Numerical simulations of scattering of light from two-dimensional surfaces using the reduced Rayleigh equation,” ArXiv 1204.4984 (2012).

Maradudin, A. A.

P. A. Letnes, A. A. Maradudin, T. Nordam, and I. Simonsen, “Calculation of the Mueller matrix for scattering of light from two-dimensional rough surfaces,” Phys. Rev. A 86, 031803 (2012).
[CrossRef]

T. Nordam, P. A. Letnes, I. Simonsen, and A. A. Maradudin, “Satellite peaks in the scattering of light from the two-dimensional randomly rough surface of a dielectric film on a planar metal surface,” Opt. Express 20, 11336–11350 (2012).
[CrossRef]

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 (2011).
[CrossRef]

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

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

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).
[CrossRef]

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

Marvin, A.

G. C. Brown, V. Celli, M. Haller, and A. Marvin, “Vector theory of light scattering from a rough surface: unitary and reciprocal expansions,” Surf. Sci. 136, 381–397 (1984).
[CrossRef]

McGurn, A. R.

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).
[CrossRef]

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

Mendéz, E. R.

Méndez, E. R.

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

Michel, T.

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

Nordam, T.

P. A. Letnes, A. A. Maradudin, T. Nordam, and I. Simonsen, “Calculation of the Mueller matrix for scattering of light from two-dimensional rough surfaces,” Phys. Rev. A 86, 031803 (2012).
[CrossRef]

T. Nordam, P. A. Letnes, I. Simonsen, and A. A. Maradudin, “Satellite peaks in the scattering of light from the two-dimensional randomly rough surface of a dielectric film on a planar metal surface,” Opt. Express 20, 11336–11350 (2012).
[CrossRef]

T. Nordam, P. A. Letnes, and I. Simonsen, “Numerical simulations of scattering of light from two-dimensional surfaces using the reduced Rayleigh equation,” ArXiv 1204.4984 (2012).

O’Donnell, K. A.

Ozbay, E.

E. Ozbay, “Plasmonics: merging photonics and electronics at nanoscale dimensions,” Science 311, 189–193 (2006).
[CrossRef]

Polman, A.

H. A. Atwater and A. Polman, “Plasmonics for improved photovoltaic devices,” Nat. Mater. 9, 205–213 (2010).
[CrossRef]

Press, W. H.

W. H. Press, S. A. Teukolsky, W. T. Vetterling, and B. P. Flannery, Numerical Recipes: The Art of Scientific Computing, 3rd ed. (Cambridge University, 2007), pp. 605–608.

Rayleigh, Lord

Lord Rayleigh, “On the dynamical theory of gratings,” Proc. R. Soc. London, Ser. A 79, 399–416 (1907).
[CrossRef]

Savchenko, A.

A. Savchenko, E. Kashuba, V. Kashuba, and B. Snopok, “Imaging of plasmid DNA microarrays by scattering light under surface plasmon resonance conditions,” Sens. Lett. 6, 705–713 (2008).
[CrossRef]

A. Savchenko, E. Kashuba, V. Kashuba, and B. Snopok, “Imaging technique for the screening of protein–protein interactions using scattered light under surface plasmon resonance conditions,” Anal. Chem. 79, 1349–1355 (2007).
[CrossRef]

Simonsen, I.

T. Nordam, P. A. Letnes, I. Simonsen, and A. A. Maradudin, “Satellite peaks in the scattering of light from the two-dimensional randomly rough surface of a dielectric film on a planar metal surface,” Opt. Express 20, 11336–11350 (2012).
[CrossRef]

P. A. Letnes, A. A. Maradudin, T. Nordam, and I. Simonsen, “Calculation of the Mueller matrix for scattering of light from two-dimensional rough surfaces,” Phys. Rev. A 86, 031803 (2012).
[CrossRef]

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 (2011).
[CrossRef]

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

I. Simonsen, A. A. Maradudin, and T. A. Leskova, “The 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, “Enhanced back and forward scattering in the reflection of light from weakly rough random metal surfaces,” Phys. Status Solidi B 247, 2075–2083 (2010).
[CrossRef]

I. Simonsen, “Optics of surface disordered systems: a random walk through rough surface scattering phenomena,” Eur. Phys. J. Spec. Top. 181, 1–103 (2010).
[CrossRef]

T. Nordam, P. A. Letnes, and I. Simonsen, “Numerical simulations of scattering of light from two-dimensional surfaces using the reduced Rayleigh equation,” ArXiv 1204.4984 (2012).

Snopok, B.

A. Savchenko, E. Kashuba, V. Kashuba, and B. Snopok, “Imaging of plasmid DNA microarrays by scattering light under surface plasmon resonance conditions,” Sens. Lett. 6, 705–713 (2008).
[CrossRef]

A. Savchenko, E. Kashuba, V. Kashuba, and B. Snopok, “Imaging technique for the screening of protein–protein interactions using scattered light under surface plasmon resonance conditions,” Anal. Chem. 79, 1349–1355 (2007).
[CrossRef]

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. A.

W. H. Press, S. A. Teukolsky, W. T. Vetterling, and B. P. Flannery, Numerical Recipes: The Art of Scientific Computing, 3rd ed. (Cambridge University, 2007), pp. 605–608.

Vetterling, W. T.

W. H. Press, S. A. Teukolsky, W. T. Vetterling, and B. P. Flannery, Numerical Recipes: The Art of Scientific Computing, 3rd ed. (Cambridge University, 2007), pp. 605–608.

Voronovich, A. G.

A. G. Voronovich, Wave Scattering from Rough Surfaces, 2nd ed. (Springer-Verlag, 1999), pp. 54–63.

West, C. S.

Anal. Chem.

A. Savchenko, E. Kashuba, V. Kashuba, and B. Snopok, “Imaging technique for the screening of protein–protein interactions using scattered light under surface plasmon resonance conditions,” Anal. Chem. 79, 1349–1355 (2007).
[CrossRef]

Ann. Phys.

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

Comput. Phys. Commun.

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 (2011).
[CrossRef]

Eur. Phys. J. Spec. Top.

I. Simonsen, “Optics of surface disordered systems: a random walk through rough surface scattering phenomena,” Eur. Phys. J. Spec. Top. 181, 1–103 (2010).
[CrossRef]

J. Opt. Soc. Am. A

Nat. Mater.

H. A. Atwater and A. Polman, “Plasmonics for improved photovoltaic devices,” Nat. Mater. 9, 205–213 (2010).
[CrossRef]

Opt. Express

Phys. Rev.

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

Phys. Rev. A

P. A. Letnes, A. A. Maradudin, T. Nordam, and I. Simonsen, “Calculation of the Mueller matrix for scattering of light from two-dimensional rough surfaces,” Phys. Rev. A 86, 031803 (2012).
[CrossRef]

I. Simonsen, A. A. Maradudin, and T. A. Leskova, “The 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

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]

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]

Phys. Rev. Lett.

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

Phys. Status Solidi B

I. Simonsen, “Enhanced back and forward scattering in the reflection of light from weakly rough random metal surfaces,” Phys. Status Solidi B 247, 2075–2083 (2010).
[CrossRef]

Proc. R. Soc. London, Ser. A

Lord Rayleigh, “On the dynamical theory of gratings,” Proc. R. Soc. London, Ser. A 79, 399–416 (1907).
[CrossRef]

Science

E. Ozbay, “Plasmonics: merging photonics and electronics at nanoscale dimensions,” Science 311, 189–193 (2006).
[CrossRef]

Sens. Lett.

A. Savchenko, E. Kashuba, V. Kashuba, and B. Snopok, “Imaging of plasmid DNA microarrays by scattering light under surface plasmon resonance conditions,” Sens. Lett. 6, 705–713 (2008).
[CrossRef]

Surf. Sci.

G. C. Brown, V. Celli, M. Haller, and A. Marvin, “Vector theory of light scattering from a rough surface: unitary and reciprocal expansions,” Surf. Sci. 136, 381–397 (1984).
[CrossRef]

Waves Random Media

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).
[CrossRef]

Other

A. G. Voronovich, Wave Scattering from Rough Surfaces, 2nd ed. (Springer-Verlag, 1999), pp. 54–63.

We have chosen to use the term “enhanced forward scattering,” because it is an enhancement in the incoherently scattered light and because “specular scattering” is often understood to mean “coherent scattering.”

W. H. Press, S. A. Teukolsky, W. T. Vetterling, and B. P. Flannery, Numerical Recipes: The Art of Scientific Computing, 3rd ed. (Cambridge University, 2007), pp. 605–608.

V. Agranovich and D. Mills, eds., Surface Polaritons: Electromagnetic Waves at Surfaces and Interfaces (North-Holland, 1982), pp. 93–145.

A. A. Maradudin, ed., Light Scattering and Nanoscale Surface Roughness (Springer-Verlag, 2007), pp. 107–126.

T. Nordam, P. A. Letnes, and I. Simonsen, “Numerical simulations of scattering of light from two-dimensional surfaces using the reduced Rayleigh equation,” ArXiv 1204.4984 (2012).

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Figures (7)

Fig. 1.
Fig. 1.

Sketches of the system under study (surface roughness not shown). (a) The light of wave vector k incident on the surface causes scattering into various propagating modes (of wave vector q) and the excitation of SPPs (kspp). In this study, we assume ε1(ω)1, and ε2(ω) is taken from [11]. (b) Definition of the lateral wave vectors (k and q) as well as the polar angles of incidence and scattering.

Fig. 2.
Fig. 2.

Four scattering processes important for understanding the results of this study. A detailed discussion of the figure is found in the text. All subfigures (a)–(d) are drawn to correct and identical scale for the parameters k±(i) and ε2 used throughout this study. The blue annular regions indicate the nonzero parts of the power spectrum, that is, the ranges of ksc allowed by the power spectrum. The lengths of k in (a) and (b) correspond to (θ0,ϕ0)=(27°,45°).

Fig. 3.
Fig. 3.

Full angular distribution of the incoherent contribution to the MDRC, assuming the surface properties stated in the text. The angles of incidence were (θ0,ϕ0)=(12.5°,45°). The subplots show scattering (b) from p polarization to p polarization, (e) sp, (c) ps, and (f) ss. In (a), the incident light was p-polarized, but the polarization of the scattered light was not recorded, and in (d) the incident light was s-polarized. The enhanced forward scattering peak is most easily seen in the pp configuration (b). The sharp circular edge, centered on k, is caused by the suppression of single scattering due to the form of the power spectrum; see discussion in Section 2.D, Eq. (3), and Fig. 2(a).

Fig. 4.
Fig. 4.

In-plane (i.e., for ϕs=ϕ0) part of the MDRC for light scattered from a rough silver surface with rms roughness δ=0.025λ. The angles of incidence were (θ0,ϕ0)=(12.5°,45°). The results were obtained by averaging over 10,825 surface realizations. The most prominent enhanced forward scattering peak is in pp polarization, but a small contribution in sp polarization can also be seen. Enhanced backscattering is observed in all polarization combinations.

Fig. 5.
Fig. 5.

pp contribution to the MDRC for the same surface properties as in Fig. 4 for several different angles of incidence. In all cases, we observe the enhanced forward scattering peak. The effect is most powerful in the vicinity of θ012°. For polar angle of incidence θ0=29.5°, it is not possible to achieve enhanced forward scattering through the in-plane SPP channel; hence, the peak at θs=29.5° has a different explanation.

Fig. 6.
Fig. 6.

Contour plots of the incoherent, in-plane, and pp part of the MDRC as a function of angle of incidence (θ0) and scattering (θs). We assume ϕs=ϕ0 in these figures. (a) The enhanced backscattering peak is shown as a purple “ridge” at θs=θ0. The oscillatory behavior with angle of incidence that the enhanced backscattering peak seems to exhibit in (a) is believed to be an artifact of the interpolation routine used to produce the figure from the discrete simulation data. (b) The enhanced forward scattering peak is shown as a purple “ridge” at θs=θ0. Note that the color map has been truncated [cf. (a)] to show the peak more clearly.

Fig. 7.
Fig. 7.

In-plane pp scattering for power spectra with (a) γ1=1, γ2=0 and (b) γ1=0, γ2=1. With γ1=0, γ2=1, coupling into SPPs is suppressed. With γ1=1, γ2=0, coupling into SPPs is allowed but not scattering from an SPP to a counterpropagating SPP. This allows enhanced backscattering but not enhanced forward scattering.

Equations (24)

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ζ(x)=0,
ζ(x)ζ(x)=δ2W(xx),
g(k)=d2xW(x)exp(ik·x),
g(k)=γ1g1(k)+γ2g2(k)
gi(k)=4πk+2k2θ(kk(i))θ(k+(i)k).
E(x|t)=[E(0)(x|ω)+E(s)(x|ω)]exp(iωt),
E(0)(x|ω)={cω[k^α1(k)+x^3k]Ep(0)(k)+(x^3×k^)Es(0)(k)}exp[ik·xiα1(k)x3],
E(s)(x|ω)=d2q(2π)2{cω[q^α1(q)x^3q]Ep(s)(q)+(x^3×q^)Es(s)(q)}exp[iq·x+iα1(q)x3],
αi(q)=[εi(ωc)2q2]1/2,Reαi(q)>0,Imαi(q)>0.
Eα(s)(q)=β=p,sRαβ(q|k)Eβ(0)(k).
R(q|k)=(Rpp(q|k)Rps(q|k)Rsp(q|k)Rss(q|k)),
d2q(2π)2I(α2(p)α1(q)|pq)α2(p)α1(q)M+(p|q)R(q|k)=I(α2(p)+α1(k)|pk)α2(p)+α1(k)M(p|k),
I(γ|Q)=d2xexp[iγζ(x)]exp(iQ·x),
M±(p|q)=(pq±α2(p)p^·q^α1(q)ωcα2(p)[p^×q^]3±ωc[p^×q^]3α1(q)ω2c2p^·q^).
RαβΩs=1L2ω24π2c2cos2θscosθ0|Rαβ(q|k)|2.
RαβΩsincoh=1L2ω24π2c2cos2θscosθ0×[|Rαβ(q|k)|2|Rαβ(q|k)|2].
kspp(ω)=ωc(ε2(ω)ε2(ω)+1)1/2,
g(ksc)>0,ksc=qk.
g(|ksc|)>0.
k(1)<|ksppk|<k+(1),
k(2)<|ksppk|<k+(2).
k(1)<|kspp+k|<k+(1).
k(1)<|kspp(2)kspp(1)|<k+(1)
k(2)<|kspp(2)kspp(1)|<k+(2).

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