Poynting's theorem and electromagnetic wave multiple scattering in dense media near resonance: Modified radiative transfer equation

A new version of nonstationary radiative transfer theory for vector electromagnetic wave multiple scattering in a discrete random medium is presented in which the electromagnetic energy within dielectric scatterers may be large. The starting point is the general two frequency Bethe-Salpeter equation for the coherence tenser-function of the wave electric field. In the two frequency domain it is proved that the Poynting's theorem can be decomposed into (1) a theorem for the spectral component of the electric energy density multiplied by two and (2) a theorem for the difference between the spectral components of the electric and the magnetic energy densities. The Poynting's theorem is closely connected with a generalized two-frequency Ward-Takahashi identity according to which the extinction of a nonsteady radiation is conditioned by the incoherent scattering, the real absorption and changing of the energy accumulation inside scatterers. As result a new radiative transfer equation is obtained for the radiance tensor of a pulse radiation in unbounded random medium. This equation differs from the traditional one by a term with the time derivative where the inverse value of the group velocity is replaced by a tenser-operator which determines the average rate of the electromagnetic energy change within scatterers.