Modal analyses of semiconductor rib waveguides employing nonequidistant grids

We establish, through explicit finite-difference calculations of semiconductor rib-waveguide modes, that considerable numerical error arises from the presence of discontinuities in the refractive-index profile. We accordingly consider two split-operator finite-difference formalisms that are second- and fourth-order accurate with respect to the transverse grid-point spacing on a suitably chosen grid of nonequidistant points and demonstrate that these algorithms greatly improved accuracy relative to analogous procedures on equidistant grids.