We have already mentioned that different combinations of electric and magnetic field vectors can yield the same Poynting vector. This means that forming the vector product of the electric and magnetic field vectors results in a quantity that does not carry unique information about the participating fields. In particular, the Poynting vector contains no information about the polarization state of a transverse electromagnetic field. Thus, by its very deinition, the Poynting vector cannot be used to describe the phenomenon of electromagnetic scattering by, for example, expressing the Poynting vector of the scattered field in that of the incident field.

We have seen in the preceding chapter that the standard descriptor of polarization is the Stokes column vector (7.3). However, this quantity contains no explicit information on the direction of the Poynting vector and can be defined only for a transverse (i.e., plane or spherical) electromagnetic wave, whereas the total electromagnetic field in the near zone of any object (e.g., at any observation point inside a cloud of particles) is never a transverse wave. It is, therefore, highly desirable to introduce an alternative quantity that:

1. • can be defined for any electromagnetic field;

2. • has the dimension of electromagnetic energy flux; and

3. • enables a complete and self-contained description of electromagnetic scattering in the context of practical optical analysis.