Rayleigh-Gans theory

Rayleigh-Gans theory, the values for major and minor particle half-axes were used for each single particle. The nanostructural information given from the TEM micrographs was very well considered for the optical calculations. 

In Chapter 8 we shall derive the field scattered by an infinite cylinder of arbitrary radius and refractive index we shall also consider scattering by a finite cylinder in the diffraction theory approximation. Although the finite cylinder scattering problem is not exactly soluble, we can obtain analytical expressions for the amplitude scattering matrix elements in the Rayleigh-Gan s approximation. 

Chapter 7 of Kerker (1969) is a more thorough treatment of Rayleigh-Gans (RG) theory than we have given here. There is a good concise derivation of this theory in the appendix of a paper by Wyatt (1968). 

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... 

Rayleigh-Debye-Gans Theory Theory of Mie Interacting Particles... 

FIGURE 5.71 The Rayleigh-Debye-Gans theory is based on the assumptions that (1) the incident beam propagates without being affected by the particles, and (2) the scattered hght, received by the detector, is a superposition of the beams emitted from the induced dipoles in the different parts of the particle. 

Farias, T.L., Koylu, U.O., and Carvalho, M.G., Range of validity of the Rayleigh-Debye-Gans theory for optics of fractal aggregates, Appl. Opt, 35, 6560, 1996. 

Throughout this discussion, we have implicitly assumed that the rod is optically homogenous with a single index of refraction and that the Rayleigh-Debye-Gans theory is valid, which basically restricts the theory to thin rods, unless the refractive index of the cylinder is close to that of the solvent used [73]. 

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