The principal-volume method of expressing the spatial representation of the dyadic Green's function in free space is reviewed, followed by the eigenfunction expansion method of deriving the dyadic Green's function in free space and an arbitrarily shaped waveguide. In both cases, there are Dirac delta function singularities. It is shown that Dirac delta function in the eigenfunction representation has the same physical interpretation as the Dirac delta function singularity in the principal-volume method. However, in the eigenfunction representation, there is no need to specify a principal volume. This study shows some relationships between the principal-volume method and the eigenfunction-expansion method and reasserts that the dyadic Green's function should be regarded as a distribution or a generalized function.
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