An Exact Single Real Image Represntation for Sommerfeld Integrals above an Impedance Interface

The Sommerfeld integrals are known for time-consuming to evaluate due to the oscillating and slow decay integrand. In this work, a highly efficient evaluation of Sommerfeld integrals in the half-space with an impedance boundary condition interface is addressed. Using the coordinate system transformation, the original Sommerfeld integral is transformed into a single image representation. The validity of the proposed formulations is also numerically verified and studied.