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The propagation of linear and nonlinear edge modes in bounded photonichoneycomb lattices formed by an array of rapidly varying helical waveguides isstudied. These edge modes are found to exhibit strong transmission (reflection)around sharp corners when the dispersion relation is topologically nontrivial(trivial), and can also remain stationary. An asymptotic theory is developedthat establishes the presence (absence) of edge states on all four sides,including in particular armchair edge states, in the topologically nontrivial(trivial) case. In the presence of topological protection, nonlinear edgesolitons can persist over very long distances.

Strong transmission and reflection of edge modes in bounded photonic graphene