On the existence of the Sommerfeld integral pole and its contribution to the electromagnetic field

Evidence for the existence of a complex plane pole in the Sommerfeld integral for a source in air over a dielectric half-space and its contribution to the electromagnetic field is addressed. We present a detailed analysis of a simple model whereby a magnetic line source lies on the interface of the air-dielectric boundary. It is demonstrated that a Sommerfeld pole does indeed exist and that this pole can account for surface and lateral waves. It is also shown that a space wave is accounted for by the Sommerfeld integral branch cut.