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Electromagnetic mechanism in surface-enhanced Raman scattering from Gaussian-correlated randomly rough metal substrates

José A. Sánchez-Gil, José V. García-Ramos, and Eugenio R. Méndez

Open Access Open Access

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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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).

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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).

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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]

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Fig. 4.
Fig. 4. Spectral dependence of the maximum local SERS enhancement factor for the randomly rough Ag surfaces used in Fig. 2.

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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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