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Coupled-mode theory for binary optical lattices

The coupled-mode theory is developed for description of the nonlinear wave dynamics in binary optical lattices. The obtained equations of motion accurately describe nonlinear wave dynamics close to the band edges and in the gap of the linear spectrum of the system. In order to demonstrate the power of the presented approach, bright gap solitary wave solutions of the nonlinear coupled- mode equations are derived and examined both analytically and numerically. The presented results are relevant to nonlinear wave phenomena in coupled waveguide arrays, coupled nano-cavities in photonic crystals, metallo-dielectric systems, and the Bose-Einstein condensates in deep optical lattices.