Exploring nonlinear topological states of matter with exciton-polaritons: Edge solitons in kagome lattice

Abstract

Matter in nontrivial topological phase possesses unique properties, such as support of unidirectional edge modes on its interface. It is the existence of such modes which is responsible for the wonderful properties of a topological insulator – material which is insulating in the bulk but conducting on its surface, along with many of its recently proposed photonic and polaritonic analogues. We show that exciton-polariton fluid in a nontrivial topological phase in kagome lattice, supports nonlinear excitations in the form of solitons built up from wavepackets of topological edge modes – topological edge solitons. Our theoretical and numerical results indicate the appearance of bright, dark and grey solitons dwelling in the vicinity of the boundary of a lattice strip. In a parabolic region of the dispersion the solitons can be described by envelope functions satisfying the nonlinear Schrödinger equation. Upon collision, multiple topological edge solitons emerge undistorted, which proves them to be true solitons as opposed to solitary waves for which such requirement is waived. Importantly, kagome lattice supports topological edge mode with zero group velocity unlike other types of truncated lattices. This gives a finer control over soliton velocity which can take both positive and negative values depending on the choice of forming it topological edge modes.

Topologically enhanced harmonic generation in a nonlinear transmission line metamaterial

“…One of the most interesting questions raised by the emergence of topologically nontrivial classical lattices is how topological edge states interact with nonlinear media. Previous studies have focused on nonlinearityinduced local self-interactions in the fundamental harmonic, which can give rise to solitons with anomalous * blzhang@ntu.edu.sg † yidong@ntu.edu.sg plateau-like decay profiles in nonlinear SSH chains [8,21], or chiral solitons in two-dimensional lattices [22][23][24][25][26][27]. It has also been suggested that topological edge states in nonlinear lattices could be used for robust traveling-wave parametric amplification [28], optical isolation [29], and other applications [30][31][32][33].…”

Nonlinear topological states in the Su–Schrieffer–Heeger model

“…Very recently, the quest for tunable topological states has given rise to the nonlinear topological photonics, which offers even broader spectrum of opportunities including soliton-like [4][5][6], self-induced [7,8], tunable [7] and many-particle [9,10] topological states.…”

Resonant Edge‐State Switching in Polariton Topological Insulators

“…In particular, photonic topological systems include gyromagnetic photonic crystals [12,13], semiconductor quantum wells [14], arrays of coupled resonators [15,16], metamaterial superlattices [17] and other periodic metamaterial structures [18,19], helical waveguide arrays [20][21][22][23], non-Hermitian guiding structures [24], and microcavities supporting excitonpolaritons [25][26][27][28]. Including nonlinear effects substantially enriches the behaviour of modes in topological systems [29], leading to, e.g., nonlinearity-mediated inversion of the propagation direction of the edge states [30,31], dynamical instabilities [32,33], formation of the topological edge solitons [34][35][36] and vortices [37], bistability [38], or nonlinear optical isolation [39].…”