Modulational instability and solitary waves in polariton topological insulators

Yaroslav V Kartashov,Dmitry V Skryabin

doi:10.1364/optica.3.001228

Yaroslav V Kartashov, Dmitry V Skryabin

Open Access

https://doi.org/10.1364/optica.3.001228

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Journal: Optica	Publication Date: Oct 24, 2016
Citations: 131	License type: cc-by

Affiliation: Institute of Photonic Sciences, University of Bath

Abstract

Optical microcavities supporting exciton–polariton quasi-particles offer one of the most powerful platforms for the investigation of the rapidly developing area of topological photonics in general, and of photonic topological insulators in particular. Energy bands of the microcavity polariton graphene are readily controlled by a magnetic field and influenced by the spin-orbit (SO) coupling effects, a combination leading to the formation of linear unidirectional edge states in polariton topological insulators as very recently predicted. In this work we depart from the linear limit of non-interacting polaritons and predict instabilities of the nonlinear topological edge states resulting in the formation of the localized topological quasi-solitons, which are exceptionally robust and immune to backscattering wave packets propagating along the graphene lattice edge. Our results provide a background for experimental studies of nonlinear polariton topological insulators and can influence other subareas of photonics and condensed matter physics, where nonlinearities and SO effects are often important and utilized for applications.

Highlights

Topological insulators and topologically protected edge states attract nowadays unprecedented attention in diverse areas of science, including solid‐state physics, acoustics, matter waves, graphene‐based applications and photonics, see, e.g., [1,2] for recent reviews
Topological insulators are characterized by the presence of the complete band‐gap in the bulk of the material, like in a usual insulator, while at the same time they admit in‐gap edge states propagating at the surface, where conduction of electrons becomes possible in the presence of magnetic field
Spin‐orbit interac‐ tions for electrons is the key phenomenon underpinning existence of the topological insulator phase, whose physics is closely linked with quantum Hall effect and integer Hall conductance [1,2]

Summary

Introduction

Topological insulators and topologically protected edge states attract nowadays unprecedented attention in diverse areas of science, including solid‐state physics, acoustics, matter waves, graphene‐based applications and photonics, see, e.g., [1,2] for recent reviews. Main advantages of polaritons include sufficiently strong spin‐orbit coupling originating in the cavity induced TE‐TM splitting of the polariton energy levels [19,20], established technology of the microcavity structuring into arbitrary lattice potentials [19,21], and very strong non‐ linear interactions of polaritons through their excitonic component The latter was used for recent demonstrations of superfluidity [22,23], genera‐ tion of dark quasi‐solitons and vortices [24,25,26,27], bright spatial and tem‐ poral solitons [28,29,30], and other effects. The approximate expression for the shape of quasi‐solitons is derived

Topological edge states in the linear regime

Findings

Summary