Mode coupling analysis for the design of refractive ion exchange integrated optical components

Refractive integrated optical planar components such as prisms and lenses, consist of alternating regions of high- and low-index planar waveguides. Boundary transmission losses depend on the coupling efficiency between the fundamental modes in the two regions. Hence, a choice of appropriate parameters to achieve maximum coupling efficiency is an important design criterion of these components. We propose the use of the Ritz-Galerkin (RG) procedure to characterize the modal fields in planar graded index waveguides for obtaining coupling efficiency and, hence, the optimal design features. The procedure is "exact" and simple analytical expressions have been obtained for coupling efficiency. Further, coupling to higher order modes can also be obtained to estimate the background noise in component design when parameters deviate from the optimum. To confirm the convergence, results have been compared with the exact numerical procedure based on the multilayer staircase approximation. Various variational procedures limited to the fundamental mode coupling efficiency calculations are also summarized in this paper along with a discussion on their accuracies.