# Nonlinear one-way edge-mode interactions for frequency mixing in topological photonic crystals

## TL;DR

This paper explores nonlinear frequency mixing in topological photonic crystals, demonstrating robust edge-mode interactions for harmonic generation and slow-light enhancement, opening new avenues for topologically protected nonlinear photonics.

## Contribution

It introduces the study of nonlinear wave mixing in topological photonic edge modes, a largely unexplored area, and demonstrates practical frequency conversion processes in such systems.

## Key findings

- Second- and third-harmonic generation via edge modes
- Slow-light enhancement of nonlinear interactions
- Harmonic generation with backward-propagating edge modes

## Abstract

Topological photonics aims to utilize topological photonic bands and corresponding edge modes to implement robust light manipulation, which can be readily achieved in the linear regime of light-matter interaction. Importantly, unlike solid state physics, the common test bed for new ideas in topological physics, topological photonics provide an ideal platform to study wave mixing and other nonlinear interactions. These are well-known topics in classical nonlinear optics but largely unexplored in the context of topological photonics. Here, we investigate nonlinear interactions of one-way edge-modes in frequency mixing processes in topological photonic crystals. We present a detailed analysis of the band topology of two-dimensional photonic crystals with hexagonal symmetry and demonstrate that nonlinear optical processes, such as second- and third-harmonic generation can be conveniently implemented via one-way edge modes of this setup. Moreover, we demonstrate that more exotic phenomena, such as slow-light enhancement of nonlinear interactions and harmonic generation upon interaction of backward-propagating (left-handed) edge modes can also be realized. Our work opens up new avenues towards topology-protected frequency mixing processes in photonics.