A semivcetorial method based on a variable transformed Galerkin method is proposed for optical waveguides. It is successfully applied to analyze the eigenvalues of rectangular and rib optical waveguides. The modal propagation constants and field distributions of rectangular and rib waveguides are presented. The calculated results agree well with the published data. Adopting a proper variable transformation, the artificial boundary condition is avoided, and the polarization characteristics of the mode field are displayed.

A 3D trapered spot-size converter (3D-SSC) on a rib cross-sectional optical waveguide, one of the key components in photonic devices connecting with single mode optical fibers,is investigated through simulating lightwave transmission in this component based on 3D-FD beam propagation method.Geometry parameters,such as laterally boundaries,length,width of the large section,thickness and those of the transitional optical waveguide for connecting SMOF to 3D-SSC are discussed and analyzed.The simulation shows that the insert loss of 3D-SSC can be lower than 2 dB as the width in the area of 11.5 μm~13.5 μm and the thickness in the area of 4.5 μm~6.5 μm at the large end of the taper when the taper length is in the region of 200 μm~500 μm.The capability and the alignment tolerance of the 3D-SSC is better than those of the planar SSC,and the 3D-SSC with a nonlinear lateral boundary acquires lower insertion loss than that with a linear lateral boundary.It is found that the 3D-SSC converts gradually the guided modes from multi-mode to single mode finally.