Analysis of Z-invariant and Z-variant semiconductor rib waveguides by explicit finite difference beam propagation method with nonuniform mesh configuration

An efficient and simple explicit finite difference beam propagation method (EFD-BPM) incorporating nonuniform mesh is described. The criteria for stability are developed, and it is shown that this algorithm is power conserving when the stability criteria are met. EFD-BPM is applied to the analysis of single and coupled semiconductor rib waveguides and its accuracy is confirmed by comparing the results with the reported results. Nonuniform mesh is found to improve the efficiency of the method significantly for the analysis of weakly guiding waveguide structures. Several coupled rib waveguide structures with curved input and output branching sections are analyzed using both three-dimensional EFD-BPM and two-dimensional finite difference BPM combined with effective index approximation.>