Scalar coupled mode theory and variational analysis for planar SOI waveguide arrays: a detailed comparison

We present a detailed analytical comparison of two extensively used theories to study the coupled optical waveguide arrays. Various formulations of the scalar Coupled Mode Theory and the Ritz Galerkin variational analysis have been applied to 1-D SOI coupled waveguide arrays to study the TE modes of the structure having identical and non-identical waveguides. Equivalence between scalar Ritz Galerkin variational formulation and the coupled mode theory without any approximations is shown. Comparisons of various modal characteristics obtained from the different coupled mode and variational formulations have been shown along with the exact results obtained from the solution of the scalar wave equation. For the 1-D SOI array under consideration the non-identical waveguide configuration leads to stronger coupling which results in non-orthogonal supermodes using two of the coupled mode formulations. The excellent agreement with exact results and the much lower computational time compared to numerical techniques, make these analytical methods a preferred choice for the simulation of coupled waveguide arrays.