Amplified emission and lasing in photonic time crystals

Photonic time crystals - materials whose dielectric permittivity is modulated periodically in time - offer new concepts in light manipulation. We study theoretically the emission of light from a radiation source placed inside a photonic time crystal, and find that radiation corresponding to the momentum band gap is exponentially amplified, whether initiated by a macroscopic source, an atom, or by vacuum fluctuations, drawing the amplification energy from the modulation. The radiation linewidth becomes narrower with time, eventually shrinking to the middle of the bandgap, which enables to propose the concept of non-resonant tunable photonic time-crystal laser. Finally, we find that the spontaneous decay rate of an atom embedded in a photonic time-crystal vanishes at the band edge due to low density of photonic states.