Electromagnetic edge diffraction revisited: the transient field of magnetic dipole sources

A surprisingly simple exact solution is derived for the transient electromagnetic field scattered by a perfectly conducting half-plane, which is embedded in a uniformly conducting host and energized by a unit step impulse of an arbitrarily oriented magnetic dipole. Despite its simplicity, the model has some relevance for geophysical applications (e.g. mineral exploration), provides insight into the physics of the transient scattering process, and has merits in validating numerical 2.5-D or 3-D codes. The diffraction of electromagnetic waves at a perfectly conducting edge is one of the few vectorial diffraction problems that allows an exact treatment. In the past, attention has been confined to harmonic excitation in a lossless dielectric host, whereas the transient field in a lossy medium has escaped attention. In the quasi-static approximation in particular, this solution turns out to be simple compared to the explicit form of the field using harmonic excitation. However, even the inclusion of displacement currents, which may be necessary when applying transient electromagnetic methods to environmental geophysics, does not lead to complications. The electric field and the time derivative of the magnetic field are given explicitly both in the quasi-static limit and with the inclusion of displacement currents. The late-time behaviour of the field is remarkable: whereas the full-space parts of these fields show the well-known t(-5/2) decay, the diffracted wave emerging from the edge decays only as t(-2) and therefore dominates the field geometry at late times. The appendices briefly treat the quasi-static transient field of a grounded electric dipole and sketch the formal solution for a perfectly conducting half-plane in a layered host.