PLANAR WAVE-GUIDE ANALYSIS BY THE SPECTRAL INDEX METHOD .1. RIB AND UNIFORMLY BURIED WAVE-GUIDES

The scope of the spectral index method for solving general planar waveguiding problems is analysed by first showing how simple it is to set up a closed-form transcendental equation whose solution is very accurate; the solution is so fast that the method can be used as a subroutine, making it possible to solve many two-dimensional problems fully, even for coupled rib waveguides, without using effective index approximations. The method is then extended to the uniformly buried waveguide of rectangular cross-section, and the corresponding coupler, thereby unifying the effective index, transverse resonance and spectral index methods for the first time, and giving an asymptotic expression for the coupling length without using overlap integrals. Finally, sample numerical results and optical field profiles are given for the rib waveguide and rib waveguide coupler.