2D Topological Edge States in Periodic Space-Time Interfaces

TL;DR

This paper introduces topological edge states in photonic space-time crystals, where refractive index varies periodically in space and time, leading to robust, scattering-free wave propagation and unique exponentially growing edge states.

Contribution

It demonstrates the existence of topological phases and edge states in 2D space-time modulated photonic materials, combining concepts from topological insulators and time crystals.

Findings

Identification of topological invariants in space-time photonic systems

Observation of propagating edge states in space-time crystals

Discovery of an edge state that grows exponentially in power

Abstract

Topological edge states in systems of two (or more) dimensions offer scattering-free transport, exhibiting robustness to inhomogeneities and disorder. In a different domain, time-modulated systems, such as photonic time crystals (PTCs), offer non-resonant amplification drawing energy from the modulation. Combining these concepts, we explore topological systems that vary periodically in both time and space, manifesting the best of both worlds. We present topological phases and topological edge states in photonic space-time crystals - materials in which the refractive index varies periodically in both space and time, displaying bandgaps in both frequency and momentum. The topological nature of this system leads to topological invariants that govern the phase between refracted and reflected waves generated from both the spatial and the temporal interfaces. The 2D nature of this system leads to propagating edge states, and a unique edge state that grows exponentially in power whilst following the space-time edge.