An exact series representation for the EM field from a circular loop antenna on a lossy half-space

This letter introduces an analytical approach for the evaluation of the complete integral expressions for the time-harmonic electromagnetic (EM) field components generated by an arbitrarily large thin-wire circular loop antenna lying on the surface of a flat and homogeneous half-space. The method consists of casting the integrands of the field integrals into forms in which the square-root terms, originating branch cuts, are replaced with their rational function representations via Newton's method. Explicit expressions for the fields are then derived by applying the residue theorem. The proposed procedure is exact since previous authors have shown that the sequence of rational functions generated by Newton's method converges quadratically to the square root, even if the independent variable is a complex number. Numerical simulations are performed to confirm the validity of the developed formulation.