Coupled modes of multiwaveguide systems and phased arrays

A new theory describing coupled mode propagation in an array of arbitrary optical waveguides is developed. The formulation unambiguously accounts for real and/or imaginary index perturbations and its solutions yield supermode patterns and propagation constants. Several examples of coupled TE slab waveguides are evaluated and the results are shown to compare very favorably with exact solutions. The calculated propagation constants and mode patterns differ quantitatively and qualitatively from those derived from the prior theory. In particular, the supermode gains derived according to the new theory agree very well with exact solutions and predict different supermode ordering and splitting than those derived by the prior theory.