High-frequency asymptotic analysis of diffraction of plane waves by a perfectly conducting half-plane in motion

The scattering of a time-harmonic plane wave by a perfectly conducting half-plane in relativistic uniform motion is discussed. This problem is formulated by means of the Special Theory of Relativity, considering a homogeneous and isotropic medium. Exact and explicit fields are obtained, valid for all space. High-frequency asymptotic approximations are derived and it is shown that the shadow boundaries of incident and reflected waves are no longer parallel to those propagation directions. Field equations are shown to reduce to the classical Sommerfeld solution when the speed of the scatterer goes to zero.