Nonlinear Waves Seminar - Sean Nixon
Analytical study of Floquet topological insulatorsÌý
The search for novel phenomena in photonic waveguides centers on engineering systems that feature unique dispersive properties oftenÌýinvolving spectral degeneracies. From optical graphene to unidirectionalÌýinvisibility to the anomalous quantum Hall effect, spectral degeneracies are a drivingÌýfactor even when the system has beenÌýperturbed away from the degenerate case. Recently this hasÌýextended the study of topologicalÌý(global) properties of the spectrum. Here longitudinal driving of the waveguides produce topologicalÌýinsulators and protectedÌýedge modes. This talk will give an introduction to topological photonicsÌýand the analytical tools capableÌýof deriving reduced dynamical systems to model the Floquet spectrum. These tool range from tight-binding approximations to multiple-scales analysis and provide an approach that will be applicable in a wide range of waveguide arrays with nontrivial topologies. Key topolical constants like the Chern number are obtained as well as governing equations for the envelope dynamics in the presenceÌýof Kerr nonlinearity.Ìý
Recorded video of this seminar is available (click ).