Comparison of spectral index, semi-vectorial finite difference and vector finite element methods for the modal analysis of semiconductor optical rib waveguides

Semiconductor rib waveguides, a typical example of which is illustrated, now have various important applications in the field of integrated optics as passive and active devices such as bends, tapers, splitters, routing switches, laser cavities, and modulators. Since the early 1980s, the UK has seen considerable progress in the modal analysis of such waveguiding structures (including directional couplers) by the use of the vector H-field finite element (VFE) method, the semi-vectorial E-field and H-field finite difference (SVFD) methods, and the spectral index (SI) methods. The SI methods, which have been implemented on mainframes and 80286-based PCs (with and without coprocessors), have far more economical computer memory and CPU time requirements than the VFE and SVFD methods which are mainly suitable for use on mainframes, powerful workstations and 80486-based PCs