  In this paper, we extend the resonant modal theory (RMT) developed previously
for a metal object to an arbitrary source region consisting of metals,
dielectrics, or the combination of both. The influences of dielectrics on the
fields are replaced by equivalent volume sources through the use of the
compensation theorem in electromagnetic theory. The resonant frequencies can be
determined by finding the roots of the determinant of the matrix resulted from
the discretization of the real homogeneous volume-surface integral equation
derived from the requirement that the difference of stored field energies in
the source region vanishes. As applications of the extended RMT, three examples
have been investigated. The first example is a dielectric resonator antenna,
and is designed by exciting the first resonant mode of the composite structure
in which the dielectric cylinder is combined with a conformal metallic strip.
The second example is a dual-band dielectric-coated metallic wire antenna. The
third example studies the resonant modes of a rectangular patch antenna.
