Title :
Finite-difference beam propagation method based on the generalized Douglas scheme for a nonuniform grid
Author :
Yamauchi, Junji ; Shibayama, Jun ; Sekiguchi, Minoru ; Nakano, Hisamatsu
Author_Institution :
Coll. of Eng., Hosei Univ., Tokyo, Japan
Abstract :
The finite-difference beam propagation method based on the Douglas scheme is extended to a nonuniform grid. The truncation error is reduced to O(/spl Delta/x)/sup 4/, provided the grid growth factor is r=1+O(/spl Delta/x), while maintaining a tridiagonal matrix. The numerical results show that the accuracy is improved as compared with that obtained from the conventional nonuniform Crank-Nicholson scheme.
Keywords :
finite difference methods; optical waveguide theory; Douglas scheme; finite-difference beam propagation method; grid growth factor; nonuniform grid; numerical method; tridiagonal matrix; truncation error; Computational efficiency; Equations; Finite difference methods; Finite wordlength effects; Nonuniform sampling; Optical propagation; Optical waveguides; Sampling methods; Taylor series; Transmission line matrix methods;
Journal_Title :
Photonics Technology Letters, IEEE
