An Efficient Numerical Approach for Evaluating Sommerfeld Integrals Arising in the Construction of Green's Functions for Layered Media

Abstract

This paper presents an approach for evaluating the Sommerfeld integrals in the spectral domain, whose integrands typically show an oscillatory and slowly decaying behavior at high frequencies, e.g., in the mm-wave regime. It is well known that these integrals arise in the representations of the dyadic Green's functions of layered media and efficient computation of these Green's functions is key to rapid CEM modeling of patch antennas and printed circuits designed for 5G applications in the mm-wave range. The underlying concept of the approach is to partition the spectral domain representation of a Green's function into multiple domains and to represent the envelope of the integrand in each domain with a few exponentials such that the integrals in these domains can be evaluated analytically very efficiently and accurately in a numerically stable manner. Additionally, a new interpolation strategy is proposed in this work to decrease the matrix fill time in the MoM solution of the integral equations whose kernels contain Green's functions mentioned above. The performance enhancement realized by using the approaches is demonstrated through several illustrative examples.