An improved finite difference method in solving vector wave equations based on H fields for full-vectorial analysis of optical waveguides is described.A six-point finite difference scheme of high accuracy is constructed to approximate cross-coupling terms.It takes into account the discontinuities in derivatives of magnetic component at horizontal and vertical interfaces.Moreover,the scheme is independent of structure of waveguide due to explicit expressions.The guided-mode patterns and normalized propagation constants of a step-index fiber,a rectangular waveguide and a rib waveguide are presented.The hybrid nature of full-vectorial guided-modes is demonstrated.The results agree well with analytical solutions and the benchmark results of modal transverse resonance method.It demonstrates accuracy and convergence of the method.

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.

It assesses the Rayleigh inverse-iteration method and boundary layer asymptotic expansion method, and uses them into the stability equations of compressible boundary layer and the numerical method for forecasting the transition point. It gives also a stability analysis on the first mode of the boundary layer of flat plane and a forecasting of transition point. Results are discussed and compared with observations.