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Diffraction by a perfectly conducting wedge illuminated by a complex point source

An elementary dipole in presence of a perfectly conducting wedge radiates a field whose analytic expression can be written in terms of a double infinite series. A dipole located at a point characterized by complex coordinates behaves in the real space as a directive source akin to a Gaussian beam in the paraxial region. In this article, the series solution, originally conceived for a dipole located at a point characterized by real coordinates, is extended to the case of a complex coordinates source, hence providing an analytical solution approximating the problem of a wedge illuminated by a Gaussian beam.