A variational coupled-mode theory for periodic waveguides

A simple variational theorem for the dispersion relations and propagation constants of periodic waveguides is derived. The trial fields used in the variational formula incorporate all the Floquet components correct to first order. This yields a propagation constant in which errors enter only to fourth order in the trial field. The analysis yields a new coupled mode formulation which is shown to yield excellent agreement with exact analytic solutions (in l-D), and numerical simulations (in 2-D), for high-index contrast structures.