Duality Lemma for Power Cross-Flows and Energy Balance at Scattering in an Absorbing Medium

Abstract

A duality lemma is derived that relates power cross-flows to their corresponding functions of sources in an absorbing medium. This lemma allows simplifying the description of energy exchange between arbitrarily chosen volumes in a dissipative medium containing radiation sources and scatterers. To illustrate the use of the lemma, derivation of the optical theorem for a scatterer in a lossy medium is considered. It is shown that local power flows are naturally divided into dissipative ones (i.e., drains associated with medium absorption), energy ones, which describe interaction of extrinsic and scatterer-induced currents with the electromagnetic field, and interference ones, which arise from superposition of the incident-wave and scattered-wave fields.