Fourier analysis of high-index-contrast slab waveguide with step discontinuity: An analytical and exact solution

We propose a novel technique based on Fourier analysis and perturbation theory to describe completely the step discontinuity in a slab waveguide of any index contrast without the need for analytical approximations or assumptions. Through this technique, we derive a spectral overlapping criterion and a coupling matrix that analyzes effectively the roles of the radiation modes in the resultant computation accuracy. A symmetric nano-waveguide with 55.9% index contrast is investigated under normal incident light condition along TE polarization. The total reflectance and the guided power reflectivity are computed at the waveguide-air interface. Results obtained are consistent with the FDTD simulation and only requires very short computational time.