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Oppositely Directional Coupler: Example of the Forward Backward Waves Interaction in the Metamaterials

We consider the coupled electromagnetic waves propagating in a nonlinear coupler and in nonlinear waveguide array, which consists of alternating waveguides of positive and negative refraction indexes. The forward wave and backward wave interaction is realized in these devices. Gap solitons in a nonlinear oppositely directional coupler with one channel or both channels fabricated from nonlinear medium having negative refraction index are discussed. Generalization of the usually waveguide array is zigzag array. Due to zigzag configuration there are interactions between both nearest and next nearest neighboring waveguides exist. The system of evolution equations for coupled waves has the steady state solution describing the electromagnetic pulse running in the array. Numerical simulation demonstrates robustness of these solitary waves.