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

作　　者：Xiuye Liu Jianhua Zeng 

机构地区：[1]Center for Attosecond Science and Technology,State Key Laboratory of Transient Optics and Photonics,Xi’an Institute of Optics and Precision Mechanics of Chinese Academy of Sciences,Xi’an 710119,China [2]University of Chinese Academy of Sciences,Beijing 100049,China [3]Collaborative lnnovation Center of Extreme Optics,Shanxi University,Taiyuan 030006,China

出　　处：《Frontiers of physics》2024年第4期265-273,共9页物理学前沿（英文版）

基　　金：This work was supported by the National Natural Science Foundation of China(NSFC)(No.12074423);Young Scholar of Chinese Academy of Sciences in Western China(No.XAB2021YN18);China Postdoctoral Science Foundation(No.2023M733722).

摘　　要：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.

关 键 词：moiréoptical lattices gap solitons and vortices ultracold atoms Gross-Pitaevskii/nonlinear fractional Schrödinger equation nonlinear fractional systems 

分 类 号：O43[机械工程—光学工程]