Rayleigh-Gans approximation

Figure 6.1 Coordinate systems for determining scattering by an arbitrary particle in the Rayleigh-Gans approximation. 

For spheres sufficiently small that Rayleigh theory (Chapter 5) is applicable, or for arbitrarily shaped particles that satisfy the requirements of the Rayleigh-Gans approximation (Chapter 6), incident light with electric field components parallel and perpendicular to the scattering plane may be scattered with different amplitudes however, there is no phase shift between the two components. Hence, the amplitude scattering matrix has the form... 

If Vs/Is is to be nonzero, either S34/Sn and Ums/Ims, or S44/S] i and Vms/Ims, or both, must not be zero. S34 is zero for nonabsorbing particles in the Rayleigh limit and for arbitrary particles in the Rayleigh-Gans approximation. Even for particles—spherical and nonspherical—of size comparable with the wavelength, however, 34 tends to be small, particularly in the forward direction (see Figs. 13.13 and 13.14). 

The distance, d, is measured from an arbitrary reference point and may include a portion of the distance traveled by the incident beam as well as by the scattered beam. These equations assume that the electric field at the scattering point is not modified on crossing dielectric boundaries. This assumption is referred to as the Rayleigh-Gans approximation . Deviations from this assumption can be treated in simple cases such as in the Mie scattering from spheres. 

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