Topological edge solitons in dislocated extended photonic Lieb lattices

The Lieb lattice is notable for its unique band structure, which features a bosonic-like Dirac cone with flat band crossing the singularity point. It has found applications in a variety of physical fields, including condensed matter physics, optics, acoustics, and cold atomic systems. Extension and dislocation of the regular Lieb lattice introduce new properties and possibilities for generating topological edge states, particularly when the lattice is modulated by a Floquet mechanism mimicked by helical waveguide arrays. Here, we report both bright and dark topological edge solitons in helical dislocated extended Lieb waveguide arrays, which exhibit bearded, pointy, and solid boundaries. The topological edge states on different boundaries display distinct dispersion relations, resulting in either bright or dark solitons. This work provides a promising platform for manipulating the localization of topological objects, and the results offer potential applications in fabricating all-optical functional devices.