Nonlinear Waves Seminar: Yiping Ma
Traveling edge waves in photonic graphene
Applied Mathematics,Ìý
Date and time:Ìý
Tuesday, September 15, 2015 - 4:00pm
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ECOT 226
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PhotonicÌýgraphene, namelyÌýanÌýhoneycomb array of opticalÌýwaveguide, has attractedÌýmuch interest in the opticsÌýcommunity.ÌýIn recent experimentsÌýit was shown that introducing edges and suitable waveguides in the direction of propagation, unidirectional edge wave propagation at optical frequencies occurs in photonic graphene. The system is described analytically by the lattice nonlinear Schrodinger (NLS) equation with a honeycomb potential and a pseudo-magnetic field. In certain parameter regimes, these edge waves were found to be nearly immune to backscattering, and thus exhibit the hallmarks of (Floquet) topological insulators.
Ìý
This talk addresses the linear and nonlinear dynamics of traveling edge waves in photonic graphene, using a tight-binding model derived from the lattice NLS equation. Two different asymptotic regimes are discussed, in which the pseudo-magnetic field is respectively assumed to vary rapidly and slowly.ÌýIn the presence of nonlinearity,Ìýnonlinear edge solitons can exist due to the balance between dispersion and nonlinearity; these edge solitons appear to be immune to backscatteringÌýwhen the dispersion relation is topologically nontrivial. A remarkableÌýeffect of topology in bounded photonicÌýgraphene will alsoÌýbe demonstrated:ÌýtheÌýedge modes are found toÌýexhibit strong transmission (reflection) around sharp corners when the dispersion relation is topologically nontrivial (trivial).