The transient electromagnetic field of a pulsed line source located above a dispersively reflecting surface

An exact representation for the transient field of a pulsed line source above a plane reflecting surface is obtained as a finite integral over the transient plane-wave solution for complex angles of incidence. When applied to the reflection from a conducting half-space, a solution for the transient field is obtained as a finite double integral, which permits accurate calculations in a minimum of computer time. Comparison with early-time and late-time approximations available in the literature shows that there is a wide range of times for which neither is accurate.