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The full spectral dyadic Green's function exhibits certain properties that its popular transversal portion does not. In particular, it is shown that the dyad is identically singular, the singularity being a manifestation of the plane wave properties of each spectral component. This singularity has an impact on the use of certain computational algorithms which in general would require an inversion of the dyad. Other plane wave properties, being dual to Maxwell's equations, are also discussed.