Full-Vectorial Finite Element Beam Propagation Method Based on Curvilinear Hybrid Edge/Nodal Elements for Optical Waveguide Problems

• Main Authors: Sen-Ming Hsu, 許森明
• Other Authors: Hung-Chun Chang
• Format: Others
• Language: en_US
• Published: 2004
• Online Access: http://ndltd.ncl.edu.tw/handle/69371658699655182573

碩士 === 國立臺灣大學 === 電信工程學研究所 === 92 === A full-vectorial finite element beam propagation method based on curvilinear hybrid edge/nodal elements is adopted in this thesis for studying optical waveguide problems. Several difficulties of the finite element method eigenmode solver based on the (modified) shift inverse power method are overcome in this work by taking advantages of the characteristics of the beam propagation method. By analyzing the elliptical-core fibers, we find that the procedure for finding higher order modes using the beam propagation method is straightforward, while that of the eigenmode solver based on the shift inverse power method converges to the desired mode only when the initial guess for the effective index of the desired mode is properly assigned. Incorporating the general closed-form perfectly matched layer into the beam propagation method as the boundary condition to absorb waves out of the computational window, the proton-exchanged LiNbO3 optical waveguides with non-diagonal permittivity and permeability tensors can still be analyzed. For the cases in which the tensors are in diagonal form, the imaginary-distance beam propagation method can be employed to speed up the analysis process. Through the calculation of the leakage properties of two kinds of photonic crystal fibers with different air hole arrangements, we demonstrate that the finite element imaginary-distance beam propagation method can analyze the leaky modes reliably and it is more suitable for the waveguides with large structures and large number of unknowns than the finite element method eigenmode solver based on the modified shift inverse power method.