Floquet quadrupole photonic crystals protected by space-time symmetry

TL;DR

This paper introduces Floquet quadrupole phases in driven nonlinear photonic crystals protected by space-time symmetries, expanding the understanding of topological phases in optical systems and enabling new optoelectronic applications.

Contribution

It presents the first demonstration of Floquet quadrupole phases in nonlinear photonic crystals protected by space-time screw symmetries, with a new framework for symmetry analysis in driven optical materials.

Findings

Floquet quadrupole phases confirmed by symmetry indices and Wannier bands.

Space-time symmetries tracked via optical axes trajectories.

Framework established for symmetry analysis in driven optical systems.

Abstract

High-order topological phases, such as those with nontrivial quadrupole moments, protect edge states that are themselves topological insulators in lower dimensions. So far, most quadrupole phases of light are explored in linear optical systems, which are protected by spatial symmetries or synthetic symmetries. Here we present Floquet quadrupole phases in driven nonlinear photonic crystals (PhCs) that are protected by space-time screw symmetries. We start by illustrating space-time symmetries by tracking the trajectory of instantaneous optical axes of the driven media. Our Floquet quadrupole phase is then confirmed in two independent ways: symmetry indices at high-symmetry momentum points and calculations of the nested Wannier bands. Our work presents a general framework to analyze symmetries in driven optical materials and paves the way to further exploring symmetry-protected topological phases in Floquet systems and their optoelectronic applications.