Comparison of Coupled Mode Theory and FDTD Simulations of Coupling between Bent and Straight Optical Waveguides

Analysis of cylindrical integrated optical microresonators involves the coupling between a straight waveguide and a bent waveguide. Our (2D) variant of coupled mode theory is based on analytically represented mode profiles. With the bend modes expressed in Cartesian coordinates, coupled mode equations can be derived in a classical way, and solved by numerical integration. Proper manipulation of the propagation matrix leads to stable results that satisfy the reciprocity properties for symmetric coupler devices, even in parameter domains of rather compact, radiative structures and strong interaction, which before seemed unaccessible by a perturbational approach. Comparisons with FDTD calculations show convincing agreement.