Radiation of a line source by a half-plane located at the interface between isorefractive media

In 1902, MacDonald obtained an exact solution to the boundary-value problem of radiation of a line source parallel to the edge of a metallic half-plane, as an infinite series of circular cylindrical wave functions. That solution is herein extended to the case of a half-plane located at the planar interface separating two media that are isorefractive to each other. The case of a plane wave incident on the same structure was recently solved exactly and in closed form (P.L.E. Uslenghi, USNC-URSI National Radio Science Meeting, Boulder, CO, January 2014; P.L.E. Uslenghi, IEEE Antennas Wireless Propag. Lett., vol. 13, 2014).