Gain in time-dependent media—a new mechanism

Time-dependent systems do not in general conserve energy, invalidating much of the theory developed for static systems and turning our intuition on its head. This is particularly acute in luminal space-time crystals, where the structure moves at or close to the velocity of light. Conventional Bloch wave theory no longer applies, energy grows exponentially with time, and a new perspective is required to understand the phenomenology. In this paper, we identify a new mechanism for amplification: the compression of lines of force that are nevertheless conserved in number.