Abstract

We investigate the electromagnetic mechanism in surface-enhanced Raman scattering (SERS) from randomly rough metal surfaces with Gaussian statistics and Gaussian correlation function. By means of rigorous numerical calculations, large average SERS enhancement factors (above 104) are encountered when the correlation length is of the order of (or lower than) a hundred nanometers, with excitation in the visible and near infrared. These Gaussian-correlated metal surfaces can be used as SERS substrates. Furthermore, local SERS enhancement factors are obtained of up to 108 that make them appropriate for resonant SERS single molecule detection.

© 2002 Optical Society of America

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  1. R. K. Chang and T. E. Furtak, Surface Enhanced Raman Scattering (Plenum, New York, 1982).
  2. J. A. Creighton, in Advances in Spectroscopy of Surfaces, vol. 16, edited by R. J. H. Clark and R. E. Hester (Wiley, Chichester, 1988).
  3. C. J. L. Constantino, T. Lemma, P. A. Antunes, and R. Aroca, “Single-molecule detection using surface-enhanced resonance Raman scattering and Langmuir-Blodgett monolayers,” Anal. Chem. 73, 3674–3678 (2001).
    [CrossRef] [PubMed]
  4. P. F. Gray, “A method of forming optical diffusers of simple known statistical properties,” Opt. Acta 31, 765–775 (1978).
    [CrossRef]
  5. K. A. O’Donnell and E. R. Mendez, “Experimental study of scattering from characterized random surfaces,” J. Opt. Soc. Am. A 4, 1194–1205 (1987).
    [CrossRef]
  6. A. J. Sant, J. C. Dainty, and M.-J. Kim, “Comparison of surface scattering between identical, randomly rough metal and dielectric diffusers,” Opt. Lett. 14, 1183–1185 (1989).
    [CrossRef] [PubMed]
  7. M. E. Knotts and K. A. O’Donnell, “Measurements of light scattering by a series of conducting surfaces with one-dimensional roughness,” J. Opt. Soc. Am. A 11, 697–710 (1994).
    [CrossRef]
  8. R. E. Luna, E. R. Méndez, J. Q. Lu, and Z.-H. Gu, “Enhanced backscattering due to total internal reflection at a dielectric-air interface,” J. Mod. Opt. 42, 257–269 (1995).
    [CrossRef]
  9. M. Switkes, T. M. Bloomstein, and M. Rothschild, “Patterning of sub-50 nm dense features with space-invariant 157 nm interference lithography,” Appl. Phys. Lett. 77, 3149–3151 (2000).
    [CrossRef]
  10. H. H. Solak, D. He, W. Li, S. Singh-Gasson, F. Cerrina, B. H. Sohn, X. M. Yang, and P. Nealey, “Exposure of 38 nm period grating patterns with extreme ultaviolet interferometric lithography,” Appl. Phys. Lett. 75, 2328–2330 (1999).
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  14. J. A. Sánchez-Gil and M. Nieto-Vesperinas, “Resonance effects in multiple light scattering from statistically rough metallic surfaces,” Phys. Rev. B 45, 8623–8633 (1992).
    [CrossRef]
  15. M. I. Stockman, L. N. Pandey, L. S. Muratov, and T. F. George, “Giant fluctuations of local optical fields in fractal clusters,” Phys. Rev. Lett. 72, 2486–2489 (1994).
    [CrossRef] [PubMed]
  16. V. M. Shalaev, “Electromagnetic properties of small-particle composites,” Phys. Rep. 272, 61–137 (1996).
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  17. E. Y. Poliakov, V. M. Shalaev, V. A. Markel, and R. Botet, “Enhanced Raman scattering from self-affine thin films,” Opt. Lett. 21, 1628–1630 (1996).
    [CrossRef] [PubMed]
  18. S. Grésillon, L. Aigouy, A. C. Boccara, J. C. Rivoal, X. Quelin, C. Desmaret, P. Gadenne, V. A. Shubin, A. K. Sarychev, and V. M. Shalaev, “Experimental observation of localized optical excitations in random metal-dielectric films,” Phys. Rev. Lett. 82, 4520–4523 (1999).
    [CrossRef]
  19. F. J. García-Vidal and J. B. Pendry, “Collective theory for surface-enhanced Raman scattering,” Phys. Rev. Lett. 77, 1163–1166 (1996).
    [CrossRef] [PubMed]
  20. H. Xu, J. Aizpurua, M. Käll, and P. Apell, “Electromagnetic contributions to single-molecule sensitivity in surface-enhanced Raman scattering,” Phys. Rev. E 62, 4318–4324 (2000).
    [CrossRef]
  21. J. P. Kottmann and O. J. F. Martin, “Plasmon resonant coupling in metallic nanowires,” Opt. Express 8, 655–663 (2001), http://www.opticsexpress.org/abstract.cfm?URI=OPEX-8-12-655.
    [CrossRef] [PubMed]
  22. J. P. Kottmann, O. J. F. Martin, D. R. Smith, and S. Schultz, “Spectral response of plasmon resonant nanoparticles with a non-regular shape,” Opt. Express 6, 213–219 (2000), http://www.opticsexpress.org/abstract.cfm?URI=OPEX-6-11-213.
    [CrossRef] [PubMed]
  23. J. P. Kottmann, O. J. F. Martin, D. R. Smith, and S. Schultz, “Dramatic localized electromagnetic enhancement in plasmon resonant nanowires,” Chem. Phys. Lett. 341, 1–6 (2001).
    [CrossRef]
  24. J. A. Sánchez-Gil and J. V. García-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]
  25. J. A. Sánchez-Gil, J. V. García-Ramos, and 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]
  26. J. A. Sánchez-Gil, J. V. García-Ramos, and 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]
  27. D. W. Lynch and W. R. Hunter, in: Handbook of Optical Constants of Solids, edited by E. D. Palik (Academic Press, New York, 1985), p. 356.
  28. S. Nie and S. R. Emory, “Probing single molecules and single nanoparticles by surface-enhanced Raman scattering,” Science 275, 1102–1106 (1997).
    [CrossRef] [PubMed]
  29. K. Kneipp, Y. Wang, H. Kneipp, L. T. Perlman, I. Itzkan, R. R. Dasari, and M. S. Feld, “Single molecule detection using surface-enhanced Raman scattering (SERS),” Phys. Rev. Lett. 78, 1667–1670 (1997).
    [CrossRef]
  30. H. Xu, E. J. Bjerneld, M. Käll, and L. Börjesson, “Spectroscopy of single hemoglobin molecules by surface enhanced Raman scattering,” Phys. Rev. Lett. 83, 4357–4360 (1999).
    [CrossRef]
  31. K. A. O’Donnell and R. Torre, “Second harmonic generation from a strongly rough metal surface,” Opt. Comm. 138 (1997) 341.
    [CrossRef]
  32. M. Leyva-Lucero, E. R. Méndez, T. A. Leskova, and A. A. Maradudin, “Destructive interference effects in the second harmonic light generated at randomly rough metal surfaces,” Opt. Commun. 161, 79–94 (1999).
    [CrossRef]

2001 (4)

C. J. L. Constantino, T. Lemma, P. A. Antunes, and R. Aroca, “Single-molecule detection using surface-enhanced resonance Raman scattering and Langmuir-Blodgett monolayers,” Anal. Chem. 73, 3674–3678 (2001).
[CrossRef] [PubMed]

J. P. Kottmann and O. J. F. Martin, “Plasmon resonant coupling in metallic nanowires,” Opt. Express 8, 655–663 (2001), http://www.opticsexpress.org/abstract.cfm?URI=OPEX-8-12-655.
[CrossRef] [PubMed]

J. P. Kottmann, O. J. F. Martin, D. R. Smith, and S. Schultz, “Dramatic localized electromagnetic enhancement in plasmon resonant nanowires,” Chem. Phys. Lett. 341, 1–6 (2001).
[CrossRef]

J. A. Sánchez-Gil, J. V. García-Ramos, and 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]

2000 (4)

H. Xu, J. Aizpurua, M. Käll, and P. Apell, “Electromagnetic contributions to single-molecule sensitivity in surface-enhanced Raman scattering,” Phys. Rev. E 62, 4318–4324 (2000).
[CrossRef]

J. A. Sánchez-Gil, J. V. García-Ramos, and 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. P. Kottmann, O. J. F. Martin, D. R. Smith, and S. Schultz, “Spectral response of plasmon resonant nanoparticles with a non-regular shape,” Opt. Express 6, 213–219 (2000), http://www.opticsexpress.org/abstract.cfm?URI=OPEX-6-11-213.
[CrossRef] [PubMed]

M. Switkes, T. M. Bloomstein, and M. Rothschild, “Patterning of sub-50 nm dense features with space-invariant 157 nm interference lithography,” Appl. Phys. Lett. 77, 3149–3151 (2000).
[CrossRef]

1999 (4)

H. H. Solak, D. He, W. Li, S. Singh-Gasson, F. Cerrina, B. H. Sohn, X. M. Yang, and P. Nealey, “Exposure of 38 nm period grating patterns with extreme ultaviolet interferometric lithography,” Appl. Phys. Lett. 75, 2328–2330 (1999).
[CrossRef]

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

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

M. Leyva-Lucero, E. R. Méndez, T. A. Leskova, and A. A. Maradudin, “Destructive interference effects in the second harmonic light generated at randomly rough metal surfaces,” Opt. Commun. 161, 79–94 (1999).
[CrossRef]

1998 (1)

J. A. Sánchez-Gil and J. V. García-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]

1997 (3)

K. A. O’Donnell and R. Torre, “Second harmonic generation from a strongly rough metal surface,” Opt. Comm. 138 (1997) 341.
[CrossRef]

S. Nie and 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, and M. S. Feld, “Single molecule detection using surface-enhanced Raman scattering (SERS),” Phys. Rev. Lett. 78, 1667–1670 (1997).
[CrossRef]

1996 (3)

F. J. García-Vidal and J. B. Pendry, “Collective theory for surface-enhanced Raman scattering,” Phys. Rev. Lett. 77, 1163–1166 (1996).
[CrossRef] [PubMed]

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, and R. Botet, “Enhanced Raman scattering from self-affine thin films,” Opt. Lett. 21, 1628–1630 (1996).
[CrossRef] [PubMed]

1995 (1)

R. E. Luna, E. R. Méndez, J. Q. Lu, and Z.-H. Gu, “Enhanced backscattering due to total internal reflection at a dielectric-air interface,” J. Mod. Opt. 42, 257–269 (1995).
[CrossRef]

1994 (2)

M. E. Knotts and K. A. O’Donnell, “Measurements of light scattering by a series of conducting surfaces with one-dimensional roughness,” J. Opt. Soc. Am. A 11, 697–710 (1994).
[CrossRef]

M. I. Stockman, L. N. Pandey, L. S. Muratov, and T. F. George, “Giant fluctuations of local optical fields in fractal clusters,” Phys. Rev. Lett. 72, 2486–2489 (1994).
[CrossRef] [PubMed]

1992 (1)

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

1990 (1)

A. A. Maradudin, T. Michel, A. R. McGurn, and E. R. Méndez, “Enhanced backscattering of light from a random grating,” Ann. Phys. (New York)  201255–307 (1990).

1989 (1)

1987 (1)

1978 (1)

P. F. Gray, “A method of forming optical diffusers of simple known statistical properties,” Opt. Acta 31, 765–775 (1978).
[CrossRef]

Aigouy, L.

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

Aizpurua, J.

H. Xu, J. Aizpurua, M. Käll, and P. Apell, “Electromagnetic contributions to single-molecule sensitivity in surface-enhanced Raman scattering,” Phys. Rev. E 62, 4318–4324 (2000).
[CrossRef]

Antunes, P. A.

C. J. L. Constantino, T. Lemma, P. A. Antunes, and R. Aroca, “Single-molecule detection using surface-enhanced resonance Raman scattering and Langmuir-Blodgett monolayers,” Anal. Chem. 73, 3674–3678 (2001).
[CrossRef] [PubMed]

Apell, P.

H. Xu, J. Aizpurua, M. Käll, and P. Apell, “Electromagnetic contributions to single-molecule sensitivity in surface-enhanced Raman scattering,” Phys. Rev. E 62, 4318–4324 (2000).
[CrossRef]

Aroca, R.

C. J. L. Constantino, T. Lemma, P. A. Antunes, and R. Aroca, “Single-molecule detection using surface-enhanced resonance Raman scattering and Langmuir-Blodgett monolayers,” Anal. Chem. 73, 3674–3678 (2001).
[CrossRef] [PubMed]

Bjerneld, E. J.

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

Bloomstein, T. M.

M. Switkes, T. M. Bloomstein, and M. Rothschild, “Patterning of sub-50 nm dense features with space-invariant 157 nm interference lithography,” Appl. Phys. Lett. 77, 3149–3151 (2000).
[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, and 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, and L. Börjesson, “Spectroscopy of single hemoglobin molecules by surface enhanced Raman scattering,” Phys. Rev. Lett. 83, 4357–4360 (1999).
[CrossRef]

Botet, R.

Cerrina, F.

H. H. Solak, D. He, W. Li, S. Singh-Gasson, F. Cerrina, B. H. Sohn, X. M. Yang, and P. Nealey, “Exposure of 38 nm period grating patterns with extreme ultaviolet interferometric lithography,” Appl. Phys. Lett. 75, 2328–2330 (1999).
[CrossRef]

Chang, R. K.

R. K. Chang and T. E. Furtak, Surface Enhanced Raman Scattering (Plenum, New York, 1982).

Constantino, C. J. L.

C. J. L. Constantino, T. Lemma, P. A. Antunes, and R. Aroca, “Single-molecule detection using surface-enhanced resonance Raman scattering and Langmuir-Blodgett monolayers,” Anal. Chem. 73, 3674–3678 (2001).
[CrossRef] [PubMed]

Creighton, J. A.

J. A. Creighton, in Advances in Spectroscopy of Surfaces, vol. 16, edited by R. J. H. Clark and R. E. Hester (Wiley, Chichester, 1988).

Dainty, J. C.

Dasari, R. R.

K. Kneipp, Y. Wang, H. Kneipp, L. T. Perlman, I. Itzkan, R. R. Dasari, and M. S. Feld, “Single molecule detection using surface-enhanced Raman scattering (SERS),” Phys. Rev. Lett. 78, 1667–1670 (1997).
[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, and V. M. Shalaev, “Experimental observation of localized optical excitations in random metal-dielectric films,” Phys. Rev. Lett. 82, 4520–4523 (1999).
[CrossRef]

Emory, S. R.

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

Feld, M. S.

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

Furtak, T. E.

R. K. Chang and T. E. Furtak, Surface Enhanced Raman Scattering (Plenum, New York, 1982).

Gadenne, P.

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

García-Ramos, J. V.

J. A. Sánchez-Gil, J. V. García-Ramos, and 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. García-Ramos, and 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 and J. V. García-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]

García-Vidal, F. J.

F. J. García-Vidal and J. B. Pendry, “Collective theory for surface-enhanced Raman scattering,” Phys. Rev. Lett. 77, 1163–1166 (1996).
[CrossRef] [PubMed]

George, T. F.

M. I. Stockman, L. N. Pandey, L. S. Muratov, and T. F. George, “Giant fluctuations of local optical fields in fractal clusters,” Phys. Rev. Lett. 72, 2486–2489 (1994).
[CrossRef] [PubMed]

Gray, P. F.

P. F. Gray, “A method of forming optical diffusers of simple known statistical properties,” Opt. Acta 31, 765–775 (1978).
[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, and V. M. Shalaev, “Experimental observation of localized optical excitations in random metal-dielectric films,” Phys. Rev. Lett. 82, 4520–4523 (1999).
[CrossRef]

Gu, Z.-H.

R. E. Luna, E. R. Méndez, J. Q. Lu, and Z.-H. Gu, “Enhanced backscattering due to total internal reflection at a dielectric-air interface,” J. Mod. Opt. 42, 257–269 (1995).
[CrossRef]

He, D.

H. H. Solak, D. He, W. Li, S. Singh-Gasson, F. Cerrina, B. H. Sohn, X. M. Yang, and P. Nealey, “Exposure of 38 nm period grating patterns with extreme ultaviolet interferometric lithography,” Appl. Phys. Lett. 75, 2328–2330 (1999).
[CrossRef]

Hunter, W. R.

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

Itzkan, I.

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

Käll, M.

H. Xu, J. Aizpurua, M. Käll, and P. Apell, “Electromagnetic contributions to single-molecule sensitivity in surface-enhanced Raman scattering,” Phys. Rev. E 62, 4318–4324 (2000).
[CrossRef]

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

Kim, M.-J.

Kneipp, H.

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

Knotts, M. E.

Kottmann, J. P.

Lemma, T.

C. J. L. Constantino, T. Lemma, P. A. Antunes, and R. Aroca, “Single-molecule detection using surface-enhanced resonance Raman scattering and Langmuir-Blodgett monolayers,” Anal. Chem. 73, 3674–3678 (2001).
[CrossRef] [PubMed]

Leskova, T. A.

M. Leyva-Lucero, E. R. Méndez, T. A. Leskova, and A. A. Maradudin, “Destructive interference effects in the second harmonic light generated at randomly rough metal surfaces,” Opt. Commun. 161, 79–94 (1999).
[CrossRef]

Leyva-Lucero, M.

M. Leyva-Lucero, E. R. Méndez, T. A. Leskova, and A. A. Maradudin, “Destructive interference effects in the second harmonic light generated at randomly rough metal surfaces,” Opt. Commun. 161, 79–94 (1999).
[CrossRef]

Li, W.

H. H. Solak, D. He, W. Li, S. Singh-Gasson, F. Cerrina, B. H. Sohn, X. M. Yang, and P. Nealey, “Exposure of 38 nm period grating patterns with extreme ultaviolet interferometric lithography,” Appl. Phys. Lett. 75, 2328–2330 (1999).
[CrossRef]

Lu, J. Q.

R. E. Luna, E. R. Méndez, J. Q. Lu, and Z.-H. Gu, “Enhanced backscattering due to total internal reflection at a dielectric-air interface,” J. Mod. Opt. 42, 257–269 (1995).
[CrossRef]

Luna, R. E.

R. E. Luna, E. R. Méndez, J. Q. Lu, and Z.-H. Gu, “Enhanced backscattering due to total internal reflection at a dielectric-air interface,” J. Mod. Opt. 42, 257–269 (1995).
[CrossRef]

Lynch, D. W.

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

Maradudin, A. A.

M. Leyva-Lucero, E. R. Méndez, T. A. Leskova, and A. A. Maradudin, “Destructive interference effects in the second harmonic light generated at randomly rough metal surfaces,” Opt. Commun. 161, 79–94 (1999).
[CrossRef]

A. A. Maradudin, T. Michel, A. R. McGurn, and E. R. Méndez, “Enhanced backscattering of light from a random grating,” Ann. Phys. (New York)  201255–307 (1990).

Markel, V. A.

Martin, O. J. F.

McGurn, A. R.

A. A. Maradudin, T. Michel, A. R. McGurn, and E. R. Méndez, “Enhanced backscattering of light from a random grating,” Ann. Phys. (New York)  201255–307 (1990).

Mendez, E. R.

Méndez, E. R.

J. A. Sánchez-Gil, J. V. García-Ramos, and 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. García-Ramos, and 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]

M. Leyva-Lucero, E. R. Méndez, T. A. Leskova, and A. A. Maradudin, “Destructive interference effects in the second harmonic light generated at randomly rough metal surfaces,” Opt. Commun. 161, 79–94 (1999).
[CrossRef]

R. E. Luna, E. R. Méndez, J. Q. Lu, and Z.-H. Gu, “Enhanced backscattering due to total internal reflection at a dielectric-air interface,” J. Mod. Opt. 42, 257–269 (1995).
[CrossRef]

A. A. Maradudin, T. Michel, A. R. McGurn, and E. R. Méndez, “Enhanced backscattering of light from a random grating,” Ann. Phys. (New York)  201255–307 (1990).

Michel, T.

A. A. Maradudin, T. Michel, A. R. McGurn, and E. R. Méndez, “Enhanced backscattering of light from a random grating,” Ann. Phys. (New York)  201255–307 (1990).

Muratov, L. S.

M. I. Stockman, L. N. Pandey, L. S. Muratov, and T. F. George, “Giant fluctuations of local optical fields in fractal clusters,” Phys. Rev. Lett. 72, 2486–2489 (1994).
[CrossRef] [PubMed]

Nealey, P.

H. H. Solak, D. He, W. Li, S. Singh-Gasson, F. Cerrina, B. H. Sohn, X. M. Yang, and P. Nealey, “Exposure of 38 nm period grating patterns with extreme ultaviolet interferometric lithography,” Appl. Phys. Lett. 75, 2328–2330 (1999).
[CrossRef]

Nie, S.

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

Nieto-Vesperinas, M.

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

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

O’Donnell, K. A.

Ogilvy, J. A.

J. A. Ogilvy, Theory of Wave Scattering from Rough Surfaces (Adam Hilger, Bristol, 1991).

Pandey, L. N.

M. I. Stockman, L. N. Pandey, L. S. Muratov, and T. F. George, “Giant fluctuations of local optical fields in fractal clusters,” Phys. Rev. Lett. 72, 2486–2489 (1994).
[CrossRef] [PubMed]

Pendry, J. B.

F. J. García-Vidal and J. B. Pendry, “Collective theory for surface-enhanced Raman scattering,” Phys. Rev. Lett. 77, 1163–1166 (1996).
[CrossRef] [PubMed]

Perlman, L. T.

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

Poliakov, E. Y.

Quelin, X.

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

Rothschild, M.

M. Switkes, T. M. Bloomstein, and M. Rothschild, “Patterning of sub-50 nm dense features with space-invariant 157 nm interference lithography,” Appl. Phys. Lett. 77, 3149–3151 (2000).
[CrossRef]

Sánchez-Gil, J. A.

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

Sant, A. J.

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, and V. M. Shalaev, “Experimental observation of localized optical excitations in random metal-dielectric films,” Phys. Rev. Lett. 82, 4520–4523 (1999).
[CrossRef]

Schultz, S.

J. P. Kottmann, O. J. F. Martin, D. R. Smith, and S. Schultz, “Dramatic localized electromagnetic enhancement in plasmon resonant nanowires,” Chem. Phys. Lett. 341, 1–6 (2001).
[CrossRef]

J. P. Kottmann, O. J. F. Martin, D. R. Smith, and S. Schultz, “Spectral response of plasmon resonant nanoparticles with a non-regular shape,” Opt. Express 6, 213–219 (2000), http://www.opticsexpress.org/abstract.cfm?URI=OPEX-6-11-213.
[CrossRef] [PubMed]

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, and V. M. Shalaev, “Experimental observation of localized optical excitations in random metal-dielectric films,” Phys. Rev. Lett. 82, 4520–4523 (1999).
[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, and R. Botet, “Enhanced Raman scattering from self-affine thin films,” Opt. Lett. 21, 1628–1630 (1996).
[CrossRef] [PubMed]

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, and V. M. Shalaev, “Experimental observation of localized optical excitations in random metal-dielectric films,” Phys. Rev. Lett. 82, 4520–4523 (1999).
[CrossRef]

Singh-Gasson, S.

H. H. Solak, D. He, W. Li, S. Singh-Gasson, F. Cerrina, B. H. Sohn, X. M. Yang, and P. Nealey, “Exposure of 38 nm period grating patterns with extreme ultaviolet interferometric lithography,” Appl. Phys. Lett. 75, 2328–2330 (1999).
[CrossRef]

Smith, D. R.

J. P. Kottmann, O. J. F. Martin, D. R. Smith, and S. Schultz, “Dramatic localized electromagnetic enhancement in plasmon resonant nanowires,” Chem. Phys. Lett. 341, 1–6 (2001).
[CrossRef]

J. P. Kottmann, O. J. F. Martin, D. R. Smith, and S. Schultz, “Spectral response of plasmon resonant nanoparticles with a non-regular shape,” Opt. Express 6, 213–219 (2000), http://www.opticsexpress.org/abstract.cfm?URI=OPEX-6-11-213.
[CrossRef] [PubMed]

Sohn, B. H.

H. H. Solak, D. He, W. Li, S. Singh-Gasson, F. Cerrina, B. H. Sohn, X. M. Yang, and P. Nealey, “Exposure of 38 nm period grating patterns with extreme ultaviolet interferometric lithography,” Appl. Phys. Lett. 75, 2328–2330 (1999).
[CrossRef]

Solak, H. H.

H. H. Solak, D. He, W. Li, S. Singh-Gasson, F. Cerrina, B. H. Sohn, X. M. Yang, and P. Nealey, “Exposure of 38 nm period grating patterns with extreme ultaviolet interferometric lithography,” Appl. Phys. Lett. 75, 2328–2330 (1999).
[CrossRef]

Stockman, M. I.

M. I. Stockman, L. N. Pandey, L. S. Muratov, and T. F. George, “Giant fluctuations of local optical fields in fractal clusters,” Phys. Rev. Lett. 72, 2486–2489 (1994).
[CrossRef] [PubMed]

Switkes, M.

M. Switkes, T. M. Bloomstein, and M. Rothschild, “Patterning of sub-50 nm dense features with space-invariant 157 nm interference lithography,” Appl. Phys. Lett. 77, 3149–3151 (2000).
[CrossRef]

Torre, R.

K. A. O’Donnell and R. Torre, “Second harmonic generation from a strongly rough metal surface,” Opt. Comm. 138 (1997) 341.
[CrossRef]

Wang, Y.

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

Xu, H.

H. Xu, J. Aizpurua, M. Käll, and P. Apell, “Electromagnetic contributions to single-molecule sensitivity in surface-enhanced Raman scattering,” Phys. Rev. E 62, 4318–4324 (2000).
[CrossRef]

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

Yang, X. M.

H. H. Solak, D. He, W. Li, S. Singh-Gasson, F. Cerrina, B. H. Sohn, X. M. Yang, and P. Nealey, “Exposure of 38 nm period grating patterns with extreme ultaviolet interferometric lithography,” Appl. Phys. Lett. 75, 2328–2330 (1999).
[CrossRef]

Anal. Chem. (1)

C. J. L. Constantino, T. Lemma, P. A. Antunes, and R. Aroca, “Single-molecule detection using surface-enhanced resonance Raman scattering and Langmuir-Blodgett monolayers,” Anal. Chem. 73, 3674–3678 (2001).
[CrossRef] [PubMed]

Ann. Phys. (1)

A. A. Maradudin, T. Michel, A. R. McGurn, and E. R. Méndez, “Enhanced backscattering of light from a random grating,” Ann. Phys. (New York)  201255–307 (1990).

Appl. Phys. Lett. (2)

M. Switkes, T. M. Bloomstein, and M. Rothschild, “Patterning of sub-50 nm dense features with space-invariant 157 nm interference lithography,” Appl. Phys. Lett. 77, 3149–3151 (2000).
[CrossRef]

H. H. Solak, D. He, W. Li, S. Singh-Gasson, F. Cerrina, B. H. Sohn, X. M. Yang, and P. Nealey, “Exposure of 38 nm period grating patterns with extreme ultaviolet interferometric lithography,” Appl. Phys. Lett. 75, 2328–2330 (1999).
[CrossRef]

Chem. Phys. Lett. (1)

J. P. Kottmann, O. J. F. Martin, D. R. Smith, and S. Schultz, “Dramatic localized electromagnetic enhancement in plasmon resonant nanowires,” Chem. Phys. Lett. 341, 1–6 (2001).
[CrossRef]

J. Chem. Phys. (1)

J. A. Sánchez-Gil and J. V. García-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. (1)

R. E. Luna, E. R. Méndez, J. Q. Lu, and Z.-H. Gu, “Enhanced backscattering due to total internal reflection at a dielectric-air interface,” J. Mod. Opt. 42, 257–269 (1995).
[CrossRef]

J. Opt. Soc. Am. A (2)

Opt. Acta (1)

P. F. Gray, “A method of forming optical diffusers of simple known statistical properties,” Opt. Acta 31, 765–775 (1978).
[CrossRef]

Opt. Comm. (1)

K. A. O’Donnell and R. Torre, “Second harmonic generation from a strongly rough metal surface,” Opt. Comm. 138 (1997) 341.
[CrossRef]

Opt. Commun. (1)

M. Leyva-Lucero, E. R. Méndez, T. A. Leskova, and A. A. Maradudin, “Destructive interference effects in the second harmonic light generated at randomly rough metal surfaces,” Opt. Commun. 161, 79–94 (1999).
[CrossRef]

Opt. Express (2)

Opt. Lett. (3)

Phys. Rep. (1)

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

Phys. Rev. B (2)

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

Phys. Rev. E (1)

H. Xu, J. Aizpurua, M. Käll, and P. Apell, “Electromagnetic contributions to single-molecule sensitivity in surface-enhanced Raman scattering,” Phys. Rev. E 62, 4318–4324 (2000).
[CrossRef]

Phys. Rev. Lett. (5)

K. Kneipp, Y. Wang, H. Kneipp, L. T. Perlman, I. Itzkan, R. R. Dasari, and 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, and L. Börjesson, “Spectroscopy of single hemoglobin molecules by surface enhanced Raman scattering,” Phys. Rev. Lett. 83, 4357–4360 (1999).
[CrossRef]

M. I. Stockman, L. N. Pandey, L. S. Muratov, and T. F. George, “Giant fluctuations of local optical fields in fractal clusters,” Phys. Rev. Lett. 72, 2486–2489 (1994).
[CrossRef] [PubMed]

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

F. J. García-Vidal and J. B. Pendry, “Collective theory for surface-enhanced Raman scattering,” Phys. Rev. Lett. 77, 1163–1166 (1996).
[CrossRef] [PubMed]

Science (1)

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

Other (5)

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

J. A. Ogilvy, Theory of Wave Scattering from Rough Surfaces (Adam Hilger, Bristol, 1991).

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

R. K. Chang and T. E. Furtak, Surface Enhanced Raman Scattering (Plenum, New York, 1982).

J. A. Creighton, in Advances in Spectroscopy of Surfaces, vol. 16, edited by R. J. H. Clark and R. E. Hester (Wiley, Chichester, 1988).

Supplementary Material (1)

» Media 1: MPG (161 KB)     

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Figures (4)

Fig. 1.
Fig. 1.

Surface realizations extracted from ensembles of randomly rough surfaces with Gaussian statistics and Gaussian correlation function: δ = 102.8 nm and a = 514, 102.8, 51.4, and 25.7 nm (shifted vertically for the sake of clarity).

Fig. 2.
Fig. 2.

Spectral dependence of the average SERS enhancement factor for randomly rough Ag surfaces with Gaussian statistics and correlation function: a (nm) =102.8 (blue), 51.4 (green), and 25.7 (red). Circles: δ = 51.4 nm; Triangles: δ = 257 nm. Black squares: a = δ = 514 nm. The result for self-affine surfaces with D = 1.9, δ = 257 nm, and ξL = 25.7 nm is also included (stars).

Fig. 3.
Fig. 3.

Movie of the spectral dependence of the near-field image of the enhancement of the p-polarized electric field intensity (log10 scale) in an area of 386×514 nm2 close to a random surface realization (a = 51.4 nm and δ = 257 nm), where a hot spot is observed. Incident beam: θ 0 =0°, W = 1.285 μm. The frequency range is ω/ω 0 = 0.88, 0.9, 0.92,…, 1.1, 1.12. The surface profile is depicted in blue. Front picture: λ = 2πc/ω 0 = 826.6 nm. [Media 1]

Fig. 4.
Fig. 4.

Spectral dependence of the maximum local SERS enhancement factor for the randomly rough Ag surfaces used in Fig. 2.

Equations (3)

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

W ( r r ) = δ 2 exp ( r r 2 a 2 ) ,
σ ( ω ) = E ( x | ω ) 2 E ( i ) ( x | ω ) 2 ;
𝓖 SERS ( ω ) = σ ( ω ) σ ( ω R ) σ 2 ( ω ) ,

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