Topological edge solitons in \{chi}(2) waveguide arrays

TL;DR

This paper explores the formation and stability of topological edge solitons in  waveguide arrays, revealing two types with distinct properties influenced by phase mismatch, advancing control of topological states via parametric interactions.

Contribution

It introduces the concept of topological edge solitons in  waveguides, identifying two types with different thresholds and stability, influenced by phase mismatch, which was not previously demonstrated.

Findings

Two types of topological edge solitons identified

One is thresholdless, the other requires a power threshold

Both types can be stable depending on phase mismatch

Abstract

We address the formation of \{chi}(2) topological edge solitons emerging in topologically nontrivial phase in Su-Schrieffer-Heeger (SSH) waveguide arrays. We consider edge solitons, whose fundamental frequency (FF) component belongs to the topological gap, while phase mismatch determines whether second harmonic (SH) component falls into topological or trivial forbidden gaps of the spectrum for SH wave. Two representative types of edge solitons are found, one of which is thresholdless and bifurcates from topological edge state in FF component, while other exists above power threshold and emanates from topological edge state in SH wave. Both types of solitons can be stable. Their stability, localization degree, and internal structure strongly depend on phase mismatch between FF and SH waves. Our results open new prospects for control of topologically nontrivial states by parametric wave interactions.