Transfer Operator Theory and Inter-Reciprocity of Non-Reciprocal Multiport Antennas

The present article expounds a formalism for the representation of multi-port non-reciprocal antenna structures in an arbitrary surrounding linear medium. In the most general approach the antenna, the waveguides connected to it, as well as the surrounding medium may contain any distribution of anisotropic magneto-electric media. Furthermore, an arbitrary external field is taken into consideration which need not be of plane wave form. A reciprocally adjoint system is introduced to derive relations which describe the antenna under such general conditions. Since the antenna may contain media which prohibit the use of ordinary scattering, admittance or impedance matrices, an approach by means of generalized scattering matrices, or by a generalized admittance and a generalized impedance matrix, is applied. This leads to an n-port description of the whole waveguide-antenna-environment where transfer operators render the interaction between the external field and the state of the ports. These operators are the generalizations of effective length vectors. For its importance the case of reciprocal reflection-symmetric waveguides is treated in detail, including a derivation of the consequences of abstract network reciprocity and complex power relation for voltage-current representations. The formalism is adequate for the description of radar and radio astronomy antennas, in particular when wave polarization plays a crucial role and/or a magnetized plasma environment is present (which is responsible for anisotropy and non-reciprocal conditions).