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Title: Tight-binding Approximations for Longitudinally Driven Photonic Lattices
Abstract: Systematic tight-binding methods are used to describe the dynamics of general longitudinally driven photonic lattices. In particular, honeycomb (graphene) and staggered square lattices are examined. The lattice is helically driven along the direction of beam propagation and, as a result, topologically protected edge modes are found via Floquet theory. Several intricate sublattice rotation patterns and their corresponding edge states are inspected. Topological edge modes are observed to propagate unidirectionally and through lattice defects without scattering. An asymptotic theory for both linear and nonlinear solutions is found to agree well with direct numerics. Nonlinear soliton edge states are identified and are shown to propagate over long distances with little diminishment of their initial form. More complex lattices (e.g. Lieb. Kagome lattices), can also be analyzed with these methods.