Spatial Domain Green´s Functions of Layered Media Using a New Method for Sommerfeld Integrals

A simplified approach for accurate and efficient computation of infinite domain Sommerfeld integrals (SI) associated with spatial domain Green´s functions of layered media is described in this article. Integrand in SI excluding Bessel function is expressed as sum of complex exponentials using the matrix pencil method (MPM) which requires fewer terms than when we include oscillating Bessel functions. By using a novel three term representation for small arguments and classical large argument formulas of Bessel functions, analytical expressions for computing integrals along infinite domain SI tails are derived. The newly derived analytical formulas use the same MPM expansions for any given set of radial distance parameter ρ, enabling us to efficiently solve closed form Green´s functions in layered media.