Controlling spontaneous emission through the preparation of a photonic time-crystal

Photonic time crystals (PTCs) are materials whose dielectric permittivity is strongly modulated periodically in time at rates comparable to a single cycle of the waves propagating within. Such modulations can have a large impact on the propagation of waves in the medium. For example, all waves with wave vectors associated with the momentum gap are exponentially amplified, which in turn can lead to enhanced light-matter interaction. Here, we study the emission of radiation in a PTC and show that the power of the spontaneous radiation depends on the initial state of the field, and can be controlled through the turn-on process of the PTC. Specifically, if the PTC starts abruptly, the spontaneous emission rate grows monotonically towards the momentum gap, whereas if the PTC is turned on gradually the rate decreases towards the gap. This finding implies that the spontaneous emission rate can be designed and controlled by shaping the temporal modulation of the refractive index, a feature having major consequences for radiation generated in PTCs, such as PTC lasers and antennas.