The method of lines for analysis of integrated optical waveguide structures with arbitrary curved interfaces

An efficient analysis of integrated optical waveguide structures with arbitrary curved interfaces based on the method of lines (MoL) is presented. The structures to be analyzed have a geometry of multilayer cross section and a homogeneous or periodic variation in the propagation direction. The discretization lines of varying length according to the layer thickness are used. No stairstep approximation is needed for the curved region. The same transformation matrices are used for all layers in the analysis. Only the Helmholtz wave equation has to be solved. The analysis is a full wave analysis valid also for the cylindrical waveguide. The new approach is verified especially by analyzing the rib waveguide and the Bragg gratings. The results are consistent with those published in literature.