Efficient and accurate numerical analysis of multilayer planar optical waveguides

This paper presents a numerical method for computing the propagation constant of electromagnetic modes supported by multilayer planar optical waveguides. We report a method for solving the dispersion equation for a guided wave structure of interest in the complex plane via Chauchy's integration. The method is applicable to lossless, lossy and ARROW waveguide structures and can handle both leaky and guided modes. Contrary to the methods currently published in the literature, which are based on a numerical derivative of the dispersion equation, we propose an analytical derivative for the latter. This has a double impact: improved accuracy and reduced CPU time. The specific integration contour for leaky modes will be discussed. The results are in excellent agreement with several results published in the literature.