Scattering in superluminal space-time (ST) modulated electromagnetic crystals

Space-time (ST) modulated media manipulate the ST spectra, i.e. the k-ω frequencies, of waves. Here, we examine the scattering of electromagnetic waves from a superluminal periodic ST medium, or ST crystal. We rigorously solve, for the first time, the scattering problem for a single crystal period and explain the corresponding phenomenology using a geometrical construction in the Minkowski diagram. From these results, we infer the existence and locations of instabilities in the dispersion diagram of a ST crystal. FDTD-computed scattered fields are briefly described.