Topology of photonic time-crystals

TL;DR

This paper introduces topological phases in Photonic Time-Crystals, where periodic temporal variations in refractive index lead to novel Floquet-Bloch states, topological invariants, and localized edge states in time.

Contribution

It demonstrates that Photonic Time-Crystals can host topologically non-trivial phases and calculates the associated topological invariants, linking temporal interference to topological properties.

Findings

Photonic Time-Crystals exhibit Floquet-Bloch states with band gaps in momentum.

Topological invariants are derived from phase relations between forward and backward waves.

Localized edge states in time are identified as a consequence of non-trivial topology.

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.