Floquet Engineering of Two Dimensional Photonic Waveguide Arrays with $\pi$ or $\pm2\pi/3$ Corner states

TL;DR

This paper explores how periodic modulation in 2D photonic waveguide arrays can induce Floquet corner states with fractional quasi-energies, offering new avenues for on-chip photonic device engineering.

Contribution

It introduces a theoretical framework for Floquet engineering of corner states in various 2D photonic lattices, revealing fractional quasi-energy states not previously demonstrated.

Findings

Floquet corner states appear within band gaps at specific modulation frequencies.

Fractional quasi-energy corner states are protected by symmetry.

The study provides a basis for on-chip photonic device design using Floquet states.

Abstract

In this paper, we theoretically study the Floquet engineering of two dimensional photonic waveguide arrays in three types of lattices: honeycomb lattice with Kekule distortion, breathing square lattice and breathing Kagome lattice. The Kekule distortion factor or the breathing factor in the corresponding lattice is periodically changed along the axial direction of the photonic waveguide with frequency $\omega$. Within certain ranges of $\omega$, the Floquet corner states in the Floquet band gap of quasi-energy spectrum are found, which are localized at the corner of the finite two-dimensional arrays. Due to particle-hole symmetric in the model of honeycomb and square lattice, the quasi-energy level of the Floquet $\pi$ corner states is $\pm\omega/2$. On the other hand, Kagome lattice does not have particle-hole symmetric, so that the quasi-energy level of the Floquet $\pm2\pi/3$ corner states is near to $\pm1\omega/3$. The corner states are either protected by crystalline symmetry or reflection symmetry. The finding of Floquet fractional-$\pi$ corner states could provide more options for engineering of on-chip photonic devices.