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Abstract
The dyadic Green's functions for a rectangular waveguide filled with two dielectrics are obtained by starting with the functions for a parallel plate waveguide then applying the method of scattering superposition to construct the desired functions. By means of a contour integration of the Fourier integral we can obtain a series representation of the desired electric dyadic Green's function. The characteristic equations for the wave numbers of two sets of residue waves agree with the early works based on the matching of transversal wave impedances across the interface of the two dielectrics.