A semi-analytic method for solving rib-type waveguide problems

Abstract

A semi-analytic method for solving rib-type waveguide problems, Journal of Modern Optics, 55:8, 1315-1329, A new semi-analytic method for solving optical rib-type waveguide problems is presented. In the method, the cross-section of a rib-type waveguide is divided into several regions. In each region, the refractive index profile and field distribution are expanded into Fourier cosine series, and then are substituted in the wave equation. A second-order differential matrix equation is then derived for each region, with a closed-form solution obtainable. With the boundary conditions used, an eigenmode equation for the rib waveguide can be derived and solved numerically to give the modal indices. Here, the presented method is used to deal with two rib waveguides in different geometric dimensions and/or compositions, respectively. Computational results show that the presented method is quite efficient, in terms of CPU time, in finding the modal indices accurately. The relative error in computing the modal index with the method is about 10 À5 -10 À6 . IntroductionFor more than a decade, considerable effort has been directed to computing the modes of optical rib waveguides, which form the important parts of photonic integrated circuits. Many kinds of numerical and semi-analytic methods were utilized for the computation of modal fields and the modal indices of rib-type waveguides. These include finite difference method [1-4], finite element method [5][6][7][8], beam propagation method [9-12] and many other semi-analytic methods [13][14][15][16]. Numerical methods based on finite element or finite difference basically discretize the transverse domain of an optical waveguide to induce an eigenvalue problem. A beam propagation algorithm was also introduced in the finite-difference discretization [10] or Fourier transform scheme [12] to determine the modal field and the modal index of a z-invariant structure. With the use of some