Power reciprocity in antenna theory

A rigorous derivation of the power-reciprocity theorem in antenna theory is presented. It relates the absorption cross-section of the load in the receiving situation to the power gain of the antenna in the transmitting situation. The most general case is considered, namely (a) the materialof which the antenna is made may be lossy, anisotropic and inhomogeneous, if only linear in its electromagnetic behaviour, (b) the vectorial amplitude radiation characteristic of the antenna in the transmitting situation and the incident plane wave in the receiving situation may be arbitrarily elliptically polarised, and (c) the impedance of the load in the receiving situation may be arbitrarily mismatched to the input impedance of the antenna in the transmitting situation. Therefore the known, restricted form of the theorem is generalised; also some notions are made more precise. As a corollary, a generalised theorem is presented as to the average value of the absorption cross-section of the load taken over all directions of incidence.