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Efficient nonuniform schemes for paraxial and wide-angle finite-difference beam propagation methods

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5 Author(s)
Shibayama, J. ; Coll. of Eng., Hosei Univ., Tokyo, Japan ; Matsubara, K. ; Sekiguchi, M. ; Yamauchi, J.
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Efficient nonuniform schemes, based on the generalized Douglas (GD) scheme, are developed for the finite-difference beam propagation method (FD-BPM). For a two-dimensional (2-D) problem, two methods are presented: a computational space method and a physical space method. In the former, the GD scheme is employed, after replacing a nonuniform grid in the physical space with a uniform one in the computational space. In the latter, the GD scheme is directly extended to a nonuniform grid in the physical space. We apply these two methods to paraxial and wide-angle FD-BPM's. The fourth-order accuracy is achieved in the transverse direction, provided that the grid growth factor between two adjacent grids is r=1+O(Δx). For the paraxial BPM, the reduction in the truncation error is demonstrated through modal calculations of a graded-index waveguide using an imaginary distance procedure. For the wide-angle BPM, the propagating field in a tilted waveguide is analyzed to show the effectiveness of the present scheme. As an application of the physical space method, an adaptive grid is introduced into the multistep method

Published in:

Lightwave Technology, Journal of  (Volume:17 ,  Issue: 4 )

Date of Publication:

Apr 1999

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