GENERALIZED MODES IN WAVEGUIDES WITH INHOMOGENEOUS DIELECTRIC

Abstract

It is shown that at certain singular values of the complex frequency the field in a waveguide with inhomogeneous dielectric cannot be described as a superposition of modes, because the eigenfunctions do not form a complete set. At these singular complex frequencies the fields of two different modes become identical and this common field is a special form of a generalized mode which exists only at singular complex frequencies. The generalized mode has a more complicated mathematical form than the usual mode. As for certain waveguides singular complex frequencies may assume pure imaginary values, these gen- eralized modes may exist also at pure harmonic time dependence. In another paper it will be shown that the modal expansion is possible at singular complex frequencies, too, if generalized modes are used in addition to the usual modes.