Evaluation of sommerfeld integrals using contour deformation paths for nano and microstrip antenna applications

A quantitative comparison is carried out between various transformations for evaluating the finite region of Sommerfeld Integral (SI). These transformations deform the integration path into upper half plane (u.h.p) and avoids location of pole singularities. Results are shown for the case of Horizontal Electric Dipole (HED) located in the superstate of a two-layer microstrip configuration backed by a perfect electric conductor (PEC). Comparisons suggests that the semi-elliptic contour for finite part of SI, and the weighted averages method (WAM) for SI tail is the best approach for small and large lateral electrical separation (ρ/λ).