Two-dimensional localized modes in nonlinear systems with linear nonlocality and moiré lattices

Periodic structures structured as photonic crystals and optical lattices are fascinating for nonlinear waves engineering in the optics and ultracold atoms communities.Moiréphotonic and optical lattices—two-dimensional twisted patterns lie somewhere in between perfect periodic structures and aperiodic ones—are a new emerging investigative tool for studying nonlinear localized waves of diverse types.Herein,a theory of two-dimensional spatial localization in nonlinear periodic systems with fractional-order diffraction(linear nonlocality)and moiréoptical lattices is investigated.Specifically,the flat-band feature is well preserved in shallow moiréoptical lattices which,interact with the defocusing nonlinearity of the media,can support fundamental gap solitons,bound states composed of several fundamental solitons,and topological states(gap vortices)with vortex charge s=1 and 2,all populated inside the finite gaps of the linear Bloch-wave spectrum.Employing the linear-stability analysis and direct perturbed simulations,the stability and instability properties of all the localized gap modes are surveyed,highlighting a wide stability region within the first gap and a limited one(to the central part)for the third gap.The findings enable insightful studies of highly localized gap modes in linear nonlocality(fractional)physical systems with shallow moirépatterns that exhibit extremely flat bands.

Dissipative gap solitons and vortices in moiré optical lattices

Considerable attention has been recently paid to elucidation the linear,nonlinear and quantum physics of moire patterns because of the innate extraordinary physical properties and potential applications.Particularly,moire superlattices consisted of two periodic structures with a twist angle offer a new platform for studying soliton theory and its practical applications in various physical systems including optics,while such studies were so far limited to reversible or conservative nonlinear systems.Herein,we provide insight into soliton physics in dissipative physical settings with moire optical lattices,using numerical simulations and theoretical analysis.We reveal linear localization-delocalization transitions,and find that such nonlinear settings support plentiful localized gap modes representing as dissipative gap solitons and vortices in periodic and aperiodic moire optical lattices,and identify numerically the stable regions of these localized modes.Our predicted dissipative localized modes provide insightful understanding of soliton physics in dissipative nonlinear systems since dissipation is everywhere.