Classical multipole theory can be extended to multipoles located in complex space and applied in scattering and diffraction problems with the advantage that, if the point of the multipole is correctly chosen, the first term may give an order of magnitude better approximation to the source than when the multipole is in real space. The basic theory, given elsewhere, is presented here in a more straightforward manner and the improvement in radiation pattern is demonstrated for sources of constant polarization. Applications on scattering by spheroidal dielectric bodies and diffraction by a dielectric half-space are discussed.
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