| Summary: | 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.
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