Some investigations toward closed-form solutions of sommerfeld integrals

Sommerfeld integrals, that appear in problems related to electromagnetic wave propagation through layered media, have been traditionally evaluated by locating the poles of the integrand and accounting for their corresponding residue contributions. For multilayer problems, implementation of this procedure could potentially become computationally inefficient because the number of poles with significant residue contributions increases with frequency or equivalently the electrical thickness of the individual layers. This observation suggests that the well-known and popular discrete complex image method (DCIM) could also need significant modifications to its conventional algorithmic implementation for electrically thick layers.