Rayleigh dipole approximation

In general, the study of the scattered intensity by systems where multiple scattering is non-negligible is a difficult task. In order to resolve these difficulties we have used several approximations the particle size is assumed to be much smaller than the incident wavelength, so the Rayleigh dipole approximation is used to characterize the particle scattering. For the surface case, the perfect conductor approximation (PCA) ( = -go) for the substrate is applied. In both systems, the scattered field is calculated in the far-field approximation. For the purpose of this research, these approximations do not constitute serious restrictions and facilitate the numerical calculations. For real substrates (metallic or dielectric) and/or finite size particles, the main conclusions are unaffected [9]. The scattered intensity is calculated by means of the coupled dipole method (CDM) [10] for both the volume case and the surface case. In the latter, the PCA allows us to apply the image theory [11]. 

Light scattering by a dipole in a plane is considered. Colloidal scattering is discussed using the Rayleigh-Debye approximation, which holds for optically-soft any-form particles comparable with the wavelength. 

The polarization state of the scattered light from the surface contaminants shown in Figure 3 strongly resemble those of a single dipole located at the approximate center of the contaminant, even though the contaminant sizes are well outside the Rayleigh limit. It should be noted that the structures in the polarization responses can be modeled more accurately by changing the dipole... 

In the Rayleigh approximation, the particle is so small that an applied electric field Eq only induces a dipole with dipole moment p in the particle. In general, Eq and p must not be collinear, meaning that the polarizability d of the particle is a tensor ... 

Raman and Rayleigh scattering can be understood as the light generated by oscillating electric dipoles in the material, induced by the incident excitation radiation. The induced dipole moment tensor p can be considered, in a first order approximation, a linear function of the applied field E ... 

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