Computer-aided design of dielectric optical waveguide bends by the boundary-element method based on guided-mode extracted integral equations

We show examples of accurate computer-aided design of two-dimensional dielectric waveguide bends of finite length by using the boundary-element method (BEM) based on guided-mode extracted integral equations (GMEIE's) that have been proposed previously. In contrast to integral equations used in previous papers, the unknown function in the GMEIE's that we discuss is the total field, which is the same as that in the conventional boundary integral equation method. Therefore waveguide discontinuity problems in dielectric open waveguides can be perfectly regarded as problems of scattering by isolated dielectric objects. Various properties in numerical calculations of GMEIE's are examined. The numerical results obtained satisfy the energy conservation law within an accuracy of 1.0%. It is shown that it is possible to design an optimum bend shape of a dielectric optical waveguide bend that gives small radiation losses by using the BEM based on GMEIE's. (C) 1996 Optical Society of America