1,592 research outputs found
GENERALIZED MODES IN WAVEGUIDES WITH INHOMOGENEOUS DIELECTRIC
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
- …