Enhanced backscattering of light from a random grating

Maradudin, A. A.; Michel, Thilo; McGurn, Arthur R.; Mendez, Eugenio Rafael Mendez

doi:10.1016/0003-4916(90)90172-k

Cited by 389 publications

(203 citation statements)

References 25 publications

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“…Our rigorous calculation method is based upon the exact integral equations formulation of the above mentioned scattering problem. 15,[36][37][38][39] This formulation can be briefly summarized as follows. On the basis of the Helmholtz equations satisfied by the field in the upper U ␤ Ͼ (r, )(zϾ ) and lower U ␤ Ͻ (r, )(zϽ ) semi-infinite half-spaces, and by applying the Green's theorem and recalling the radiation conditions at infinity, we are led to the following four integral equations,…”

Section: Em Scattering Theorymentioning

confidence: 99%

“…By means of a quadrature scheme the surface is truncated to a length L consisting of N sampling points. 36 In practice, for every realization of the random surface, it reduces to solving a system of 2N complex linear equations for the source functions, followed by a vectormatrix multiplication to obtain the scattered field at each position in the vacuum half-space. Furthermore, when statistical quantities such as ensemble averages ͑͗•••͒͘ or probability density functions ͑PDF͒ are needed, the procedure is repeated for a sufficiently large number N r of surface profile realizations ͑ergodicity is assumed͒.…”

Section: ͑23b͒mentioning

confidence: 99%

“…This formulation has been successfully employed through numeria͒ cal simulation calculations to study the far field scattered from one-dimensional, randomly rough, either metal or dielectric, surfaces. 15,[36][37][38][39] We will apply it to calculate the linearly-polarized EM field in the vicinity of self-affine fractal surfaces of Ag, Au, and Cu, similar to those mentioned above that are used as SERS substrates. In this regard, preliminary results point out the ability of this kind of surfaces to generate large surface FE.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Calculations of the direct electromagnetic enhancement in surface enhanced Raman scattering on random self-affine fractal metal surfaces

Sánchez‐Gil

Garcı́a-Ramos

1998

The Journal of Chemical Physics

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We study the classical electromagnetic enhancement at the excitation wavelength related to surface enhanced Raman scattering ͑SERS͒ experimental configurations in the vicinity of random rough metal surfaces possessing self-affine scaling behavior. The scattered electromagnetic intensity is obtained by means of numerical calculations based on the rigorous integral equations formulation of the electromagnetic wave scattering, free from the limitations of electrostatic and/or dipolar approximations. From the enhancement of the scattered field intensity in the immediate vicinity of the surface, originated in the excitation of transversal-magnetic surface plasmon polaritons, the SERS electromagnetic mechanism on substrates of Ag, Au, and Cu is explored as a function of the surface fractal dimension, rms height, and excitation wavelength. It is found that fractality favors the occurrence of large electromagnetic enhancements, which in turn appear to be maximum at an optimum wavelength as a result of the compromise between roughness-induced light coupling into surface plasmons and absorptive losses. This optimum wavelength is shorter for Ag than for Au and Cu. Maximum local enhancements on the order of 10 3 are encountered for the three metals being considered.

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Section: Em Scattering Theorymentioning

confidence: 99%

Section: ͑23b͒mentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Calculations of the direct electromagnetic enhancement in surface enhanced Raman scattering on random self-affine fractal metal surfaces

Sánchez‐Gil

Garcı́a-Ramos

1998

The Journal of Chemical Physics

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“…The GO approximation is a commonly used approximation in rough surface scattering theory, [2][3][4][5][6] due to its relatively simple numerical implementation and the reduced computational requirements compared to the numerical integration techniques needed for rigorous electromagnetic wave analysis. [7][8][9][10][11] The approximation is a ray-tracing approach, where energy bundles are traced throughout their interactions with the surface until they leave it. The approximation is regarded as valid when the normalized correlation length, / , as well as the normalized rms roughness, / , are larger than unity ͑ being the wavelength of the light involved͒.…”

Section: Introductionmentioning

confidence: 99%

A ray-tracing analysis of the absorption of light by smooth and rough metal surfaces

Bergström

Powell

Kaplan

2007

Journal of Applied Physics

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Ray tracing has been employed to investigate the absorption of light by smooth and random rough metal surfaces. For normally incident light the absorptance of the surface increases with surface roughness. However, for light incident at a tangent to the surface the absorptance-surface roughness relationship is more complex. For example, in certain cases the absorptance can rise, fall, and rise again as the surface roughness increases. In this paper this complex absorptance-roughness relationship is defined and explained. The wavelengths of the light chosen for this study correspond to the primary and secondary output wavelengths of Nd:YAG lasers.

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“…We make use here of the formally exact formulation for the scattering of EM waves in the form of surface integral equations by means of the Green's theorem. [35][36][37] This formulation has been used to investigate the EM field scattered from one-dimensional, randomly rough metal surfaces with arbitrarily large roughness. 22,38 Furthermore, by invoking the approximation ͑1͒, numerical results for the near-field enhancements at the pump frequency have been used to infer SERS enhancement factors.…”

Section: A Scattering Equationsmentioning

confidence: 99%

Electromagnetic model and calculations of the surface-enhanced Raman-shifted emission from Langmuir-Blodgett films on metal nanostructures

Giannini

Sánchez‐Gil

Garcı́a-Ramos

et al. 2007

The Journal of Chemical Physics

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We present a theoretical study of the electromagnetic contribution to surface-enhanced Raman scattering ͑SERS͒ from a Langmuir-Blodgett film close to a metal surface. This macroscopic dipolar model fully accounts for the Raman-shifted emission so that meaningful SERS ͑electromagnetic͒ enhancement factors that do not depend only on the local electromagnetic field enhancement at the pump frequency are defined. For a plane metal surface, analytical SERS enhancement factors that are consistent for all pump beam polarization and molecular orientation are obtained. In order to investigate SERS on complex nanostructured metal surfaces, we introduce this model into the formally exact, Green's theorem surface integral equation formulation of the scattered electromagnetic field. This formulation is thus employed to calculate numerically the near-field and far-field emissions at the Raman-shifted frequency for very rough, random nanostructured surfaces, with emphasis on the impact of collective processes for varying pump frequency and Raman shift. Our results reveal that the widely used ͉E͉ 4 approximation tends to overestimate average SERS enhancement factors.

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Enhanced backscattering of light from a random grating

Cited by 389 publications

References 25 publications

Calculations of the direct electromagnetic enhancement in surface enhanced Raman scattering on random self-affine fractal metal surfaces

Calculations of the direct electromagnetic enhancement in surface enhanced Raman scattering on random self-affine fractal metal surfaces

A ray-tracing analysis of the absorption of light by smooth and rough metal surfaces

Electromagnetic model and calculations of the surface-enhanced Raman-shifted emission from Langmuir-Blodgett films on metal nanostructures

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