A Multilevel Hybrid Inhomogeneous/Propagating Plane-Wave Algorithm for Radiation Integral Evaluations Above Planar Multilayered Media

Abstract

Electromagnetic radiation integral evaluations for planar multilayered media depend commonly on spectral integral representations in terms of mixed inhomogeneous/propagating plane waves, while purely propagating plane-wave representations are only feasible for homogeneous media. Both representations can be used to diagonalize the radiation integral for distributed source and observation configurations, where the purely propagating plane-wave representation has led to the multilevel fast multipole methods (MLFMMs) for the fast evaluation of radiation integrals. The fast inhomogeneous plane-wave algorithms (FIPWAs) map the inhomogeneous plane-wave translation operators back to propagating plane waves and they can, thus, also handle planar multilayered media. As an alternative, a hybrid algorithm for radiation integral evaluations above planar multilayered media is presented, which fully retains the MLFMM for the direct homogeneous medium radiation part, with all its flexibility, e.g., in the use of directive translation operators, and works directly with the mixed inhomogeneous plane-wave representation for the multilayered media contributions, with all its flexibility, e.g., no need of buffer boxes. The mixed inhomogeneous plane-wave radiation patterns of the sources and the observers are extrapolated from their propagating plane-wave counterparts only on the finest level of the underlying multilevel octree via spherical harmonics and a methodology is worked out for efficient numerical quadrature as well as local interpolations and anterpolations along the chosen mixed inhomogeneous plane-wave integration path. The algorithm is demonstrated and evaluated within the framework of an inverse source solver, where field evaluations from given sources as well as inverse source solutions from given observations are considered.