Wide-Angle Alternating-Direction Implicit Finite-Difference BPM

Author

Bekker, Ella V. ; Sewell, Phillip ; Benson, Trevor M. ; Vukovic, Ana

Author_Institution

Univ. of Nottingham, Nottingham

Volume

1

fYear

2007

fDate

1-5 July 2007

Firstpage

250

Lastpage

253

Abstract

We introduce an improved Alternating Direction Implicit (ADI) scheme for each of the wide-angle (WA) Pade approximant multi-steps, and moreover, employ an iterative approach to correct for the splitting error. The resulting finite-difference scheme is conditionally stable and can be straightforwardly solved using the efficient Thomas algorithm for tri-diagonal band matrices. Valuable reductions in both the memory and calculation time are obtained, especially for complex geometries.

Keywords

approximation theory; finite difference methods; matrix algebra; optical waveguide theory; Pade approximantion; beam propagation method; finite-difference BPM; iterative method; optical waveguide; splitting error; tri-diagonal band matrices; wide-angle alternating-direction implicit scheme; Dispersion; Electromagnetic waveguides; Error correction; Finite difference methods; Geometrical optics; Optical propagation; Optical waveguides; Partial differential equations; Polynomials; Refractive index;

fLanguage

English

Publisher

ieee

Conference_Titel

Transparent Optical Networks, 2007. ICTON '07. 9th International Conference on

Conference_Location

Rome

Print_ISBN

1-4244-1249-8

Electronic_ISBN

1-4244-1249-8

Type

conf

DOI

10.1109/ICTON.2007.4296081

Filename

4296081