Efficient Evaluation of the Finite Part of Pole-Free Sommerfeld Integrals in Half-Space Problems with Predefined Accuracy

Abstract

This communication presents a novel, simple, and robust approach for the computation of the finite part of pole-free Sommerfeld integrals (SIs) in half-space problems with high and controllable accuracy over a large range of source-observer distances. The approach includes the following techniques: 1) cancellation of the branch-point singularities based on the square root change of variables for numerical integration; 2) approximation of real-axis integration path in order to enhance the singularity cancellation for arbitrary low-loss dielectrics; 3) thresholds for truncation of the interval of integration for given accuracy, which improve the efficiency of computation; and 4) prediction formulas that estimate the required number of integration points for a given accuracy up to 1000 wavelengths of source-observer distance. The proposed approach is verified through numerical examples and comparison to reference methods.