Topology of photonic time-crystals
arXiv:1803.08731 · doi:10.1364/OPTICA.5.001390
Abstract
We introduce topological phases in Photonic Time-Crystals. Photonic Time-Crystals are materials in which the refractive index varies periodically and abruptly in time. When the refractive index changes abruptly, the light propagating in the material experiences time-refraction and time-reflection, analogous to refraction and reflection in photonic crystals. Interference between time-refracted and time-reflected waves gives rise to Floquet-Bloch states and dispersion bands, which are gapped in the momentum. We show that photonic time-crystals can be in a topologically non-trivial phase, and calculate the topological invariant associated with the momentum bands of the Photonic Time-Crystal. The topological invariants are related to the phase between the forward and backward-propagating waves of the time-crystal, and to localized edge states in time.
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