Rotating Spacetime Modulation: Topological Phases and Spacetime Haldane Model

TL;DR

This paper explores topological phases in spacetime-modulated photonic crystals, extending topological band theory to dynamic systems and proposing a spacetime Haldane model with potential for nonreciprocal wave phenomena.

Contribution

It introduces a novel approach to topological photonics by applying spacetime rotation-wave modulation and proposes a spacetime Haldane model for the first time.

Findings

Spacetime modulation induces non-trivial topologies in photonic crystals.

The effective electromagnetic response becomes bianisotropic, breaking time-reversal symmetry.

Potential realization of topological phases with unidirectional edge states.

Abstract

Topological photonics has recently emerged as a very general framework for the design of unidirectional edge waveguides immune to back-scattering and deformations, as well as other platforms that feature extreme nonreciprocal wave phenomena. While the topological classification of time invariant crystals has been widely discussed in the literature, the study of spacetime crystals formed by time-variant materials remains largely unexplored. Here, we extend the methods of topological band theory to photonic crystals formed by inclusions that are subject to a spacetime rotating-wave modulation that imitates a physical rotating motion. By resorting to an approximate nonhomogeneous effective description of the electromagnetic response of the inclusions, it is shown that they possess a bianisotropic response that breaks the time-reversal symmetry and may give rise to non-trivial topologies. In particular, we propose an implementation of the Haldane model in a spacetime modulated photonic crystal.