Analysis of a bending dielectric slab waveguide by integral equation formulation

Abstract

AbstractThe waveguide bend is an indispensable circuit element in realizing optical integrated circuits. In this paper, the bend in a dielectric slab waveguide is analyzed numerically by means of the integral equation formulation. When a numerical solution of an integral equation is attempted by the boundary‐element method, two problems exist: 1) how one can connect the field distributions expressed by the boundary‐element method with those by the eigenmodes of the waveguide. In this paper, instead of representing the field at the input/output boundary of the bend in the slab waveguide in terms of the boundary‐element method, a new method is proposed in which the field distributions expressed in terms of the eigenmodes are substituted directly into the integral equation; and 2) the treatment of the radiation mode. In this paper, a discretization method based on the sampling theorem is used. As an example, numerical calculations have been carried out for a conventional bend and a reflection bend in a dielectric slab waveguide. It is confirmed that the results agree well with data obtained by other methods. It is pointed out that good results can be obtained for such cases as a structure with large difference in index of refraction between the core and cladding and the one with a large bend angle, which were difficult to analyze by the conventional methods. Further, it is shown that the bending loss of the reflection bend is substantially smaller than that of the conventional bend.