Nontrivial coupling of light into a defect: the interplay of nonlinearity and topology

Shiqi Xia,Daria Smirnova,Jingjun Xu,Dario Jukić,Alexander Szameit,Nan Wang,Liqin Tang,Daohong Song,Lev Smirnov,Zhigang Chen,Hrvoje Buljan,Daniel Leykam

doi:10.1038/s41377-020-00371-y

Abstract

The flourishing of topological photonics in the last decade was achieved mainly due to developments in linear topological photonic structures. However, when nonlinearity is introduced, many intriguing questions arise. For example, are there universal fingerprints of the underlying topology when modes are coupled by nonlinearity, and what can happen to topological invariants during nonlinear propagation? To explore these questions, we experimentally demonstrate nonlinearity-induced coupling of light into topologically protected edge states using a photonic platform and develop a general theoretical framework for interpreting the mode-coupling dynamics in nonlinear topological systems. Performed on laser-written photonic Su-Schrieffer-Heeger lattices, our experiments show the nonlinear coupling of light into a nontrivial edge or interface defect channel that is otherwise not permissible due to topological protection. Our theory explains all the observations well. Furthermore, we introduce the concepts of inherited and emergent nonlinear topological phenomena as well as a protocol capable of revealing the interplay of nonlinearity and topology. These concepts are applicable to other nonlinear topological systems, both in higher dimensions and beyond our photonic platform.

Highlights

Topological photonics has become one of the most active research frontiers in optics over the last decade[1,2]
We study the propagation of light in photonic lattices δwnitNhLÀajψrje2fÁr,awcthiveer-einnd0eixs variation given by the constant part of n0 þ δnLðxÞþ the material’s index of refraction, δnL(x) describes the linear photonic δlanttNiLcÀej,ψwj2hÁicihs is uniform along the the nonlinear index propagation axis z, and change, which depends on the intensity of the light (with ψ(x, z) being the complex amplitude of the electric field)
The interplay of nonlinearity and topology is somewhat analogous to the interplay of locality and globality, as most of the studied optical nonlinearities are local, and the topology describes the global properties of a system

Summary

Introduction

Topological photonics has become one of the most active research frontiers in optics over the last decade[1,2]. The initial ideas were drawn from condensed matter physics, where the concept of topology was found to be crucial for understanding the celebrated quantum Hall effect (QHE)[3,4] and, later on, for the development of topological insulators[5,6,7]. When two materials with different topological invariants are interfaced, bulk-edge correspondence[2,10,11] guarantees the existence of topological edge states, which enjoy robust unidirectional propagation. Such correspondence holds in both quantum and classical wave systems, which inspired the first observation of the unidirectional propagation of electromagnetic waves in the microwave regime[12]. Topological states of light and related phenomena were later realized in various systems, including photonic lattices[13], ring resonators[14], and metamaterials[15] (see Ref. 2 for a recent review)

Methods

Results

Conclusion