Rayleigh scattering by a polarizable element

Let us set the polarizable element at the origin of the reference system and let ° (z, f) be the incident electric field, propagating in OZ direction, with pulsation cu0. 

The polarizable element behaves like a dipole with electrical moment D(t) 

In principle, this dipole is a functional of ° (z, t) but the retardation effects will be neglected. Thus, the components of these vectors obey the linear relation 

In the electrostatic system of units, the txu have the dimension of a volume. The electric fields associated with a radiation scattered at point r in direction f are identified with the electric field E(r, t) produced by the dipole oscillations. We have [see (6.1.2)] 

Vectors E associated with the scattered field are determined by the relations (see Appendix D) 

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