Abstract

We study the light scattered from randomly rough, one-dimensional, self-affine fractal silver surfaces with nanoscale lower cutoff illuminated by s- or p-polarized Gaussian beams a few micrometers wide. By means of rigorous numerical calculations based on the Green’s theorem integral equation formulation (GTIEF), we obtain both the far- and near-field scattered intensities. The influence of diminishing the size of the fractal lower-scale irregularities (from ∼50 nm to a few nanometers) is analyzed in the case of both single realization and ensemble-average magnitudes. For s polarization, variations are small in the far field, being significant only in the higher-spatial-frequency components of evanescent character in the near field. In the case of p polarization, however, the nanoscale cutoff has remarkable effects stemming from the roughness-induced excitation of surface-plasmon polaritons. In the far field, the effect is noticed both in the speckle pattern variation and in the decrease of the total reflected energy upon ensemble averaging, as a result of increased absorption. In the near field, more efficient excitation of localized optical modes is achieved with smaller cutoff, which in turn leads to huge surface electric field enhancements.

© 2002 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. B. B. Mandelbrot, Fractals (Freeman, San Francisco, Calif., 1977).
  2. J. Feder, Fractals (Plenum, New York, 1988).
  3. A.-L. Barabási, H. E. Stanley, Fractal Concepts in Surface Growth (Cambridge U. Press, Cambridge, UK, 1995).
  4. M. V. Berry, “Difractals,” J. Appl. Phys. 12, 781–797 (1979).
  5. E. Jakeman, “Fraunhofer scattering by a sub-fractal diffuser,” Opt. Acta 30, 1207–1212 (1983).
    [CrossRef]
  6. D. L. Jaggard, Y. Kim, “Diffraction by band-limited fractal screens,” J. Opt. Soc. Am. A 4, 1055–1062 (1987).
    [CrossRef]
  7. R. Jullien, R. Botet, “Geometrical optics in fractals,” Physica D 38, 208–212 (1989).
    [CrossRef]
  8. S. K. Sinha, “Scattering from fractal structures,” Physica D 38, 310–314 (1989).
    [CrossRef]
  9. B. J. West, “Sensing scaled scintillations,” J. Opt. Soc. Am. A 7, 1074–1100 (1990).
    [CrossRef]
  10. D. L. Jaggard, X. Sun, “Scattering from fractally corrugated surfaces,” J. Opt. Soc. Am. A 7, 1131–1139 (1990).
    [CrossRef]
  11. H. N. Yang, T. M. Lu, G. C. Wang, “Diffraction from surface growth fronts,” Phys. Rev. B 47, 3911–3922 (1993).
    [CrossRef]
  12. P. E. McSharry, P. J. Cullen, D. Moroney, “Wave scattering by a two-dimensional band limited fractal surface based on a perturbation of the Green’s function,” J. Appl. Phys. 78, 6940–6948 (1995).
    [CrossRef]
  13. N. Lin, H. P. Lee, S. P. Lim, K. S. Lee, “Wave scattering from fractal surfaces,” J. Mod. Opt. 42, 225–241 (1995).
    [CrossRef]
  14. S. Savaidis, P. Frangos, D. L. Jaggard, K. Hizanidis, “Scattering from fractally corrugated surfaces: an exact approach,” Opt. Lett. 20, 2357–2359 (1995).
    [CrossRef] [PubMed]
  15. S. Savaidis, P. Frangos, D. L. Jaggard, K. Hizanidis, “Scattering from fractally corrugated surfaces with use of the extended boundary condition method,” J. Opt. Soc. Am. A 14, 475–485 (1997).
    [CrossRef]
  16. J. Chen, T. K. Y. Lo, H. Leung, J. Litva, “The use of fractals for modeling EM wave scattering from rough sea surface,” IEEE Trans. Geosci. Remote Sens. 34, 966–972 (1996).
    [CrossRef]
  17. C. J. R. Sheppard, “Scattering by fractal surfaces with an outer scale,” Opt. Commun. 122, 178–188 (1996).
    [CrossRef]
  18. A. Mendoza-Suárez, E. R. Méndez, “Light scattering by a reentrant fractal surface,” Appl. Opt. 36, 3521–3531 (1997).
    [CrossRef] [PubMed]
  19. J. A. Sánchez-Gil, J. V. Garcı́a-Ramos, “Far-field intensity of electromagnetic waves scattered from random, self-affine fractal metal surfaces,” Waves Random Media 7, 285–293 (1997).
    [CrossRef]
  20. I. Simonsen, A. Hansen, O. M. Nes, “Determination of Hurst exponents by use of the wavelet transform,” Phys. Rev. E 58, 2779–2787 (1998).
    [CrossRef]
  21. Y. P. Zhao, G. C. Wang, T. M. Lu, “Diffraction from non-Gaussian rough surfaces,” Phys. Rev. B 55, 13938–13952 (1997).
    [CrossRef]
  22. G. Franceschetti, A. Iodice, D. Riccio, “Scattering from dielectric random fractal surfaces via method of moments,” IEEE Trans. Geosci. Remote Sens. 38, 1644–1655 (2000).
    [CrossRef]
  23. I. Simonsen, D. Vandembroucq, S. Roux, “Wave scattering from self-affine surfaces,” Phys. Rev. E 61, 5914–5917 (2000).
    [CrossRef]
  24. I. Simonsen, D. Vandembroucq, S. Roux, “Electromagnetic wave scattering from conducting self-affine surfaces: an analytic and numerical study,” J. Opt. Soc. Am. A 18, 1101–1111 (2001).
    [CrossRef]
  25. A. A. Maradudin, T. Michel, A. R. McGurn, E. R. Méndez, “Enhanced backscattering of light from a random grating,” Ann. Phys. (New York) 203, 255–307 (1990).
    [CrossRef]
  26. M. Nieto-Vesperinas, Scattering and Diffraction in Physical Optics (Wiley, New York, 1991).
  27. J. A. Sánchez-Gil, M. Nieto-Vesperinas, “Light scattering from random rough dielectric surfaces,” J. Opt. Soc. Am. A 8, 1270–1286 (1991).
    [CrossRef]
  28. J. A. Sánchez-Gil, M. Nieto-Vesparinas, “Resonance effects in multiple light scattering from statistically rough metallic surfaces,” Phys. Rev. B 45, 8623–8633 (1992).
    [CrossRef]
  29. V. M. Shalaev, “Electromagnetic properties of small-particle composites,” Phys. Rep. 272, 61–137 (1996).
    [CrossRef]
  30. E. Y. Poliakov, V. M. Shalaev, V. A. Markel, R. Botet, “Enhanced Raman scattering from self-affine thin films,” Opt. Lett. 21, 1628–1630 (1996).
    [CrossRef] [PubMed]
  31. J. A. Sánchez-Gil, J. V. Garcı́a-Ramos, “Strong surface field enhancements in the scattering of p-polarized light from fractal metal surfaces,” Opt. Commun. 134, 11–15 (1997).
    [CrossRef]
  32. J. A. Sánchez-Gil, J. V. Garcı́a-Ramos, “Calculations of the direct electromagnetic enhancement in surface enhanced Raman scattering on random self-affine fractal metal surfaces,” J. Chem. Phys. 108, 317–325 (1998).
    [CrossRef]
  33. E. Y. Poliakov, V. A. Markel, V. M. Shalaev, R. Botet, “Nonlinear optical phenomena on rough surfaces of metal thin films,” Phys. Rev. B 57, 14901–14913 (1998).
    [CrossRef]
  34. S. Grésillon, L. Aigouy, A. C. Boccara, J. C. Rivoal, X. Quelin, C. Desmaret, P. Gadenne, V. A. Shubin, A. K. Sarychev, V. M. Shalaev, “Experimental observation of localized optical excitations in random metal-dielectric films,” Phys. Rev. Lett. 82, 4520–4523 (1999).
    [CrossRef]
  35. J. A. Sánchez-Gil, J. V. Garcı́a-Ramos, E. R. Méndez, “Near-field electromagnetic wave scattering from random self-affine fractal metal surfaces: spectral dependence of local field enhancements and their statistics in connection with surface-enhanced Raman scattering,” Phys. Rev. B 62, 10515–10525 (2000).
    [CrossRef]
  36. D. P. Tsai, J. Kovacs, Z. Wang, M. Moskovits, V. M. Shalaev, J. S. Suh, R. Botet, “Photon scanning tunneling microscopy images of optical excitations of fractal metal colloid clusters,” Phys. Rev. Lett. 72, 4149–4152 (1994).
    [CrossRef] [PubMed]
  37. S. Bozhevolnyi, B. Vohnsen, I. I. Smolyaninov, A. V. Zayats, “Direct observation of surface polariton localization caused by surface roughness,” Opt. Commun. 117, 417–423 (1995).
    [CrossRef]
  38. S. Bozhevolnyi, B. Vohnsen, A. V. Zayats, I. I. Smolyaninov, “Fractal surface characterization: implications for plasmon polariton scattering,” Surf. Sci. 356, 268–274 (1996).
    [CrossRef]
  39. P. Zhang, T. L. Haslett, C. Douketis, M. Moskovits, “Mode localization in self-affine fractal interfaces observed by near-field microscopy,” Phys. Rev. B 57, 15513–15518 (1998).
    [CrossRef]
  40. S. Bozhevolnyi, V. A. Markel, V. Coello, W. Kim, V. M. Shalaev, “Direct observation of localized dipolar excitations on rough nanostructured surfaces,” Phys. Rev. B 58, 11441–11448 (1998).
    [CrossRef]
  41. V. A. Markel, V. M. Shalaev, P. Zhang, W. Huynh, L. Tay, T. L. Haslett, M. Moskovits, “Near-field optical spectroscopy of individual surface-plasmon modes in colloid clusters,” Phys. Rev. B 59, 10903–10909 (1999).
    [CrossRef]
  42. K. A. O’Donnell, R. Torre, C. S. West, “Observations of backscattering effects in second-harmonic generation from a weakly rough metal surface,” Opt. Lett. 21, 1738–1740 (1996).
    [CrossRef] [PubMed]
  43. M. Leyva-Lucero, E. R. Méndez, T. A. Leskova, A. A. Maradudin, J. Q. Lu, “Multiple-scattering effects in the second-harmonic generation of light in reflection from a randomly rough metal surface,” Opt. Lett. 21, 1809–1811 (1996).
    [CrossRef] [PubMed]
  44. S. Nie, S. R. Emory, “Probing single molecules and single nanoparticles by surface-enhanced Raman scattering,” Science 275, 1102–1106 (1997).
    [CrossRef] [PubMed]
  45. K. Kneipp, Y. Wang, H. Kneipp, L. T. Perlman, I. Itzkan, R. R. Dasari, M. S. Feld, “Single molecule detection using surface-enhanced Raman scattering (SERS),” Phys. Rev. Lett. 78, 1667–1670 (1997).
    [CrossRef]
  46. H. Xu, E. J. Bjerneld, M. Käll, L. Börjesson, “Spectroscopy of single hemoglobin molecules by surface-enhanced Raman scattering,” Phys. Rev. Lett. 83, 4357–4360 (1999).
    [CrossRef]
  47. R. F. Voss, in The Science of Fractal Images, H.-O. Peitgen, D. Saupe, eds. (Springer, Berlin, 1988).
  48. R. F. Voss, “Random fractals: self-affinity in noise, mountains, and clouds,” Physica D 38, 362–371 (1989).
    [CrossRef]
  49. D. W. Lynch, W. R. Hunter in Handbook of Optical Constants of Solids, E. D. Palik, ed. (Academic Press, New York, 1985), p. 356.
  50. 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]
  51. J. J. Greffet, A. Sentenac, R. Carminati, “Surface profile reconstruction using near-field data,” Opt. Commun. 116, 20–24 (1995).
    [CrossRef]
  52. J. A. Sánchez-Gil, J. V. Garcı́a-Ramos, E. R. Méndez, “Influence of nanoscale cutoff in random self-affine fractal silver surfaces on the excitation of localized optical modes,” Opt. Lett. 26, 1286–1288 (2001).
    [CrossRef]
  53. E. Devaux, A. Dereux, E. Bourillot, J.-C. Weeber, Y. Lacroute, J.-P. Goudonnet, C. Girard, “Local detection of the optical magnetic field in the near zone of dielectric samples,” Phys. Rev. B 62, 10504–10514 (2000).
    [CrossRef]

2001

2000

G. Franceschetti, A. Iodice, D. Riccio, “Scattering from dielectric random fractal surfaces via method of moments,” IEEE Trans. Geosci. Remote Sens. 38, 1644–1655 (2000).
[CrossRef]

I. Simonsen, D. Vandembroucq, S. Roux, “Wave scattering from self-affine surfaces,” Phys. Rev. E 61, 5914–5917 (2000).
[CrossRef]

J. A. Sánchez-Gil, J. V. Garcı́a-Ramos, E. R. Méndez, “Near-field electromagnetic wave scattering from random self-affine fractal metal surfaces: spectral dependence of local field enhancements and their statistics in connection with surface-enhanced Raman scattering,” Phys. Rev. B 62, 10515–10525 (2000).
[CrossRef]

E. Devaux, A. Dereux, E. Bourillot, J.-C. Weeber, Y. Lacroute, J.-P. Goudonnet, C. Girard, “Local detection of the optical magnetic field in the near zone of dielectric samples,” Phys. Rev. B 62, 10504–10514 (2000).
[CrossRef]

1999

H. Xu, E. J. Bjerneld, M. Käll, L. Börjesson, “Spectroscopy of single hemoglobin molecules by surface-enhanced Raman scattering,” Phys. Rev. Lett. 83, 4357–4360 (1999).
[CrossRef]

V. A. Markel, V. M. Shalaev, P. Zhang, W. Huynh, L. Tay, T. L. Haslett, M. Moskovits, “Near-field optical spectroscopy of individual surface-plasmon modes in colloid clusters,” Phys. Rev. B 59, 10903–10909 (1999).
[CrossRef]

S. Grésillon, L. Aigouy, A. C. Boccara, J. C. Rivoal, X. Quelin, C. Desmaret, P. Gadenne, V. A. Shubin, A. K. Sarychev, V. M. Shalaev, “Experimental observation of localized optical excitations in random metal-dielectric films,” Phys. Rev. Lett. 82, 4520–4523 (1999).
[CrossRef]

1998

J. A. Sánchez-Gil, J. V. Garcı́a-Ramos, “Calculations of the direct electromagnetic enhancement in surface enhanced Raman scattering on random self-affine fractal metal surfaces,” J. Chem. Phys. 108, 317–325 (1998).
[CrossRef]

E. Y. Poliakov, V. A. Markel, V. M. Shalaev, R. Botet, “Nonlinear optical phenomena on rough surfaces of metal thin films,” Phys. Rev. B 57, 14901–14913 (1998).
[CrossRef]

I. Simonsen, A. Hansen, O. M. Nes, “Determination of Hurst exponents by use of the wavelet transform,” Phys. Rev. E 58, 2779–2787 (1998).
[CrossRef]

P. Zhang, T. L. Haslett, C. Douketis, M. Moskovits, “Mode localization in self-affine fractal interfaces observed by near-field microscopy,” Phys. Rev. B 57, 15513–15518 (1998).
[CrossRef]

S. Bozhevolnyi, V. A. Markel, V. Coello, W. Kim, V. M. Shalaev, “Direct observation of localized dipolar excitations on rough nanostructured surfaces,” Phys. Rev. B 58, 11441–11448 (1998).
[CrossRef]

1997

S. Savaidis, P. Frangos, D. L. Jaggard, K. Hizanidis, “Scattering from fractally corrugated surfaces with use of the extended boundary condition method,” J. Opt. Soc. Am. A 14, 475–485 (1997).
[CrossRef]

S. Nie, S. R. Emory, “Probing single molecules and single nanoparticles by surface-enhanced Raman scattering,” Science 275, 1102–1106 (1997).
[CrossRef] [PubMed]

K. Kneipp, Y. Wang, H. Kneipp, L. T. Perlman, I. Itzkan, R. R. Dasari, M. S. Feld, “Single molecule detection using surface-enhanced Raman scattering (SERS),” Phys. Rev. Lett. 78, 1667–1670 (1997).
[CrossRef]

Y. P. Zhao, G. C. Wang, T. M. Lu, “Diffraction from non-Gaussian rough surfaces,” Phys. Rev. B 55, 13938–13952 (1997).
[CrossRef]

J. A. Sánchez-Gil, J. V. Garcı́a-Ramos, “Strong surface field enhancements in the scattering of p-polarized light from fractal metal surfaces,” Opt. Commun. 134, 11–15 (1997).
[CrossRef]

J. A. Sánchez-Gil, J. V. Garcı́a-Ramos, “Far-field intensity of electromagnetic waves scattered from random, self-affine fractal metal surfaces,” Waves Random Media 7, 285–293 (1997).
[CrossRef]

A. Mendoza-Suárez, E. R. Méndez, “Light scattering by a reentrant fractal surface,” Appl. Opt. 36, 3521–3531 (1997).
[CrossRef] [PubMed]

1996

E. Y. Poliakov, V. M. Shalaev, V. A. Markel, R. Botet, “Enhanced Raman scattering from self-affine thin films,” Opt. Lett. 21, 1628–1630 (1996).
[CrossRef] [PubMed]

K. A. O’Donnell, R. Torre, C. S. West, “Observations of backscattering effects in second-harmonic generation from a weakly rough metal surface,” Opt. Lett. 21, 1738–1740 (1996).
[CrossRef] [PubMed]

M. Leyva-Lucero, E. R. Méndez, T. A. Leskova, A. A. Maradudin, J. Q. Lu, “Multiple-scattering effects in the second-harmonic generation of light in reflection from a randomly rough metal surface,” Opt. Lett. 21, 1809–1811 (1996).
[CrossRef] [PubMed]

J. Chen, T. K. Y. Lo, H. Leung, J. Litva, “The use of fractals for modeling EM wave scattering from rough sea surface,” IEEE Trans. Geosci. Remote Sens. 34, 966–972 (1996).
[CrossRef]

C. J. R. Sheppard, “Scattering by fractal surfaces with an outer scale,” Opt. Commun. 122, 178–188 (1996).
[CrossRef]

V. M. Shalaev, “Electromagnetic properties of small-particle composites,” Phys. Rep. 272, 61–137 (1996).
[CrossRef]

S. Bozhevolnyi, B. Vohnsen, A. V. Zayats, I. I. Smolyaninov, “Fractal surface characterization: implications for plasmon polariton scattering,” Surf. Sci. 356, 268–274 (1996).
[CrossRef]

1995

S. Bozhevolnyi, B. Vohnsen, I. I. Smolyaninov, A. V. Zayats, “Direct observation of surface polariton localization caused by surface roughness,” Opt. Commun. 117, 417–423 (1995).
[CrossRef]

P. E. McSharry, P. J. Cullen, D. Moroney, “Wave scattering by a two-dimensional band limited fractal surface based on a perturbation of the Green’s function,” J. Appl. Phys. 78, 6940–6948 (1995).
[CrossRef]

N. Lin, H. P. Lee, S. P. Lim, K. S. Lee, “Wave scattering from fractal surfaces,” J. Mod. Opt. 42, 225–241 (1995).
[CrossRef]

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]

S. Savaidis, P. Frangos, D. L. Jaggard, K. Hizanidis, “Scattering from fractally corrugated surfaces: an exact approach,” Opt. Lett. 20, 2357–2359 (1995).
[CrossRef] [PubMed]

J. J. Greffet, A. Sentenac, R. Carminati, “Surface profile reconstruction using near-field data,” Opt. Commun. 116, 20–24 (1995).
[CrossRef]

1994

D. P. Tsai, J. Kovacs, Z. Wang, M. Moskovits, V. M. Shalaev, J. S. Suh, R. Botet, “Photon scanning tunneling microscopy images of optical excitations of fractal metal colloid clusters,” Phys. Rev. Lett. 72, 4149–4152 (1994).
[CrossRef] [PubMed]

1993

H. N. Yang, T. M. Lu, G. C. Wang, “Diffraction from surface growth fronts,” Phys. Rev. B 47, 3911–3922 (1993).
[CrossRef]

1992

J. A. Sánchez-Gil, M. Nieto-Vesparinas, “Resonance effects in multiple light scattering from statistically rough metallic surfaces,” Phys. Rev. B 45, 8623–8633 (1992).
[CrossRef]

1991

1990

B. J. West, “Sensing scaled scintillations,” J. Opt. Soc. Am. A 7, 1074–1100 (1990).
[CrossRef]

D. L. Jaggard, X. Sun, “Scattering from fractally corrugated surfaces,” J. Opt. Soc. Am. A 7, 1131–1139 (1990).
[CrossRef]

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

1989

R. F. Voss, “Random fractals: self-affinity in noise, mountains, and clouds,” Physica D 38, 362–371 (1989).
[CrossRef]

R. Jullien, R. Botet, “Geometrical optics in fractals,” Physica D 38, 208–212 (1989).
[CrossRef]

S. K. Sinha, “Scattering from fractal structures,” Physica D 38, 310–314 (1989).
[CrossRef]

1987

1983

E. Jakeman, “Fraunhofer scattering by a sub-fractal diffuser,” Opt. Acta 30, 1207–1212 (1983).
[CrossRef]

1979

M. V. Berry, “Difractals,” J. Appl. Phys. 12, 781–797 (1979).

Aigouy, L.

S. Grésillon, L. Aigouy, A. C. Boccara, J. C. Rivoal, X. Quelin, C. Desmaret, P. Gadenne, V. A. Shubin, A. K. Sarychev, V. M. Shalaev, “Experimental observation of localized optical excitations in random metal-dielectric films,” Phys. Rev. Lett. 82, 4520–4523 (1999).
[CrossRef]

Barabási, A.-L.

A.-L. Barabási, H. E. Stanley, Fractal Concepts in Surface Growth (Cambridge U. Press, Cambridge, UK, 1995).

Berry, M. V.

M. V. Berry, “Difractals,” J. Appl. Phys. 12, 781–797 (1979).

Bjerneld, E. J.

H. Xu, E. J. Bjerneld, M. Käll, L. Börjesson, “Spectroscopy of single hemoglobin molecules by surface-enhanced Raman scattering,” Phys. Rev. Lett. 83, 4357–4360 (1999).
[CrossRef]

Boccara, A. C.

S. Grésillon, L. Aigouy, A. C. Boccara, J. C. Rivoal, X. Quelin, C. Desmaret, P. Gadenne, V. A. Shubin, A. K. Sarychev, V. M. Shalaev, “Experimental observation of localized optical excitations in random metal-dielectric films,” Phys. Rev. Lett. 82, 4520–4523 (1999).
[CrossRef]

Börjesson, L.

H. Xu, E. J. Bjerneld, M. Käll, L. Börjesson, “Spectroscopy of single hemoglobin molecules by surface-enhanced Raman scattering,” Phys. Rev. Lett. 83, 4357–4360 (1999).
[CrossRef]

Botet, R.

E. Y. Poliakov, V. A. Markel, V. M. Shalaev, R. Botet, “Nonlinear optical phenomena on rough surfaces of metal thin films,” Phys. Rev. B 57, 14901–14913 (1998).
[CrossRef]

E. Y. Poliakov, V. M. Shalaev, V. A. Markel, R. Botet, “Enhanced Raman scattering from self-affine thin films,” Opt. Lett. 21, 1628–1630 (1996).
[CrossRef] [PubMed]

D. P. Tsai, J. Kovacs, Z. Wang, M. Moskovits, V. M. Shalaev, J. S. Suh, R. Botet, “Photon scanning tunneling microscopy images of optical excitations of fractal metal colloid clusters,” Phys. Rev. Lett. 72, 4149–4152 (1994).
[CrossRef] [PubMed]

R. Jullien, R. Botet, “Geometrical optics in fractals,” Physica D 38, 208–212 (1989).
[CrossRef]

Bourillot, E.

E. Devaux, A. Dereux, E. Bourillot, J.-C. Weeber, Y. Lacroute, J.-P. Goudonnet, C. Girard, “Local detection of the optical magnetic field in the near zone of dielectric samples,” Phys. Rev. B 62, 10504–10514 (2000).
[CrossRef]

Bozhevolnyi, S.

S. Bozhevolnyi, V. A. Markel, V. Coello, W. Kim, V. M. Shalaev, “Direct observation of localized dipolar excitations on rough nanostructured surfaces,” Phys. Rev. B 58, 11441–11448 (1998).
[CrossRef]

S. Bozhevolnyi, B. Vohnsen, A. V. Zayats, I. I. Smolyaninov, “Fractal surface characterization: implications for plasmon polariton scattering,” Surf. Sci. 356, 268–274 (1996).
[CrossRef]

S. Bozhevolnyi, B. Vohnsen, I. I. Smolyaninov, A. V. Zayats, “Direct observation of surface polariton localization caused by surface roughness,” Opt. Commun. 117, 417–423 (1995).
[CrossRef]

Carminati, R.

J. J. Greffet, A. Sentenac, R. Carminati, “Surface profile reconstruction using near-field data,” Opt. Commun. 116, 20–24 (1995).
[CrossRef]

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]

Chen, J.

J. Chen, T. K. Y. Lo, H. Leung, J. Litva, “The use of fractals for modeling EM wave scattering from rough sea surface,” IEEE Trans. Geosci. Remote Sens. 34, 966–972 (1996).
[CrossRef]

Coello, V.

S. Bozhevolnyi, V. A. Markel, V. Coello, W. Kim, V. M. Shalaev, “Direct observation of localized dipolar excitations on rough nanostructured surfaces,” Phys. Rev. B 58, 11441–11448 (1998).
[CrossRef]

Cullen, P. J.

P. E. McSharry, P. J. Cullen, D. Moroney, “Wave scattering by a two-dimensional band limited fractal surface based on a perturbation of the Green’s function,” J. Appl. Phys. 78, 6940–6948 (1995).
[CrossRef]

Dasari, R. R.

K. Kneipp, Y. Wang, H. Kneipp, L. T. Perlman, I. Itzkan, R. R. Dasari, M. S. Feld, “Single molecule detection using surface-enhanced Raman scattering (SERS),” Phys. Rev. Lett. 78, 1667–1670 (1997).
[CrossRef]

Dereux, A.

E. Devaux, A. Dereux, E. Bourillot, J.-C. Weeber, Y. Lacroute, J.-P. Goudonnet, C. Girard, “Local detection of the optical magnetic field in the near zone of dielectric samples,” Phys. Rev. B 62, 10504–10514 (2000).
[CrossRef]

Desmaret, C.

S. Grésillon, L. Aigouy, A. C. Boccara, J. C. Rivoal, X. Quelin, C. Desmaret, P. Gadenne, V. A. Shubin, A. K. Sarychev, V. M. Shalaev, “Experimental observation of localized optical excitations in random metal-dielectric films,” Phys. Rev. Lett. 82, 4520–4523 (1999).
[CrossRef]

Devaux, E.

E. Devaux, A. Dereux, E. Bourillot, J.-C. Weeber, Y. Lacroute, J.-P. Goudonnet, C. Girard, “Local detection of the optical magnetic field in the near zone of dielectric samples,” Phys. Rev. B 62, 10504–10514 (2000).
[CrossRef]

Douketis, C.

P. Zhang, T. L. Haslett, C. Douketis, M. Moskovits, “Mode localization in self-affine fractal interfaces observed by near-field microscopy,” Phys. Rev. B 57, 15513–15518 (1998).
[CrossRef]

Emory, S. R.

S. Nie, S. R. Emory, “Probing single molecules and single nanoparticles by surface-enhanced Raman scattering,” Science 275, 1102–1106 (1997).
[CrossRef] [PubMed]

Feder, J.

J. Feder, Fractals (Plenum, New York, 1988).

Feld, M. S.

K. Kneipp, Y. Wang, H. Kneipp, L. T. Perlman, I. Itzkan, R. R. Dasari, M. S. Feld, “Single molecule detection using surface-enhanced Raman scattering (SERS),” Phys. Rev. Lett. 78, 1667–1670 (1997).
[CrossRef]

Franceschetti, G.

G. Franceschetti, A. Iodice, D. Riccio, “Scattering from dielectric random fractal surfaces via method of moments,” IEEE Trans. Geosci. Remote Sens. 38, 1644–1655 (2000).
[CrossRef]

Frangos, P.

Gadenne, P.

S. Grésillon, L. Aigouy, A. C. Boccara, J. C. Rivoal, X. Quelin, C. Desmaret, P. Gadenne, V. A. Shubin, A. K. Sarychev, V. M. Shalaev, “Experimental observation of localized optical excitations in random metal-dielectric films,” Phys. Rev. Lett. 82, 4520–4523 (1999).
[CrossRef]

Garci´a-Ramos, J. V.

J. A. Sánchez-Gil, J. V. Garcı́a-Ramos, E. R. Méndez, “Influence of nanoscale cutoff in random self-affine fractal silver surfaces on the excitation of localized optical modes,” Opt. Lett. 26, 1286–1288 (2001).
[CrossRef]

J. A. Sánchez-Gil, J. V. Garcı́a-Ramos, E. R. Méndez, “Near-field electromagnetic wave scattering from random self-affine fractal metal surfaces: spectral dependence of local field enhancements and their statistics in connection with surface-enhanced Raman scattering,” Phys. Rev. B 62, 10515–10525 (2000).
[CrossRef]

J. A. Sánchez-Gil, J. V. Garcı́a-Ramos, “Calculations of the direct electromagnetic enhancement in surface enhanced Raman scattering on random self-affine fractal metal surfaces,” J. Chem. Phys. 108, 317–325 (1998).
[CrossRef]

J. A. Sánchez-Gil, J. V. Garcı́a-Ramos, “Strong surface field enhancements in the scattering of p-polarized light from fractal metal surfaces,” Opt. Commun. 134, 11–15 (1997).
[CrossRef]

J. A. Sánchez-Gil, J. V. Garcı́a-Ramos, “Far-field intensity of electromagnetic waves scattered from random, self-affine fractal metal surfaces,” Waves Random Media 7, 285–293 (1997).
[CrossRef]

Girard, C.

E. Devaux, A. Dereux, E. Bourillot, J.-C. Weeber, Y. Lacroute, J.-P. Goudonnet, C. Girard, “Local detection of the optical magnetic field in the near zone of dielectric samples,” Phys. Rev. B 62, 10504–10514 (2000).
[CrossRef]

Goudonnet, J.-P.

E. Devaux, A. Dereux, E. Bourillot, J.-C. Weeber, Y. Lacroute, J.-P. Goudonnet, C. Girard, “Local detection of the optical magnetic field in the near zone of dielectric samples,” Phys. Rev. B 62, 10504–10514 (2000).
[CrossRef]

Greffet, J. J.

J. J. Greffet, A. Sentenac, R. Carminati, “Surface profile reconstruction using near-field data,” Opt. Commun. 116, 20–24 (1995).
[CrossRef]

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]

Grésillon, S.

S. Grésillon, L. Aigouy, A. C. Boccara, J. C. Rivoal, X. Quelin, C. Desmaret, P. Gadenne, V. A. Shubin, A. K. Sarychev, V. M. Shalaev, “Experimental observation of localized optical excitations in random metal-dielectric films,” Phys. Rev. Lett. 82, 4520–4523 (1999).
[CrossRef]

Hansen, A.

I. Simonsen, A. Hansen, O. M. Nes, “Determination of Hurst exponents by use of the wavelet transform,” Phys. Rev. E 58, 2779–2787 (1998).
[CrossRef]

Haslett, T. L.

V. A. Markel, V. M. Shalaev, P. Zhang, W. Huynh, L. Tay, T. L. Haslett, M. Moskovits, “Near-field optical spectroscopy of individual surface-plasmon modes in colloid clusters,” Phys. Rev. B 59, 10903–10909 (1999).
[CrossRef]

P. Zhang, T. L. Haslett, C. Douketis, M. Moskovits, “Mode localization in self-affine fractal interfaces observed by near-field microscopy,” Phys. Rev. B 57, 15513–15518 (1998).
[CrossRef]

Hizanidis, K.

Hunter, W. R.

D. W. Lynch, W. R. Hunter in Handbook of Optical Constants of Solids, E. D. Palik, ed. (Academic Press, New York, 1985), p. 356.

Huynh, W.

V. A. Markel, V. M. Shalaev, P. Zhang, W. Huynh, L. Tay, T. L. Haslett, M. Moskovits, “Near-field optical spectroscopy of individual surface-plasmon modes in colloid clusters,” Phys. Rev. B 59, 10903–10909 (1999).
[CrossRef]

Iodice, A.

G. Franceschetti, A. Iodice, D. Riccio, “Scattering from dielectric random fractal surfaces via method of moments,” IEEE Trans. Geosci. Remote Sens. 38, 1644–1655 (2000).
[CrossRef]

Itzkan, I.

K. Kneipp, Y. Wang, H. Kneipp, L. T. Perlman, I. Itzkan, R. R. Dasari, M. S. Feld, “Single molecule detection using surface-enhanced Raman scattering (SERS),” Phys. Rev. Lett. 78, 1667–1670 (1997).
[CrossRef]

Jaggard, D. L.

Jakeman, E.

E. Jakeman, “Fraunhofer scattering by a sub-fractal diffuser,” Opt. Acta 30, 1207–1212 (1983).
[CrossRef]

Jullien, R.

R. Jullien, R. Botet, “Geometrical optics in fractals,” Physica D 38, 208–212 (1989).
[CrossRef]

Käll, M.

H. Xu, E. J. Bjerneld, M. Käll, L. Börjesson, “Spectroscopy of single hemoglobin molecules by surface-enhanced Raman scattering,” Phys. Rev. Lett. 83, 4357–4360 (1999).
[CrossRef]

Kim, W.

S. Bozhevolnyi, V. A. Markel, V. Coello, W. Kim, V. M. Shalaev, “Direct observation of localized dipolar excitations on rough nanostructured surfaces,” Phys. Rev. B 58, 11441–11448 (1998).
[CrossRef]

Kim, Y.

Kneipp, H.

K. Kneipp, Y. Wang, H. Kneipp, L. T. Perlman, I. Itzkan, R. R. Dasari, M. S. Feld, “Single molecule detection using surface-enhanced Raman scattering (SERS),” Phys. Rev. Lett. 78, 1667–1670 (1997).
[CrossRef]

Kneipp, K.

K. Kneipp, Y. Wang, H. Kneipp, L. T. Perlman, I. Itzkan, R. R. Dasari, M. S. Feld, “Single molecule detection using surface-enhanced Raman scattering (SERS),” Phys. Rev. Lett. 78, 1667–1670 (1997).
[CrossRef]

Kovacs, J.

D. P. Tsai, J. Kovacs, Z. Wang, M. Moskovits, V. M. Shalaev, J. S. Suh, R. Botet, “Photon scanning tunneling microscopy images of optical excitations of fractal metal colloid clusters,” Phys. Rev. Lett. 72, 4149–4152 (1994).
[CrossRef] [PubMed]

Lacroute, Y.

E. Devaux, A. Dereux, E. Bourillot, J.-C. Weeber, Y. Lacroute, J.-P. Goudonnet, C. Girard, “Local detection of the optical magnetic field in the near zone of dielectric samples,” Phys. Rev. B 62, 10504–10514 (2000).
[CrossRef]

Lee, H. P.

N. Lin, H. P. Lee, S. P. Lim, K. S. Lee, “Wave scattering from fractal surfaces,” J. Mod. Opt. 42, 225–241 (1995).
[CrossRef]

Lee, K. S.

N. Lin, H. P. Lee, S. P. Lim, K. S. Lee, “Wave scattering from fractal surfaces,” J. Mod. Opt. 42, 225–241 (1995).
[CrossRef]

Leskova, T. A.

Leung, H.

J. Chen, T. K. Y. Lo, H. Leung, J. Litva, “The use of fractals for modeling EM wave scattering from rough sea surface,” IEEE Trans. Geosci. Remote Sens. 34, 966–972 (1996).
[CrossRef]

Leyva-Lucero, M.

Lim, S. P.

N. Lin, H. P. Lee, S. P. Lim, K. S. Lee, “Wave scattering from fractal surfaces,” J. Mod. Opt. 42, 225–241 (1995).
[CrossRef]

Lin, N.

N. Lin, H. P. Lee, S. P. Lim, K. S. Lee, “Wave scattering from fractal surfaces,” J. Mod. Opt. 42, 225–241 (1995).
[CrossRef]

Litva, J.

J. Chen, T. K. Y. Lo, H. Leung, J. Litva, “The use of fractals for modeling EM wave scattering from rough sea surface,” IEEE Trans. Geosci. Remote Sens. 34, 966–972 (1996).
[CrossRef]

Lo, T. K. Y.

J. Chen, T. K. Y. Lo, H. Leung, J. Litva, “The use of fractals for modeling EM wave scattering from rough sea surface,” IEEE Trans. Geosci. Remote Sens. 34, 966–972 (1996).
[CrossRef]

Lu, J. Q.

Lu, T. M.

Y. P. Zhao, G. C. Wang, T. M. Lu, “Diffraction from non-Gaussian rough surfaces,” Phys. Rev. B 55, 13938–13952 (1997).
[CrossRef]

H. N. Yang, T. M. Lu, G. C. Wang, “Diffraction from surface growth fronts,” Phys. Rev. B 47, 3911–3922 (1993).
[CrossRef]

Lynch, D. W.

D. W. Lynch, W. R. Hunter in Handbook of Optical Constants of Solids, E. D. Palik, ed. (Academic Press, New York, 1985), p. 356.

Mandelbrot, B. B.

B. B. Mandelbrot, Fractals (Freeman, San Francisco, Calif., 1977).

Maradudin, A. A.

Markel, V. A.

V. A. Markel, V. M. Shalaev, P. Zhang, W. Huynh, L. Tay, T. L. Haslett, M. Moskovits, “Near-field optical spectroscopy of individual surface-plasmon modes in colloid clusters,” Phys. Rev. B 59, 10903–10909 (1999).
[CrossRef]

S. Bozhevolnyi, V. A. Markel, V. Coello, W. Kim, V. M. Shalaev, “Direct observation of localized dipolar excitations on rough nanostructured surfaces,” Phys. Rev. B 58, 11441–11448 (1998).
[CrossRef]

E. Y. Poliakov, V. A. Markel, V. M. Shalaev, R. Botet, “Nonlinear optical phenomena on rough surfaces of metal thin films,” Phys. Rev. B 57, 14901–14913 (1998).
[CrossRef]

E. Y. Poliakov, V. M. Shalaev, V. A. Markel, R. Botet, “Enhanced Raman scattering from self-affine thin films,” Opt. Lett. 21, 1628–1630 (1996).
[CrossRef] [PubMed]

McGurn, A. R.

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

McSharry, P. E.

P. E. McSharry, P. J. Cullen, D. Moroney, “Wave scattering by a two-dimensional band limited fractal surface based on a perturbation of the Green’s function,” J. Appl. Phys. 78, 6940–6948 (1995).
[CrossRef]

Méndez, E. R.

J. A. Sánchez-Gil, J. V. Garcı́a-Ramos, E. R. Méndez, “Influence of nanoscale cutoff in random self-affine fractal silver surfaces on the excitation of localized optical modes,” Opt. Lett. 26, 1286–1288 (2001).
[CrossRef]

J. A. Sánchez-Gil, J. V. Garcı́a-Ramos, E. R. Méndez, “Near-field electromagnetic wave scattering from random self-affine fractal metal surfaces: spectral dependence of local field enhancements and their statistics in connection with surface-enhanced Raman scattering,” Phys. Rev. B 62, 10515–10525 (2000).
[CrossRef]

A. Mendoza-Suárez, E. R. Méndez, “Light scattering by a reentrant fractal surface,” Appl. Opt. 36, 3521–3531 (1997).
[CrossRef] [PubMed]

M. Leyva-Lucero, E. R. Méndez, T. A. Leskova, A. A. Maradudin, J. Q. Lu, “Multiple-scattering effects in the second-harmonic generation of light in reflection from a randomly rough metal surface,” Opt. Lett. 21, 1809–1811 (1996).
[CrossRef] [PubMed]

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

Mendoza-Suárez, A.

Michel, T.

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

Moroney, D.

P. E. McSharry, P. J. Cullen, D. Moroney, “Wave scattering by a two-dimensional band limited fractal surface based on a perturbation of the Green’s function,” J. Appl. Phys. 78, 6940–6948 (1995).
[CrossRef]

Moskovits, M.

V. A. Markel, V. M. Shalaev, P. Zhang, W. Huynh, L. Tay, T. L. Haslett, M. Moskovits, “Near-field optical spectroscopy of individual surface-plasmon modes in colloid clusters,” Phys. Rev. B 59, 10903–10909 (1999).
[CrossRef]

P. Zhang, T. L. Haslett, C. Douketis, M. Moskovits, “Mode localization in self-affine fractal interfaces observed by near-field microscopy,” Phys. Rev. B 57, 15513–15518 (1998).
[CrossRef]

D. P. Tsai, J. Kovacs, Z. Wang, M. Moskovits, V. M. Shalaev, J. S. Suh, R. Botet, “Photon scanning tunneling microscopy images of optical excitations of fractal metal colloid clusters,” Phys. Rev. Lett. 72, 4149–4152 (1994).
[CrossRef] [PubMed]

Nes, O. M.

I. Simonsen, A. Hansen, O. M. Nes, “Determination of Hurst exponents by use of the wavelet transform,” Phys. Rev. E 58, 2779–2787 (1998).
[CrossRef]

Nie, S.

S. Nie, S. R. Emory, “Probing single molecules and single nanoparticles by surface-enhanced Raman scattering,” Science 275, 1102–1106 (1997).
[CrossRef] [PubMed]

Nieto-Vesparinas, M.

J. A. Sánchez-Gil, M. Nieto-Vesparinas, “Resonance effects in multiple light scattering from statistically rough metallic surfaces,” Phys. Rev. B 45, 8623–8633 (1992).
[CrossRef]

Nieto-Vesperinas, M.

O’Donnell, K. A.

Perlman, L. T.

K. Kneipp, Y. Wang, H. Kneipp, L. T. Perlman, I. Itzkan, R. R. Dasari, M. S. Feld, “Single molecule detection using surface-enhanced Raman scattering (SERS),” Phys. Rev. Lett. 78, 1667–1670 (1997).
[CrossRef]

Poliakov, E. Y.

E. Y. Poliakov, V. A. Markel, V. M. Shalaev, R. Botet, “Nonlinear optical phenomena on rough surfaces of metal thin films,” Phys. Rev. B 57, 14901–14913 (1998).
[CrossRef]

E. Y. Poliakov, V. M. Shalaev, V. A. Markel, R. Botet, “Enhanced Raman scattering from self-affine thin films,” Opt. Lett. 21, 1628–1630 (1996).
[CrossRef] [PubMed]

Quelin, X.

S. Grésillon, L. Aigouy, A. C. Boccara, J. C. Rivoal, X. Quelin, C. Desmaret, P. Gadenne, V. A. Shubin, A. K. Sarychev, V. M. Shalaev, “Experimental observation of localized optical excitations in random metal-dielectric films,” Phys. Rev. Lett. 82, 4520–4523 (1999).
[CrossRef]

Riccio, D.

G. Franceschetti, A. Iodice, D. Riccio, “Scattering from dielectric random fractal surfaces via method of moments,” IEEE Trans. Geosci. Remote Sens. 38, 1644–1655 (2000).
[CrossRef]

Rivoal, J. C.

S. Grésillon, L. Aigouy, A. C. Boccara, J. C. Rivoal, X. Quelin, C. Desmaret, P. Gadenne, V. A. Shubin, A. K. Sarychev, V. M. Shalaev, “Experimental observation of localized optical excitations in random metal-dielectric films,” Phys. Rev. Lett. 82, 4520–4523 (1999).
[CrossRef]

Roux, S.

Sánchez-Gil, J. A.

J. A. Sánchez-Gil, J. V. Garcı́a-Ramos, E. R. Méndez, “Influence of nanoscale cutoff in random self-affine fractal silver surfaces on the excitation of localized optical modes,” Opt. Lett. 26, 1286–1288 (2001).
[CrossRef]

J. A. Sánchez-Gil, J. V. Garcı́a-Ramos, E. R. Méndez, “Near-field electromagnetic wave scattering from random self-affine fractal metal surfaces: spectral dependence of local field enhancements and their statistics in connection with surface-enhanced Raman scattering,” Phys. Rev. B 62, 10515–10525 (2000).
[CrossRef]

J. A. Sánchez-Gil, J. V. Garcı́a-Ramos, “Calculations of the direct electromagnetic enhancement in surface enhanced Raman scattering on random self-affine fractal metal surfaces,” J. Chem. Phys. 108, 317–325 (1998).
[CrossRef]

J. A. Sánchez-Gil, J. V. Garcı́a-Ramos, “Strong surface field enhancements in the scattering of p-polarized light from fractal metal surfaces,” Opt. Commun. 134, 11–15 (1997).
[CrossRef]

J. A. Sánchez-Gil, J. V. Garcı́a-Ramos, “Far-field intensity of electromagnetic waves scattered from random, self-affine fractal metal surfaces,” Waves Random Media 7, 285–293 (1997).
[CrossRef]

J. A. Sánchez-Gil, M. Nieto-Vesparinas, “Resonance effects in multiple light scattering from statistically rough metallic surfaces,” Phys. Rev. B 45, 8623–8633 (1992).
[CrossRef]

J. A. Sánchez-Gil, M. Nieto-Vesperinas, “Light scattering from random rough dielectric surfaces,” J. Opt. Soc. Am. A 8, 1270–1286 (1991).
[CrossRef]

Sarychev, A. K.

S. Grésillon, L. Aigouy, A. C. Boccara, J. C. Rivoal, X. Quelin, C. Desmaret, P. Gadenne, V. A. Shubin, A. K. Sarychev, V. M. Shalaev, “Experimental observation of localized optical excitations in random metal-dielectric films,” Phys. Rev. Lett. 82, 4520–4523 (1999).
[CrossRef]

Savaidis, S.

Sentenac, A.

J. J. Greffet, A. Sentenac, R. Carminati, “Surface profile reconstruction using near-field data,” Opt. Commun. 116, 20–24 (1995).
[CrossRef]

Shalaev, V. M.

S. Grésillon, L. Aigouy, A. C. Boccara, J. C. Rivoal, X. Quelin, C. Desmaret, P. Gadenne, V. A. Shubin, A. K. Sarychev, V. M. Shalaev, “Experimental observation of localized optical excitations in random metal-dielectric films,” Phys. Rev. Lett. 82, 4520–4523 (1999).
[CrossRef]

V. A. Markel, V. M. Shalaev, P. Zhang, W. Huynh, L. Tay, T. L. Haslett, M. Moskovits, “Near-field optical spectroscopy of individual surface-plasmon modes in colloid clusters,” Phys. Rev. B 59, 10903–10909 (1999).
[CrossRef]

S. Bozhevolnyi, V. A. Markel, V. Coello, W. Kim, V. M. Shalaev, “Direct observation of localized dipolar excitations on rough nanostructured surfaces,” Phys. Rev. B 58, 11441–11448 (1998).
[CrossRef]

E. Y. Poliakov, V. A. Markel, V. M. Shalaev, R. Botet, “Nonlinear optical phenomena on rough surfaces of metal thin films,” Phys. Rev. B 57, 14901–14913 (1998).
[CrossRef]

V. M. Shalaev, “Electromagnetic properties of small-particle composites,” Phys. Rep. 272, 61–137 (1996).
[CrossRef]

E. Y. Poliakov, V. M. Shalaev, V. A. Markel, R. Botet, “Enhanced Raman scattering from self-affine thin films,” Opt. Lett. 21, 1628–1630 (1996).
[CrossRef] [PubMed]

D. P. Tsai, J. Kovacs, Z. Wang, M. Moskovits, V. M. Shalaev, J. S. Suh, R. Botet, “Photon scanning tunneling microscopy images of optical excitations of fractal metal colloid clusters,” Phys. Rev. Lett. 72, 4149–4152 (1994).
[CrossRef] [PubMed]

Sheppard, C. J. R.

C. J. R. Sheppard, “Scattering by fractal surfaces with an outer scale,” Opt. Commun. 122, 178–188 (1996).
[CrossRef]

Shubin, V. A.

S. Grésillon, L. Aigouy, A. C. Boccara, J. C. Rivoal, X. Quelin, C. Desmaret, P. Gadenne, V. A. Shubin, A. K. Sarychev, V. M. Shalaev, “Experimental observation of localized optical excitations in random metal-dielectric films,” Phys. Rev. Lett. 82, 4520–4523 (1999).
[CrossRef]

Simonsen, I.

I. Simonsen, D. Vandembroucq, S. Roux, “Electromagnetic wave scattering from conducting self-affine surfaces: an analytic and numerical study,” J. Opt. Soc. Am. A 18, 1101–1111 (2001).
[CrossRef]

I. Simonsen, D. Vandembroucq, S. Roux, “Wave scattering from self-affine surfaces,” Phys. Rev. E 61, 5914–5917 (2000).
[CrossRef]

I. Simonsen, A. Hansen, O. M. Nes, “Determination of Hurst exponents by use of the wavelet transform,” Phys. Rev. E 58, 2779–2787 (1998).
[CrossRef]

Sinha, S. K.

S. K. Sinha, “Scattering from fractal structures,” Physica D 38, 310–314 (1989).
[CrossRef]

Smolyaninov, I. I.

S. Bozhevolnyi, B. Vohnsen, A. V. Zayats, I. I. Smolyaninov, “Fractal surface characterization: implications for plasmon polariton scattering,” Surf. Sci. 356, 268–274 (1996).
[CrossRef]

S. Bozhevolnyi, B. Vohnsen, I. I. Smolyaninov, A. V. Zayats, “Direct observation of surface polariton localization caused by surface roughness,” Opt. Commun. 117, 417–423 (1995).
[CrossRef]

Stanley, H. E.

A.-L. Barabási, H. E. Stanley, Fractal Concepts in Surface Growth (Cambridge U. Press, Cambridge, UK, 1995).

Suh, J. S.

D. P. Tsai, J. Kovacs, Z. Wang, M. Moskovits, V. M. Shalaev, J. S. Suh, R. Botet, “Photon scanning tunneling microscopy images of optical excitations of fractal metal colloid clusters,” Phys. Rev. Lett. 72, 4149–4152 (1994).
[CrossRef] [PubMed]

Sun, X.

Tay, L.

V. A. Markel, V. M. Shalaev, P. Zhang, W. Huynh, L. Tay, T. L. Haslett, M. Moskovits, “Near-field optical spectroscopy of individual surface-plasmon modes in colloid clusters,” Phys. Rev. B 59, 10903–10909 (1999).
[CrossRef]

Torre, R.

Tsai, D. P.

D. P. Tsai, J. Kovacs, Z. Wang, M. Moskovits, V. M. Shalaev, J. S. Suh, R. Botet, “Photon scanning tunneling microscopy images of optical excitations of fractal metal colloid clusters,” Phys. Rev. Lett. 72, 4149–4152 (1994).
[CrossRef] [PubMed]

Vandembroucq, D.

Vohnsen, B.

S. Bozhevolnyi, B. Vohnsen, A. V. Zayats, I. I. Smolyaninov, “Fractal surface characterization: implications for plasmon polariton scattering,” Surf. Sci. 356, 268–274 (1996).
[CrossRef]

S. Bozhevolnyi, B. Vohnsen, I. I. Smolyaninov, A. V. Zayats, “Direct observation of surface polariton localization caused by surface roughness,” Opt. Commun. 117, 417–423 (1995).
[CrossRef]

Voss, R. F.

R. F. Voss, “Random fractals: self-affinity in noise, mountains, and clouds,” Physica D 38, 362–371 (1989).
[CrossRef]

R. F. Voss, in The Science of Fractal Images, H.-O. Peitgen, D. Saupe, eds. (Springer, Berlin, 1988).

Wang, G. C.

Y. P. Zhao, G. C. Wang, T. M. Lu, “Diffraction from non-Gaussian rough surfaces,” Phys. Rev. B 55, 13938–13952 (1997).
[CrossRef]

H. N. Yang, T. M. Lu, G. C. Wang, “Diffraction from surface growth fronts,” Phys. Rev. B 47, 3911–3922 (1993).
[CrossRef]

Wang, Y.

K. Kneipp, Y. Wang, H. Kneipp, L. T. Perlman, I. Itzkan, R. R. Dasari, M. S. Feld, “Single molecule detection using surface-enhanced Raman scattering (SERS),” Phys. Rev. Lett. 78, 1667–1670 (1997).
[CrossRef]

Wang, Z.

D. P. Tsai, J. Kovacs, Z. Wang, M. Moskovits, V. M. Shalaev, J. S. Suh, R. Botet, “Photon scanning tunneling microscopy images of optical excitations of fractal metal colloid clusters,” Phys. Rev. Lett. 72, 4149–4152 (1994).
[CrossRef] [PubMed]

Weeber, J.-C.

E. Devaux, A. Dereux, E. Bourillot, J.-C. Weeber, Y. Lacroute, J.-P. Goudonnet, C. Girard, “Local detection of the optical magnetic field in the near zone of dielectric samples,” Phys. Rev. B 62, 10504–10514 (2000).
[CrossRef]

West, B. J.

West, C. S.

Xu, H.

H. Xu, E. J. Bjerneld, M. Käll, L. Börjesson, “Spectroscopy of single hemoglobin molecules by surface-enhanced Raman scattering,” Phys. Rev. Lett. 83, 4357–4360 (1999).
[CrossRef]

Yang, H. N.

H. N. Yang, T. M. Lu, G. C. Wang, “Diffraction from surface growth fronts,” Phys. Rev. B 47, 3911–3922 (1993).
[CrossRef]

Zayats, A. V.

S. Bozhevolnyi, B. Vohnsen, A. V. Zayats, I. I. Smolyaninov, “Fractal surface characterization: implications for plasmon polariton scattering,” Surf. Sci. 356, 268–274 (1996).
[CrossRef]

S. Bozhevolnyi, B. Vohnsen, I. I. Smolyaninov, A. V. Zayats, “Direct observation of surface polariton localization caused by surface roughness,” Opt. Commun. 117, 417–423 (1995).
[CrossRef]

Zhang, P.

V. A. Markel, V. M. Shalaev, P. Zhang, W. Huynh, L. Tay, T. L. Haslett, M. Moskovits, “Near-field optical spectroscopy of individual surface-plasmon modes in colloid clusters,” Phys. Rev. B 59, 10903–10909 (1999).
[CrossRef]

P. Zhang, T. L. Haslett, C. Douketis, M. Moskovits, “Mode localization in self-affine fractal interfaces observed by near-field microscopy,” Phys. Rev. B 57, 15513–15518 (1998).
[CrossRef]

Zhao, Y. P.

Y. P. Zhao, G. C. Wang, T. M. Lu, “Diffraction from non-Gaussian rough surfaces,” Phys. Rev. B 55, 13938–13952 (1997).
[CrossRef]

Ann. Phys. (New York)

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

Appl. Opt.

IEEE Trans. Geosci. Remote Sens.

J. Chen, T. K. Y. Lo, H. Leung, J. Litva, “The use of fractals for modeling EM wave scattering from rough sea surface,” IEEE Trans. Geosci. Remote Sens. 34, 966–972 (1996).
[CrossRef]

G. Franceschetti, A. Iodice, D. Riccio, “Scattering from dielectric random fractal surfaces via method of moments,” IEEE Trans. Geosci. Remote Sens. 38, 1644–1655 (2000).
[CrossRef]

J. Appl. Phys.

M. V. Berry, “Difractals,” J. Appl. Phys. 12, 781–797 (1979).

P. E. McSharry, P. J. Cullen, D. Moroney, “Wave scattering by a two-dimensional band limited fractal surface based on a perturbation of the Green’s function,” J. Appl. Phys. 78, 6940–6948 (1995).
[CrossRef]

J. Chem. Phys.

J. A. Sánchez-Gil, J. V. Garcı́a-Ramos, “Calculations of the direct electromagnetic enhancement in surface enhanced Raman scattering on random self-affine fractal metal surfaces,” J. Chem. Phys. 108, 317–325 (1998).
[CrossRef]

J. Mod. Opt.

N. Lin, H. P. Lee, S. P. Lim, K. S. Lee, “Wave scattering from fractal surfaces,” J. Mod. Opt. 42, 225–241 (1995).
[CrossRef]

J. Opt. Soc. Am. A

Opt. Acta

E. Jakeman, “Fraunhofer scattering by a sub-fractal diffuser,” Opt. Acta 30, 1207–1212 (1983).
[CrossRef]

Opt. Commun.

J. A. Sánchez-Gil, J. V. Garcı́a-Ramos, “Strong surface field enhancements in the scattering of p-polarized light from fractal metal surfaces,” Opt. Commun. 134, 11–15 (1997).
[CrossRef]

C. J. R. Sheppard, “Scattering by fractal surfaces with an outer scale,” Opt. Commun. 122, 178–188 (1996).
[CrossRef]

S. Bozhevolnyi, B. Vohnsen, I. I. Smolyaninov, A. V. Zayats, “Direct observation of surface polariton localization caused by surface roughness,” Opt. Commun. 117, 417–423 (1995).
[CrossRef]

J. J. Greffet, A. Sentenac, R. Carminati, “Surface profile reconstruction using near-field data,” Opt. Commun. 116, 20–24 (1995).
[CrossRef]

Opt. Lett.

Phys. Rep.

V. M. Shalaev, “Electromagnetic properties of small-particle composites,” Phys. Rep. 272, 61–137 (1996).
[CrossRef]

Phys. Rev. B

E. Devaux, A. Dereux, E. Bourillot, J.-C. Weeber, Y. Lacroute, J.-P. Goudonnet, C. Girard, “Local detection of the optical magnetic field in the near zone of dielectric samples,” Phys. Rev. B 62, 10504–10514 (2000).
[CrossRef]

J. A. Sánchez-Gil, J. V. Garcı́a-Ramos, E. R. Méndez, “Near-field electromagnetic wave scattering from random self-affine fractal metal surfaces: spectral dependence of local field enhancements and their statistics in connection with surface-enhanced Raman scattering,” Phys. Rev. B 62, 10515–10525 (2000).
[CrossRef]

P. Zhang, T. L. Haslett, C. Douketis, M. Moskovits, “Mode localization in self-affine fractal interfaces observed by near-field microscopy,” Phys. Rev. B 57, 15513–15518 (1998).
[CrossRef]

S. Bozhevolnyi, V. A. Markel, V. Coello, W. Kim, V. M. Shalaev, “Direct observation of localized dipolar excitations on rough nanostructured surfaces,” Phys. Rev. B 58, 11441–11448 (1998).
[CrossRef]

V. A. Markel, V. M. Shalaev, P. Zhang, W. Huynh, L. Tay, T. L. Haslett, M. Moskovits, “Near-field optical spectroscopy of individual surface-plasmon modes in colloid clusters,” Phys. Rev. B 59, 10903–10909 (1999).
[CrossRef]

J. A. Sánchez-Gil, M. Nieto-Vesparinas, “Resonance effects in multiple light scattering from statistically rough metallic surfaces,” Phys. Rev. B 45, 8623–8633 (1992).
[CrossRef]

Y. P. Zhao, G. C. Wang, T. M. Lu, “Diffraction from non-Gaussian rough surfaces,” Phys. Rev. B 55, 13938–13952 (1997).
[CrossRef]

E. Y. Poliakov, V. A. Markel, V. M. Shalaev, R. Botet, “Nonlinear optical phenomena on rough surfaces of metal thin films,” Phys. Rev. B 57, 14901–14913 (1998).
[CrossRef]

H. N. Yang, T. M. Lu, G. C. Wang, “Diffraction from surface growth fronts,” Phys. Rev. B 47, 3911–3922 (1993).
[CrossRef]

Phys. Rev. E

I. Simonsen, A. Hansen, O. M. Nes, “Determination of Hurst exponents by use of the wavelet transform,” Phys. Rev. E 58, 2779–2787 (1998).
[CrossRef]

I. Simonsen, D. Vandembroucq, S. Roux, “Wave scattering from self-affine surfaces,” Phys. Rev. E 61, 5914–5917 (2000).
[CrossRef]

Phys. Rev. Lett.

S. Grésillon, L. Aigouy, A. C. Boccara, J. C. Rivoal, X. Quelin, C. Desmaret, P. Gadenne, V. A. Shubin, A. K. Sarychev, V. M. Shalaev, “Experimental observation of localized optical excitations in random metal-dielectric films,” Phys. Rev. Lett. 82, 4520–4523 (1999).
[CrossRef]

K. Kneipp, Y. Wang, H. Kneipp, L. T. Perlman, I. Itzkan, R. R. Dasari, M. S. Feld, “Single molecule detection using surface-enhanced Raman scattering (SERS),” Phys. Rev. Lett. 78, 1667–1670 (1997).
[CrossRef]

H. Xu, E. J. Bjerneld, M. Käll, L. Börjesson, “Spectroscopy of single hemoglobin molecules by surface-enhanced Raman scattering,” Phys. Rev. Lett. 83, 4357–4360 (1999).
[CrossRef]

D. P. Tsai, J. Kovacs, Z. Wang, M. Moskovits, V. M. Shalaev, J. S. Suh, R. Botet, “Photon scanning tunneling microscopy images of optical excitations of fractal metal colloid clusters,” Phys. Rev. Lett. 72, 4149–4152 (1994).
[CrossRef] [PubMed]

Physica D

R. F. Voss, “Random fractals: self-affinity in noise, mountains, and clouds,” Physica D 38, 362–371 (1989).
[CrossRef]

R. Jullien, R. Botet, “Geometrical optics in fractals,” Physica D 38, 208–212 (1989).
[CrossRef]

S. K. Sinha, “Scattering from fractal structures,” Physica D 38, 310–314 (1989).
[CrossRef]

Science

S. Nie, S. R. Emory, “Probing single molecules and single nanoparticles by surface-enhanced Raman scattering,” Science 275, 1102–1106 (1997).
[CrossRef] [PubMed]

Surf. Sci.

S. Bozhevolnyi, B. Vohnsen, A. V. Zayats, I. I. Smolyaninov, “Fractal surface characterization: implications for plasmon polariton scattering,” Surf. Sci. 356, 268–274 (1996).
[CrossRef]

Waves Random Media

J. A. Sánchez-Gil, J. V. Garcı́a-Ramos, “Far-field intensity of electromagnetic waves scattered from random, self-affine fractal metal surfaces,” Waves Random Media 7, 285–293 (1997).
[CrossRef]

Other

B. B. Mandelbrot, Fractals (Freeman, San Francisco, Calif., 1977).

J. Feder, Fractals (Plenum, New York, 1988).

A.-L. Barabási, H. E. Stanley, Fractal Concepts in Surface Growth (Cambridge U. Press, Cambridge, UK, 1995).

D. W. Lynch, W. R. Hunter in Handbook of Optical Constants of Solids, E. D. Palik, ed. (Academic Press, New York, 1985), p. 356.

R. F. Voss, in The Science of Fractal Images, H.-O. Peitgen, D. Saupe, eds. (Springer, Berlin, 1988).

M. Nieto-Vesperinas, Scattering and Diffraction in Physical Optics (Wiley, New York, 1991).

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (10)

Fig. 1
Fig. 1

Illustration of the scattering geometry.

Fig. 2
Fig. 2

Angular distribution of the speckle pattern intensity scattered from Ag fractal surface profiles with L=5.14 µm, D=1.9, and δ=51.4 nm [(a), (b)] and δ=257 nm [(c), (d)], differing only in ξL=51.4, 25.7, 12.85, and 6.425 nm, that are illuminated by a Gaussian beam with θ0=-10°, λ=629.9 nm, and W=L/4 cos θ0. (a), (c) s polarization; (b), (d) p polarization.

Fig. 3
Fig. 3

Same as in Fig. 2 but for the mean-scattered intensity averaged over Nrea=200 realizations, with θ0=10°.

Fig. 4
Fig. 4

Same as in Figs. 3(c) (s polarization, with dots) and 3(d) (p polarization, without dots) but renormalizing by the total reflectance S.

Fig. 5
Fig. 5

Surface electric [(a)] and magnetic [normal (b) and tangential (c)] field intensities on the center spot of the illuminated area (L=5.14 µm) for s-polarized scattering with θ0=-10°, λ=629.9 nm, and W=L/4 cos θ0, from Ag fractal surfaces with D=1.9, δ=51.4 nm, and ξL=51.4, 25.7, 12.85, and 6.425 nm. The KA field intensity is also included (see text). The corresponding surface profiles [(d)].

Fig. 6
Fig. 6

Surface magnetic [(a)] and electric [(b) normal and (c) tangential] field intensities on the center spot of the illuminated area (L=5.14 µm) for p-polarized scattering with θ0=-10°, λ=629.9 nm, and W=L/4 cos θ0, from Ag fractal surfaces with D=1.9, δ=51.4 nm, and ξL=51.4, 25.7, 12.85, and 6.425 nm. The KA field intensity is also included (see text). The corresponding surface profiles [(d)].

Fig. 7
Fig. 7

Surface-EM-field intensities (in a semi-log10 scale) for s polarization as in Fig. 5, but for rougher surface profiles [(d)] with δ=257 nm.

Fig. 8
Fig. 8

Surface-EM-field intensities (in a semi-log10 scale) for p polarization as in Fig. 6, but for rougher surface profiles [(d)] with δ=257 nm.

Fig. 9
Fig. 9

Near-field intensity images in s polarization [(a) electric, (b) magnetic, the former split into (c) x, horizontal component, and (d) z, vertical component, all of them in a log10 scale] in a rectangle of 0.5×0.44 µm2 close to the fractal surface in Fig. 7(d) with δ=257 nm and ξL=12.85 nm. Other parameters as in Fig. 7.

Fig. 10
Fig. 10

Near-field intensity images in p polarization [(a) electric and (b) magnetic, the latter split into (c) x, horizontal component, and (d) z, vertical component, all of them in a log10 scale] in a rectangle of 0.5×0.44 µm2 close to the fractal surface in Fig. 8(d) with δ=257 nm and ξL=12.85 nm, where a strong localized optical mode is observed. Other parameters as in Fig. 8.

Equations (18)

Equations on this page are rendered with MathJax. Learn more.

E(s)E(s)(r, ω)yˆ,
H(s)Hx(s)(r, ω)xˆ+Hz(s)(r, ω)zˆ,
H(p)H(p)(r, ω)yˆ,
E(p)Ex(p)(r, ω)xˆ+Ez(p)(r, ω)zˆ,
Hn(s)(x)=-icωγ-1dE(s)(x)dx,
Ht(s)(x)=icωγ-1F(s)(x),
E(s)(x)=E(s,>)(x, ζ(x)),
F(s)(x)=γ E(s,>)(r)nz=ζ(+)(x),
En(p)(x)=icωγ-1dH(p)(x)dx,
Et(p)(x)=-icωγ-1L(p)(x),
H(p)(x)=H(p,>)(x, ζ(x)),
L(p)(x)=γ H(p,>)(r)nz=ζ(+)(x).
|E(s, KA)|2|1+Rs|2|E(s, i)|2,
|Hn(s, KA)|2sin2 θ0|1+Rs|2|H(s, i)|,
|Ht(s, KA)|2cos2 θ0|1-Rs|2|H(s, i)|,
|H(p, KA)|2|1+Rp|2|H(p, i)|2,
|En(p, KA)|2sin2 θ0|1+Rp|2|E(p, i)|,
|Et(p, KA)|2cos2 θ0|1-Rp|2|E(p, i)|,

Metrics