On the electromagnetic wave interaction with subluminal, luminal, and superluminal mirrors

As predicted by A. Einstein [Ann. Phys. (Leipzig) 17, 891 (1905)], the electromagnetic wave reflected at a moving mirror is frequency-upshifted and intensified as high as the mirror velocity is close to the speed of light in vacuum. However, at this limit the mirror reflectivity vanishes, because the higher the wave frequency the more transparent matter is. To resolve this paradox, we analyse the electromagnetic wave propagation in medium where the refractive index modulation moves at the speed of light in vacuum. Although the luminal and superluminal modulations are unconditionally transparent for the incident radiation, they both can reflect. We find the new type of the electromagnetic wave reflection with the increasing in time frequency inside the luminal mirror. If the modulation disappears the high frequency radiation is released as a short wavepacket.