An Electrodynamic Perturbation Theorem, with Application to Nonreciprocal Systems

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Abstract
By means of a slight modification of the macroscopic electrodynamic reciprocity theorem it is possible to obtain the perturbation of the admittance matrix of an electrodynamic device due to a suitable perturbation of the dielectric susceptibility, conductivity, and magnetic susceptibility tensors in the device. The theory is applicable to nonreciprocal systems, but in practice can be used to obtain only the first-order perturbation of the admittance matrix. An expression relating the current induced in part of a system due to the motion of current in another part of the system is similarly obtained. Dc and microwave gyrators are treated, and the connection is pointed out between Faraday rotation in a transmission cavity and the magnetic energy splitting of its circularly polarized normal modes.