Analysis of an infinite current source above a semi-infinite lossy ground using fictitious current auxiliary sources in conjunction with complex image theory techniques

The canonical problem of an infinitely long electric current line radiating above a lossy infinite half space is examined. The solution is based on the method of auxiliary sources (MAS). In this method one can, in general, apply a numerical solution by introducing sets of fictitious current sources whose fields are elementary analytical solutions to the boundary value problem, in order to approximately describe the actual electromagnetic (EM) fields in each domain. In general, the convergence rate and the accuracy of the MAS solution depend on the spatial distributions of the fictitious current sources sets and their locations in regard to the singularities of the actual EM field simulated by each set. Here, both the accuracy and the convergence rate of the method are examined, investigating complex image approximations in order to optimally choose the auxiliary sources placements. It is proved that the convergence rate and the accuracy of the method are significantly improved by utilizing the complex images as locations of the auxiliary sources. The main contribution of the paper consists in the application of MAS to an open structure, which involves lossy dielectrics excited by a nonuniform EM field, as well as in the optimal choice of the locations of the fictitious current sources according to complex image techniques.