Abstract

A reciprocity theorem¹ widely used in the design of antennas treats antennas as part of an electronic circuit and relates the input and output currents and voltages. Some limited work has been done to obtain reciprocity theorems for the electromagnetic fields themselves,² but this work does not provide explicit mathematical expressions relating to the propagation of reciprocal fields. We give a proof for the following theorem. If two wave fields taken one at a time within a source-free, isotropic, and homogeneous medium are composed only of homogeneous plane waves so that their angular spectra are related by they are defined to be reciprocal so that the forward propagator in a diffraction integral for one field is the complex conjugate for the inverse propagator in a similar inverse diffraction integral for the other field.

© 1988 Optical Society of America