Higher-order topological insulators(HOTIs)are recently discovered topological phases,possessing symmetry-protected corner states with fractional charges.An unexpected connection between these states and the seemingly ...Higher-order topological insulators(HOTIs)are recently discovered topological phases,possessing symmetry-protected corner states with fractional charges.An unexpected connection between these states and the seemingly unrelated phenomenon of bound states in the continuum(BICs)was recently unveiled.When nonlinearity is added to the HOTI system,a number of fundamentally important questions arise.For example,how does nonlinearity couple higher-order topological BICs with the rest of the system,including continuum states?In fact,thus far BICs in nonlinear HOTIs have remained unexplored.Here we unveil the interplay of nonlinearity,higher-order topology,and BICs in a photonic platform.We observe topological corner states that are also BICs in a laser-written second-order topological lattice and further demonstrate their nonlinear coupling with edge(but not bulk)modes under the proper action of both self-focusing and defocusing nonlinearities.Theoretically,we calculate the eigenvalue spectrum and analog of the Zak phase in the nonlinear regime,illustrating that a topological BIC can be actively tuned by nonlinearity in such a photonic HOTI.Our studies are applicable to other nonlinear HOTI systems,with promising applications in emerging topology-driven devices.展开更多
基金This research is supported by the National Key R&D Program of China under Grant No.2017YFA0303800the National Natural Science Foundation(11922408,91750204,11674180)+2 种基金PCSIRT,and the 111 Project(No.B07013)in ChinaD.B.acknowledges support from the 66 Postdoctoral Science Grant of ChinaD.J.and H.B.acknowledge support in part by the Croatian Science Foundation Grant No.IP-2016-06-5885 SynthMagIA and the QuantiXLie Center of Excellence,a project co-financed by the Croatian Government and European Union through the European Regional Development Fund-the Competitiveness and Cohesion Operational Programme(Grant KK.01.1.1.01.0004)。
文摘Higher-order topological insulators(HOTIs)are recently discovered topological phases,possessing symmetry-protected corner states with fractional charges.An unexpected connection between these states and the seemingly unrelated phenomenon of bound states in the continuum(BICs)was recently unveiled.When nonlinearity is added to the HOTI system,a number of fundamentally important questions arise.For example,how does nonlinearity couple higher-order topological BICs with the rest of the system,including continuum states?In fact,thus far BICs in nonlinear HOTIs have remained unexplored.Here we unveil the interplay of nonlinearity,higher-order topology,and BICs in a photonic platform.We observe topological corner states that are also BICs in a laser-written second-order topological lattice and further demonstrate their nonlinear coupling with edge(but not bulk)modes under the proper action of both self-focusing and defocusing nonlinearities.Theoretically,we calculate the eigenvalue spectrum and analog of the Zak phase in the nonlinear regime,illustrating that a topological BIC can be actively tuned by nonlinearity in such a photonic HOTI.Our studies are applicable to other nonlinear HOTI systems,with promising applications in emerging topology-driven devices.
