The angular spectrum representation of the electromagnetic Green's tensor has a part that is a superposition of exponentially decaying waves in the +z and -z directions (evanescent part) and a part that is a superposition of traveling waves, both of which are defined by integral representations. We have derived an asymptotic expansion for the z dependence of the evanescent part of the Green's tensor and obtained a closed-form solution in terms of the Lommel functions, which holds in all space. We have shown that the traveling part can be extracted from the Green's tensor by means of a filter operation on the tensor, without regard to the angular spectrum integral representation of this part. We also show that the so-called self-field part of the tensor is properly included in the integral representation, and we were able to identify this part explicitly.
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