A VARIATIONAL COUPLED-MODE THEORY FOR PERIODIC WAVE-GUIDES

A simple variational theorem for the dispersion relations and propagat ion constants of periodic waveguides is derived, The trial fields used in the variational formula incorporate an the Floquet components corr ect 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 agreeme nt with exact analytic solutions (in 1-D), and numerical simulations ( in 2-D), for high-index contrast structures.