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Modes in Honeycomb Optical Lattices

Banff International Research Station for Mathematical Innovation and Discovery

Optical graphene, or an optical honeycomb waveguide, has become a material of much interest and excitement in the optics community. This is due to the presence of Dirac points in the dispersion relationship which is a result of the symmetry of the lattice. In this talk, we study two classes of perturbations which have significant impacts on the Dirac points. The first class are so called parity-time (PT) symmetric perturbations. We show that certain types of PT- perturbations separate Dirac points while keeping the associated dispersion relationships real. This allows for novel nonlinear wave equations to be derived which model the propagation of waves in the gap. We then briefly study one-dimensional gap solitons, which are shown to be unstable. The second class of perturbations are due to helical variations in the index of refraction of the underlying optical lattice. This allows for the formation of so-called topological edge modes. In the linear regime, we find families of these modes for different classes of lattice perturbations. We then study the impact of nonlinearity on these modes showing that nonlinear edge modes form. We show via numerical experiments that these modes appear to posses the same type of stability to backscattering that the linear modes do, hinting at the existence of nonlinear topological edge-modes.

Mathematics; Partial differential equations; Dynamical systems and ergodic theory

video/mp4

Author affiliation: SDSU

2017-01-30

Attribution-NonCommercial-NoDerivatives 4.0 International

http://hdl.handle.net/2429/60077

Unreviewed

http://creativecommons.org/licenses/by-nc-nd/4.0/