Analytical Pole Extraction for Surface Wave Modes in Microstrip Structures: A Complete Residue Calculus Treatment

This paper presents a rigorous analytical treatment of the electric field dyadic Green’s function for a canonical microstrip geometry using pole extraction and residue calculus. The formulation provides explicit closed-form expressions for surface wave contributions and asymptotic radiation fields, enabling efficient computation and direct physical insight into electromagnetic wave propagation in layered media. The approach offers computational advantages over traditional numerical integration methods whilst maintaining mathematical rigour.