Rayleigh Scattering by a Nanosphere

We now consider a simple application for the scattering formalism introduced above. We consider a dielectric or a metal nanosphere in the vacuum, centered at the fq = 0 and excited by a a plane-wave with Sine given by Eq. (1.282). If the sphere is very small R -C A.) we have the so called Rayleigh scattering and we can use the quasi-static solution of Sec. 1.4.1. In particular we can assume that sphere can be modeled by a dipole 

Concerning the absorption cross-section, it can be computed from the dissipated energy by the Joule effect (see Eq. (1.46)). 

Considering that the field inside the sphere is actually uniform and it is given by Eq. (1.194), we obtain  

Csca and Cabs have a different dependence from the sphere radius (f and R, respectively) for small spheres the absorption will be larger than the scattering, while the opposite is true for large R. However for a large particle retardation effects cannot be neglect. Thus the above formulas are valid only for R X. 

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