Plane Wave Reflection by a PEC Plane in Harmonic Motion

The canonical problem of reflection of monochromatic plane waves by a Perfect Electric Conductor plane which is in harmonic motion is investigated under oblique incidence. The two modes of motion where the direction of harmonic motion is parallel and perpendicular to the normal of PEC plane are studied separately. The problem is formulated in the context of Hertzian Electromagnetism of Moving Bodies and an exact analytical solution is obtained. The reflected wave comprises an infinite number of harmonics weighted by Bessel functions similar to that of an FM signal. A verification of The Principle of Conservation of Power is also demonstrated.