On the Asymptotics of Sommerfeld Integrals over an Impedance Plane

In this communication, the asymptotic expressions for Sommerfeld integrals (SIs) over an impedance plane are studied, since the impedance boundary condition (IBC) is a widely used simplification of many discontinuous interfaces. Based on the single image representation of SI, it is found that the far-field asymptotics of SIs can be written in forms of the well-known Fresnel integrals. A simple high-order approximation to the SI is derived, the accuracy and convergence behavior are numerically investigated. The behavior difference for SIs associated with different polarizations in some special cases is also analyzed.