Research and Applications of Three Dimensional Vectorial Beam Propagation Methods

• Main Authors: Hsueh, Yu-li, 薛育理
• Other Authors: Hung-chun Chang
• Format: Others
• Language: en_US
• Published: 1998
• Online Access: http://ndltd.ncl.edu.tw/handle/60540981201359128255

碩士 === 國立臺灣大學 === 光電工程學研究所 === 86 === In this thesis a new three dimensional (3-D) noniterative full-vectorial w ide-angle beam propagation method (BPM) is proposed. The axial coordinate is d iscretized with the implicit Crank-Nicholson scheme, in which the necessary op erator inversions are performed via the alternating direction implicit (ADI) m ethod. Because of the noniterative nature of the ADI method, the algorithm has good performance in efficiency. Numerical stability is also assured thanks to the implicit discretization scheme. The proposed method is of second order ac curacy along the propagation direction, and the difficulties resulting from th e cross-coupling terms are properly dealed with. The wide-angle approach is im plemented by the Pade approximants. Rather than assuming the paraxial approxim ation, the exact propagation operator is replaced by any one of a sequence of higher-order Pade (n, n) approximant operators. The wide-angle algorithm allow s accurate propagation at large angles from the propagation axis. To absorb th e outgoing waves at the boundaries of the numerical window, the transparent bo undary condition (TBC) and the perfectly matched layer (PML) boundary conditio n are adopted in the algorithm. Several numerical simulations have been perfor med in order to examine the accuracy and the practicality of the algorithm. So me interesting optical structures including the polished-type fiber-optic coup ler, the fused fiber-optic coupler, and nonlinear waveguide structures are ana lyzed with the proposed 3-D algorithm.