A reciprocity theorem for electromagnetic fields with general time dependence

A reciprocity theorem for electromagnetic fields with general time dependence has been derived in the time domain, and thus the result is applicable to fields whose time dependences are not Fourier transformable functions. The region to which the theorem applies may consist of dissipative, dispersive, nonhomogeneous, and anisotropic (but nongyrotropic) media, and all these properties may extend to infinity. Based on this theorem a variational expression which provides an approximation for calculating scattered fields has been obtained. The meaning of the approximation for the fields as arbitrary functions of time is discussed, together with three types of practical detecting systems, namely, square law, full-wave bridge, and single diode. For the latter two types, it is found that the variational expression yields an upper bound to the signal at the output of the detector.