Towards 3-D simulations

The approach followed in this thesis can be systematically extended to 3-D settings, where at present hardly any other practically applicable tools are available. Recently, significant progress has been made in this direction. For the reliable computation of bent modes and their propagation constants, a 3-D vectorial eigenmode solver for bent waveguides based on film mode matching has been proposed [67,68]. Using these modes, a 3-D model of bent-straight waveguide couplers and microresonators has been implemented, as presented in Ref. [69]. These tools permit the reliable simulation and analysis of realistic devices, including specific 3-D features like vertical coupling or cavities that support hybrid modes.