On the Implied Approximations Appearing in Simplified Emissivity for the Investigation of the Thermal Emission from Dense Media

According to our recent modal representation, the origin of thermal radiation can be associated to the distribution of a finite number of current sources, independent one from the other (the Degrees of Freedom). In a companion paper we have also shown that, if one is only interested in the energy radiated, the current sources can be mathematically replaced by a much larger number of equivalent sources, that are unphysical, as they are imposed to be uncorrelated at any distance and are distributed all over the volume. A classic procedure for estimating the electromagnetic energy emitted by such ensemble of energetically equivalent currents is presented. The derivation presented here can just as well be applied to another set of energetically equivalent currents, the Quantum born Rytov currents. To arrive to a final analytical expression for the radiation, multiple simplifying approximations are used. Treating the problem in transmission rather than in reception provides useful insights on their limits and applicability.