Interaction of Electromagnetic Radiation with Luminal Mirror

A modulation of refractive index can move at the speed of light. How it interacts with an electromagnetic wave? Does it reflect? We show that an incident electromagnetic wave, depending on its frequency either is totally transmitted with a phase shift, or forms a standing wave, or is totally reflected with the frequency upshift. A short incident pulse is converted into a wavepacket that has all three parts (transmitted, standing and reflected waves). The reflected part near the interface exhibits an infinitely growing in time local frequency. The wavepacket's energy spectral density asymptotically is the inverse square of frequency. If the refractive index modulation disappears, the high frequency radiation is released.