Exact Closed-Form Expression of the Electromagnetic Field Excited by a Uniform Current Distribution Lying on a Cartesian Quadrant

The exact analytical solution of the electromagnetic field distribution produced by uniform electric currents excited on Cartesian half-planes and quadrants is presented. The total field is expressed in terms of geometrical optics (GO) and diffracted field contributions that remain valid for arbitrary observation points and frequency. The jump discontinuity of the GO field is exactly compensated by the diffracted field whose spatial distribution is described in terms of the incomplete Hankel functions and by means of a novel special function. The expression of the diffracted field includes contributions arising from the edges and the vertex of the considered Cartesian domain, illustrating the analytical behavior of the near-field singularities and providing insight into the physical mechanisms governing the field diffractive processes. The proposed solution yields a method to determine the physical optics (PO) response of flat metallic screens excited by uniform plane waves, as well as the fields produced by pulse-shaped basis functions used in the method-of-moments (MoM) solution of electromagnetic problems, showing the relevance of the exact analytical expressions of the GO and diffracted fields arising from edges and vertices of each rectangular pulse domain. Numerical examples validate the accuracy of the proposed field representation.