Disordered Photonic Time Crystals

We study the propagation of electromagnetic waves in disordered photonic time crystals: spatially homogenous media whose refractive index changes randomly in time. We find that the group velocity of a pulse propagating in such media decreases exponentially, eventually coming to a complete stop, while experiencing exponential growth in intensity. These effects greatly depend on the Floquet band structure of the photonic time crystal, with the strongest sensitivity to disorder occurring in superluminal modes. Finally, we analyze the ensemble statistics and find them to coincide with those of Anderson localization, exhibiting single parameter scaling.