Direct Rational Function Fitting Method for Accurate Evaluation of Sommerfeld Integrals in Stratified Media

Abstract

The current work proposes a direct rational function fitting method, employing cylindrical waves alone, for the accurate evaluation of Sommerfeld integrals for planar multilayered structures. Three are the key points of the effort. 1) Until now, relative works require the extraction of the quasi-static/asymptotic terms, and branch cut/continuous wave contribution explicitly. In the current one, the explicit treatment of those terms is avoided. The proposed methodology is based on the direct fitting of the spectrum of the Green's function by rational functions. Thus, it provides the spatial Green's function solely in terms of cylindrical waves. 2) The effectiveness, robustness and accuracy improvement of the rational function fit rely upon the proper sampling of the spectrum. This accurate fitting is possible because instead of avoiding large variations of the spectral kernel, we introduce proper paths to include more variation, and thus more spectrum information, before we apply the modified VECTFIT algorithm. 3) Furthermore, proper weighting of the VECTFIT is proposed in order to guide the algorithm in providing increased accuracy in specific desired areas of the horizontal distance between the source and observation points. Armed with the above the direct rational function fitting method provides accurate results both for the near and far-field regions. Various examples, among them the correct treatment of a two branch case, are given that prove the excellent performance and robustness of the proposed approach.