Linear and nonlinear traveling edge waves in optical honeycomb lattices

Ablowitz, Mark, Curtis, Christopher and Ma, Yi-Ping (2014) Linear and nonlinear traveling edge waves in optical honeycomb lattices. Physical Review A, 90 (2). 023813. ISSN 1050-2947

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Abstract

Traveling unidirectional localized edge states in optical honeycomb lattices are analytically constructed. They are found in honeycomb arrays of helical waveguides designed to induce a periodic pseudomagnetic field varying in the direction of propagation. Conditions on whether a given pseudofield supports a traveling edge mode are discussed; a special case of the pseudofields studied agrees with recent experiments. Interesting classes of dispersion relations are obtained. Envelopes of nonlinear edge modes are described by the classical one-dimensional nonlinear Schrödinger equation along the edge. Nonlinear states termed edge solitons are predicted analytically and are found numerically.

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