Dark topological valley Hall edge solitons

Boquan Ren,Yongdong Li,Victor O Kompanets,Yiqi Zhang,Hongguang Wang,Yaroslav V Kartashov

doi:10.1515/nanoph-2021-0385

Boquan Ren, Yongdong Li + Show 4 more

Open Access

https://doi.org/10.1515/nanoph-2021-0385

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Abstract

Abstract Topological edge solitons propagating along the edge of a photonic topological insulator are localized self-sustained hybrid states that are immune to defects/disorders due to the protection of the edge states stemming from the nontrivial topology of the system. Here, we predict that exceptionally robust dark valley Hall edge solitons may form at the domain walls between two honeycomb lattices with broken inversion symmetry. The underlying structure can be created with femtosecond laser inscription, it possesses a large bandgap where well-localized dark edge solitons form, and in contrast to systems with broken time-reversal symmetry, it does not require external magnetic fields or complex longitudinal waveguide modulations for the realization of the topological phase. We present the envelope equation allowing constructing dark valley Hall edge solitons analytically. Such solitons propagate without radiation into the bulk of the lattice and can circumvent sharp corners, which allows observing their persistent circulation along the closed triangular domain wall boundary. They survive over huge distances even in the presence of disorder in the underlying lattice. We also investigate interactions of closely located dark topological valley Hall edge solitons and show that they are repulsive and lead to the formation of two gray edge solitons, moving with different group velocities departing from group velocity of the linear edge state on which initial dark solitons were constructed. Our results illustrate that nonlinear valley Hall systems can support a rich variety of new self-sustained topological states and may inspire their investigation in other nonlinear systems, such as atomic vapors and polariton condensates.

Highlights

Topological edge solitons propagating along the edge of a photonic topological insulator are localized selfsustained hybrid states that are immune to defects/disorders due to the protection of the edge states stemming from the nontrivial topology of the system
We predict that exceptionally robust dark valley Hall edge solitons may form at the domain walls between two honeycomb lattices with broken inversion symmetry
After more than a decade of development of topological photonics [1,2,3,4], it was recognized that nonlinear effects, such as self-action and parametric interactions, may fundamentally affect the evolution of excitations and change the very structure of the spectrum of topological systems, providing sometimes a very convenient knob for manipulation of the edge states and control of related localization and transport phenomena

Summary

Introduction

After more than a decade of development of topological photonics [1,2,3,4], it was recognized that nonlinear effects, such as self-action and parametric interactions, may fundamentally affect the evolution of excitations and change the very structure of the spectrum of topological systems, providing sometimes a very convenient knob for manipulation of the edge states and control of related localization and transport phenomena. In array-based photonic Floquet topological insulators, where time-reversal symmetry is broken by the artificial magnetic field due to the helicity of the waveguides, topologically closed currents in the bulk were first reported theoretically [28] and observed experimentally [29]. The word “valley” is associated here with specific features (presence of the local extrema) of bands of corresponding systems: for example, when inversion symmetry of the underlying honeycomb lattice is broken by detuning of two constituent sublattices, the gap opens between former Dirac points and local extrema in two upper bands develop that are called valleys Even though such valley Hall structures provide weaker topological protection, their advantage is the ease of fabrication and the fact that they may be implemented with straight waveguides [54] and, for this reason, will feature drastically reduced losses. Dark valley Hall edge solitons can be experimentally realized in laser-written waveguide arrays [6, 56], in optical lattices imprinted in a photorefractive crystal [54], or in atomic vapors [44]

The model

Nonlinear valley Hall edge states

Dark valley Hall edge solitons

Topological protection of the dark valley Hall edge soliton

Repulsive interaction of valley Hall edge solitons

Conclusions