Floquet Chern insulators of light

Li He,Jicheng Jin,Bo Zhen,Eugene J Mele,Steven G Johnson,Zachariah Addison

doi:10.1038/s41467-019-12231-4

Li He, Jicheng Jin + Show 4 more

Open Access

https://doi.org/10.1038/s41467-019-12231-4

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Abstract

Achieving topologically-protected robust transport in optical systems has recently been of great interest. Most studied topological photonic structures can be understood by solving the eigenvalue problem of Maxwell’s equations for static linear systems. Here, we extend topological phases into dynamically driven systems and achieve a Floquet Chern insulator of light in nonlinear photonic crystals (PhCs). Specifically, we start by presenting the Floquet eigenvalue problem in driven two-dimensional PhCs. We then define topological invariant associated with Floquet bands, and show that topological band gaps with non-zero Chern number can be opened by breaking time-reversal symmetry through the driving field. Finally, we numerically demonstrate the existence of chiral edge states at the interfaces between a Floquet Chern insulator and normal insulators, where the transport is non-reciprocal and uni-directional. Our work paves the way to further exploring topological phases in driven optical systems and their optoelectronic applications.

Highlights

Achieving topologically-protected robust transport in optical systems has recently been of great interest
Many important applications of topological photonics, such as optical isolators and circulators, are non-reciprocal in nature, which means they are exclusive for topological phases in systems with broken time-reversal symmetry
We start by showing that new bandgaps—Floquet gaps—can be created in driven nonlinear photonic crystals (PhCs), which do not exist in the static band structure

Summary

Introduction

Achieving topologically-protected robust transport in optical systems has recently been of great interest. We study Floquet topological phases in general nonlinear PhCs under external drive and show how non-reciprocal transport can be achieved in a Floquet Chern insulator. After elucidating what time-reversal symmetry (T) entails in driven systems, we engineer the external drive to break T and to close and re-open Floquet gaps to change bands Chern numbers.

Results

Conclusion