On the Electromagnetic Wave Reflection at the Subluminal, Luminal, and Superluminal Mirrors

Abstract As predicted by A. Einstein [Ann. Phys. (Leipzig) 17, 891 (1905)] the electromagnetic wave reflected at the mirror moving with relativistic velocity undergoes the frequency upshifting and intensification as high as the mirror velocity is close to the speed of light in vacuum. On the other hand side, as high the wave frequency is as the matter becomes more transparent with the reflection coefficient tending to zero. To resolve this paradox we analyze the electromagnetic wave propagation in the medium where the modulation of the refraction index move with the velocity equal to the speed of light in vacuum. As we find although the wave reflection at the luminal mirror vanishes, i.e. the electromagnetic pulse cannot overtake the mirror, its frequency spectrum changes.