Nonlinear Waves Seminar: Yiping Ma

Traveling edge waves in photonic graphene

Yiping Ma

Applied Mathematics, University of Colorado Boulder

Date and time: 

Tuesday, September 15, 2015 - 4:00pm

Location: 

ECOT 226

Abstract: 

Photonic graphene, namely an honeycomb array of optical waveguide, has attracted much interest in the optics community. In recent experiments it 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.

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. In the presence of nonlinearity, nonlinear edge solitons can exist due to the balance between dispersion and nonlinearity; these edge solitons appear to be immune to backscattering when the dispersion relation is topologically nontrivial. A remarkable effect of topology in bounded photonic graphene will also be demonstrated: the edge modes are found to exhibit strong transmission (reflection) around sharp corners when the dispersion relation is topologically nontrivial (trivial).