In recent years, there has been considerable interest in the study of wave propagation in
nonlinear photonic lattices. The interplay between nonlinearity and periodicity has led …

We study a class of periodic Schrödinger operators, which in distinguished cases can be
proved to have linear band-crossings or “Dirac points”. We then show that the introduction of …

Optical metamaterials and metasurfaces, which emerged in the course of the last few
decades, have revolutionized our understanding of light and light–matter interaction. While …

We report on the transport properties of the super‐honeycomb lattice, the band structure of
which possesses a flat band and Dirac cones, according to the tight‐binding approximation …

We consider a nonlinear Schrödinger equation in two spatial dimensions subject to a
periodic honeycomb lattice potential. Using a multi-scale expansion together with rigorous …

This paper is a mathematical analysis of conduction effects at interfaces between insulators.
Motivated by work of Haldane and Raghu (2008), we continue the study of a linear PDE …

Mathematical analysis on electromagnetic waves in photonic graphene, a photonic
topological material which has a honeycomb structure, is one of the most important current …

We consider Laplacians on both periodic discrete and periodic metric equilateral graphs.
Their spectrum consists of an absolutely continuous part (which is a union of non …

Wave dynamics in topological materials has been widely studied recently. A striking feature
is the existence of robust and chiral wave propagations that have potential applications in …

The propagation of localized edge modes in photonic honeycomb lattices, formed from an
array of adiabatically varying periodic helical waveguides, is considered. Asymptotic …