Excitation theory for space-dispersive active media waveguides

Abstract

A unified electrodynamic approach to the guided-wave excitation theory is generalized to the waveguiding structures containing a hypothetical space-dispersive medium with drifting charge carriers possessing simultaneously elastic, piezoelectric and magnetic properties. Substantial features of our electrodynamic approach are: (i) the allowance for medium losses and (ii) the separation of potential fields peculiar to the slow quasi-static waves which propagate in such active media independently of the fast electromagnetic waves of curl nature. It is shown that the orthogonal complementary fields appearing inside the external source region are only associated with a contribution of the potential fields inherent in exciting sources. Taking account of medium losses converts the usual orthogonality relation into a novel form called the quasi-orthogonality relation. Development of the mode quasi-orthogonality relation and the equations of mode excitation is based on the generalized reciprocity relation (the extended Lorentz lemma) especially proved for this purpose that allows for specific properties of the space-dispersive active media and the separation of the potential fields. The excitation equations turn out to be the same, in form, whatever the waveguide filling, including both the time-dispersive (bi-anisotropic) and the space-dispersive media. Specific properties of such media are reflected in a particular form of the normalizing coefficients for waveguide eigenmodes. It is found that the separation of potential fields reveals the fine structure of the interaction between the exciting sources and mode eigenfields: in addition to the exciting currents (bulk and surface) interacting with the curl fields, the exciting charges (bulk and surface) and the double charge (surface dipole) layers appear to interact with the quasi-static potentials and the displacement currents, respectively.