Abstract:
Efficient nonuniform schemes, based on the generalized Douglas (GD) scheme, are developed for the finite-difference beam propagation method (FD-BPM). For a two-dimensiona...Show MoreMetadata
Abstract:
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(/spl Delta/x). 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: Journal of Lightwave Technology ( Volume: 17, Issue: 4, April 1999)
DOI: 10.1109/50.754799