Edge Solitons in Nonlinear Photonic Topological Insulators

We report localized and unidirectional nonlinear traveling edge waves discovered theoretically and numerically in a 2D mechanical (phononic) topological insulator. The lattice consists of a collection of pendula with weak Duffing nonlinearity connected by linear springs. We show that the classical 1D nonlinear Schrodinger equation governs the envelope of 2D edge modes, and study the propagation of traveling waves and rogue waves in 1D as edge solitons in 2D. As a result of to...

We study continuations of topological edge states in the Su-Schrieffer-Heeger model with on-site cubic (Kerr) nonlinearity, which is a 1D nonlinear photonic topological insulator (TI). Based on the topology of the underlying spatial dynamical system, we establish the existence of nonlinear edge states (edge solitons) for all positive energies in the topological band gap. We discover that these edge solitons are stable at any energy when the ratio between the weak and strong c...

Topological photonics has emerged recently as a novel approach for realizing robust optical circuitry, and the study of nonlinear effects in topological photonics is expected to open the door for tunability of photonic structures with topological properties. Here, we study the topological edge states and topological gap solitons which reside in the same bandgaps described by the nonlinear Dirac model, in both one- and two-dimensions. We reveal strong nonlinear interaction bet...

Topological edge solitons propagating along the edge of a photonic topological insulator are localized self-sustained hybrid states that are immune to de-fects/disorders due to protection of the edge states stemming from 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 sym-metry. The underlying structure can be created with femtosecond ...

We introduce a scheme of a photonic coupler built of two parallel topological-insulator slab waveguides with the intrinsic Kerr nonlinearity, separated by a gap. Josephson oscillations (JO) of a single edge soliton created in one slab, and of a pair of solitons created in two slabs, are considered. The single soliton jumping between the slabs is subject to quick radiative decay. On the other hand, the JO of the copropagating soliton pair may be essentially more robust, as one...

We propose and experimentally demonstrate a family of Floquet solitons in the bulk of a photonic topological insulator that have double the period of the drive. Our experimental system consists of a periodically-modulated honeycomb lattice of optical waveguides fabricated by femtosecond laser writing. We employ a Kerr nonlinearity in which self-focusing gives rise to spatial lattice solitons. Our photonic system constitutes a powerful platform where the interplay of time-peri...

We introduce a class of topological lasers based on the photonic Floquet topological insulator concept. The proposed system is realized as a truncated array of the lasing helical waveguides, where the pseudo-magnetic field arises due to twisting of the waveguides along the propagation direction that breaks the time-reversal symmetry and opens up a topological gap. When sufficient gain is provided in the edge channels of the array then the system lases into the topological edg...

Edge states emerge in diverse areas of science, offering new opportunities for the development of novel electronic or optoelectronic devices, sound and light propagation controls in acoustics and photonics. Previous experiments on edge states and exploration of topological phases in photonics were carried out mostly in linear regimes, but the current belief is that nonlinearity introduces new striking features into physics of edge states, lead-ing to the formation of edge sol...

We report the experimental observation of nonlinear light localization and edge soliton formation at the edges of fs-laser written trimer waveguide arrays, where transition from non-topological to topological phases is controlled by the spacing between neighboring trimers. We found that, in the former regime, edge solitons occur only above a considerable power threshold, whereas in the latter one they bifurcate from linear states. Edge solitons are observed in a broad power r...

Floquet systems with periodically varying in time parameters enable realization of unconventional topological phases that do not exist in static systems with constant parameters and that are frequently accompanied by appearance of novel types of the topological states. Among such Floquet systems are the Su-Schrieffer-Heeger lattices with periodically-modulated couplings that can support at their edges anomalous $\pi$ modes of topological origin despite the fact that the latti...