Floquet valley Hall edge solitons

We introduce traveling Floquet valley Hall edge solitons in a genuinely continuous system consisting of a waveguide array with a dynamically varying domain wall between two honeycomb structures exhibiting broken inversion symmetry. Inversion symmetry in our system is broken due to periodic and out-of-phase longitudinal modulation of the refractive index applied to the constituent sublattices of the honeycomb structure. By combining two honeycomb arrays with different initial phases of refractive index modulation we create a dynamically changing domain wall that supports localized linear Floquet edge states despite the fact that on average two sublattices in each honeycomb structure forming the domain wall have the same refractive index. In the presence of focusing nonlinearity, bright or dark Floquet edge solitons may bifurcate from such linear Floquet edge states. We numerically identified a family of these solitons and compared them with the results obtained from the analytical approach, which involved averaging over one longitudinal period in the evolution coordinate. These solitons exhibit localization in both spatial directions - along the interface due to nonlinear self-action and across the interface as the edge states - that allows them to travel along the domain wall over long distances without noticeable shape variations.