  The propagation of linear and nonlinear edge modes in bounded photonic
honeycomb lattices formed by an array of rapidly varying helical waveguides is
studied. 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 developed
that 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 edge
solitons can persist over very long distances.

Optics;Mesoscale and Nanoscale Physics;Pattern Formation and Solitons