Bragg solitons in topological Floquet insulators

Vector valley Hall edge solitons in distorted type-II Dirac photonic lattices

Topological edge states have recently garnered a lot of attention across various fields of physics. The topological edge soliton is a hybrid edge state that is both topologically protected and immune to defects or disorders, and a localized bound state that is diffraction-free, owing to the self-balance of diffraction by nonlinearity. Topological edge solitons hold great potential for on-chip optical functional device fabrication. In this report, we present the discovery of vector valley Hall edge (VHE) solitons in type-II Dirac photonic lattices, formed by breaking lattice inversion symmetry with distortion operations. The distorted lattice features a two-layer domain wall that supports both in-phase and out-of-phase VHE states, appearing in two different band gaps. Superposing soliton envelopes onto VHE states generates bright-bright and bright-dipole vector VHE solitons. The propagation dynamics of such vector solitons reveal a periodic change in their profiles, accompanied by the energy periodically transferring between the layers of the domain wall. The reported vector VHE solitons are found to be metastable.

Rotating topological edge solitons

We address the formation of topological edge solitons in rotating Su-Schrieffer-Heeger waveguide arrays. The linear spectrum of the non-rotating topological array is characterized by the presence of a topological gap with two edge states residing in it. Rotation of the array significantly modifies the spectrum and may move these edge states out of the topological gap. Defocusing nonlinearity counteracts this tendency and shifts such modes back into the topological gap, where they acquire the structure of tails typical of topological edge states. We present rich bifurcation structure for rotating topological solitons and show that they can be stable. Rotation of the topologically trivial array, without edge states in its spectrum, also leads to the appearance of localized edge states, but in a trivial semi-infinite gap. Families of rotating edge solitons bifurcating from the trivial linear edge states exist too, and sufficiently strong defocusing nonlinearity can also drive them into the topological gap, qualitatively modifying the structure of their tails.

Topological edge solitons in χ(2) waveguide arrays

We address the formation of χ⁽²⁾ topological edge solitons emerging in a 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 the phase mismatch determines whether the second harmonic (SH) component falls into topological or trivial forbidden gaps of the spectrum for the SH wave. Two representative types of edge solitons are found, one of which is thresholdless and bifurcates from the topological edge state in the FF component, while the other exists above a power threshold and emanates from the topological edge state in the SH wave. Both types of soliton can be stable. Their stability, localization degree, and internal structure strongly depend on the phase mismatch between the FF and SH waves. Our results open up new prospects for the control of topologically nontrivial states by parametric wave interactions.

Observation of Edge Solitons in Topological Trimer Arrays

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 nontopological 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 range where their propagation constant falls into one of the topological gaps of the system, while partial delocalization is observed when considerable nonlinearity drives the propagation constant into an allowed band, causing coupling with bulk modes. Our results provide direct experimental evidence of the coexistence and selective excitation in the same or in different topological gaps of two types of topological edge solitons with different internal structures, which can rarely be observed even in nontopological systems. This also constitutes the first experimental evidence of formation of topological solitons in a nonlinear system with more than one topological gap.

Josephson oscillations of edge quasi-solitons in a photonic-topological coupler

We introduce a scheme of a photonic coupler built of two parallel topological-insulator slab waveguides with the intrinsic Kerr nonlinearity, separated by a lattice spacing. Josephson oscillations (JOs) of a single edge quasi-soliton (QS) created in one slab, and of a pair of QSs created in two slabs, are considered. The single QS jumping between the slabs is subject to quick radiative decay. However, the JOs of the co-propagating QS pair may be essentially more robust, as one QS absorbs dispersive waves emitted by the other. The most robust JO regime is featured by the pair of QSs with phase shift π between them.

Valley Hall edge solitons in a photonic graphene

We predict the existence and study properties of the valley Hall edge solitons in a composite photonic graphene with a domain wall between two honeycomb lattices with broken inversion symmetry. Inversion symmetry in our system is broken due to detuning introduced into constituent sublattices of the honeycomb structure. We show that nonlinear valley Hall edge states with sufficiently high amplitude bifurcating from the linear valley Hall edge state supported by the domain wall, can split into sets of bright spots due to development of the modulational instability, and that such an instability is a precursor for the formation of topological bright valley Hall edge solitons localized due to nonlinear self-action and travelling along the domain wall over large distances. Topological protection of the valley Hall edge solitons is demonstrated by modeling their passage through sharp corners of the Ω-shaped domain wall.

Floquet defect solitons

We consider an array of straight nonlinear waveguides constituting a two-dimensional square lattice, with a few central layers tilted with respect to the rest of the structure. It is shown that such a configuration represents a line defect in the lattice plane, which is periodically modulated along the propagation direction. In the linear limit, such a system sustains line defect modes, whose number coincides with the number of tilted layers. In the presence of nonlinearity, the branches of defect solitons propagating along the defect line bifurcate from each of the linear defect modes. Depending on the effective dispersion induced by the Floquet spectrum of the system, the bifurcating solitons can be either bright or dark. Dynamics and stability of such solitons are studied numerically.

Four-wave mixing Floquet topological solitons

We consider a topological Floquet insulator realized as a honeycomb array of helical waveguides imprinted in a weakly birefringent medium. The system accounts for four-wave mixing occurring at a series of resonances arising due to Floquet phase matching. Under these resonant conditions, the system sustains stable linearly polarized and metastable elliptically polarized two-component edge solitons. Coupled nonlinear equations describing the evolution of the envelopes of such solitons are derived.