Comparative analysis of the method-of-lines for three-dimensional curved dielectric waveguides

We discuss the effects of waveguide geometry on the radiation loss of tightly curved multimode dielectric waveguides. Three waveguide geometries are investigated: a ridge waveguide, a buried waveguide, and an interdiffused waveguide. We compare the effective index method with both semi- and full-vectorial method-of-lines analyses for these waveguide geometries. This comparison shows that the effective index method is accurate for curved waveguides except where the outer confinement region is in cut-off or, in the case of TM-polarization, for the ridge waveguide. In the latter case, the full-vectorial method-of-lines predicts a resonant feature of the TM-mode radiation loss of curved ridge waveguides; this is not predicted by either the semivectorial method-of-lines or the effective index method.