Analytical first-order extension of coupled-mode theory for waveguide arrays.

Coupled mode theory for waveguide arrays is extended to next-nearest neighbor interactions using propagation equations. Both lateral diffraction and propagation of Floquet-Bloch waves are altered respectively by extra coupling and non-orthogonality between isolated waveguide modes. The analytical formula describing the distortions of the diffraction relation is validated by direct numerical simulation for weakly coupled InP and GaAs shallow ridge waveguides and for strongly coupled Si-SiO(2) buried strip waveguides. The impact of extended coupled mode theory on propagation and diffraction design in waveguide arrays is discussed with reference to available experimental work.