Nonadditivity of Poynting vector within opaque media

The energy flux within an opaque medium near an interface is not the sum of an incident plus a reflected term, as there is a synergistic contribution to the time-averaged Poynting vector that involves simultaneously both the incident and reflected fields. Therefore, the well-known formula R + T = 1, where R is the reflectance and T the transmittance, does not hold, and furthermore, R and T lose their accepted meanings. We illustrate the perils of assuming energy flux additivity by calculating the transmission and reflection spectrum of a film over a substrate normally illuminated by incoherent light at frequencies in the neighborhood of an optical resonance. We also show that the usual relation between the scattering, absorption, and extinction cross sections for particles immersed within a dissipative host have to be modified to account for the nonadditivity.