Relativistic Scattering of a Plane-Wave by a Uniformly Moving Half-Plane

We discuss the effect of motion on the scattering by an edge. To this end, one considers the simplest canonical structure formed by a uniformly moving perfectly conducting half-plane illuminated by a time-harmonic plane wave and investigates the effect of the motion on the reflection and shadow zones, aberration, Doppler shift, edge-diffracted wave, etc. The cases where the velocity is parallel and normal to the half-plane are considered separately. Some of the interesting results which were obtained, in addition to the classical Doppler shift and aberration phenomena, are that (i) the edge-excited wave is never time-harmonic while the waves excited by the plane (both in the shadow and in the reflection zones) are always time-harmonic, (ii) the shadow and reflection boundaries are not parallel to the incident and reflected rays, (iii) at certain values of the velocity and incidence angle, a shadow region appears in the apparent illuminated region while a lit region appears in the apparent shadow region, (iv) the moving half-plane provides, sometimes, energy to the reflected wave. The cases of upsiLtc and upsi~c are examined in detail