The Poynting–Stokes tensor and radiative transfer in discrete random media: The microphysical paradigm

This paper solves the long-standing problem of establishing the fundamental physical link between the radiative transfer theory and macroscopic electromagnetics in the case of elastic scattering by a sparse discrete random medium. The radiative transfer equation (RTE) is derived directly from the macroscopic Maxwell equations by computing theoretically the appropriately defined so-called Poynting–Stokes tensor carrying information on both the direction, magnitude, and polarization characteristics of local electromagnetic energy flow. Our derivation from first principles shows that to compute the local Poynting vector averaged over a sufficiently long period of time, one can solve the RTE for the direction-dependent specific intensity column vector and then integrate the direction-weighted specific intensity over all directions. Furthermore, we demonstrate that the specific intensity (or specific intensity column vector) can be measured with a wellcollimated radiometer (photopolarimeter), which provides the ultimate physical justification for the use of such instruments in radiation-budget and particle-characterization applications. However, the specific intensity cannot be interpreted in phenomenological terms as signifying the amount of electromagnetic energy transported in a given direction per unit area normal to this direction per unit time per unit solid angle. Also, in the case of a densely packed scattering medium the relation of the measurement with a well-collimated radiometer to the time-averaged local Poynting vector remains uncertain, and the theoretical modeling of this measurement is likely to require a much more complicated approach than solving an RTE.