General singularity extraction technique for reflected Sommerfeld integrals

A general technique for singularity extraction from reflected Sommerfeld integrals (SIs) in frequency domain is presented. The essence of the technique is an analytical evaluation of all the singular and slowly convergent terms in SIs for reflected potentials and fields. This is done starting from two basic integrals. Up to two terms for Sommerfeld potential integrals and up to three terms for Sommerfeld field integrals are extracted. The remaining well-convergent parts of integrals are evaluated by numerical integration along the real axis. A new type of singularity extraction is applied to Sommerfeld's gAzxgAzx term, yielding the generalized Foster–Lien integral. Accuracy and efficiency of the method are illustrated by a numerical example.