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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References

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    [CrossRef]
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    [CrossRef]

Anal. Chem.

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.

A. A. Maradudin, T. Michel, A. R. McGurn, E. R. Mendez, �??Enhanced backscattering of light from a random grating,�?? Ann. Phys. (New York) 201 255-307 (1990).

Appl. Phys. Lett.

M. Switkes, T. M. Bloomstein, 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.

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.

J. A. Sanchez-Gil and J. V. Garcýa-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.

R . E. Luna, E. R . Mendez, 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

Opt. Acta

P. F. Gray, �??A method of forming optical di.users of simple known statistical properties,�?? Opt. Acta 31, 765-775 (1978).
[CrossRef]

Opt. Commun.

K. A. O�??Donnell and R. Torre, �??Second harmonic generation from a strongly rough metal surface,�?? Opt. Commun. 138, 341 (1997).
[CrossRef]

M. Leyva-Lucero, E. R. Mendez, 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

Opt. Lett.

Phys. Rep.

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

Phys. Rev. B

J. A. S´anchez-Gil, J. V. Garcýa-Ramos, and E. R. Mendez, �??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. Sanchez-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

H. Xu, J. Aizpurua, M. Kall, 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.

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. Kall, and L. Borjesson, �??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. Gresillon, 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. Garcýa-Vidal and J. B. Pendry, �??Collective theory for surface-enhanced Raman scattering,�?? Phys. Rev. Lett. 77, 1163-1166 (1996).
[CrossRef] [PubMed]

Science

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

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)

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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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