Efficient semivectorial mode solvers

Author

Wijnands, Frank ; Rasmussen, Thomas ; Hoekstra, Hugo J W M ; Povlsen, Jorn H. ; De Ridder, Rene M.

Author_Institution

MESA Res. Inst., Twente Univ., Enschede, Netherlands

Volume

33

Issue

3

fYear

1997

fDate

3/1/1997 12:00:00 AM

Firstpage

367

Lastpage

374

Abstract

A method, based on a semivectorial finite difference scheme, is described to construct modal fields for any two-dimensional refractive-index profile which is constant except at abrupt interfaces. The modal fields correspond to eigenvectors of the matrix equation to be solved. In order to find the eigenvectors and their corresponding eigenvalues, the matrix equation is formulated according to the inverse iteration method (IIM). Two versions of the IIM are compared. Further, two matrix equations are compared: one is based on the propagation equation, following from the three-dimensional paraxial wave equation, and the other is the Fresnel equation, leading to the standard eigenvalue equation. A new solution method for the matrix equation is presented. It is a refinement of the alternating direction implicit (ADI) method. This refined ADI method is compared to the standard conjugate gradient (CG) method. Both methods are tested for waveguides having a rectangular core cross section. The refined ADI method is found to be computationally more efficient than the unpreconditioned CG method

Keywords

eigenvalues and eigenfunctions; finite difference methods; inverse problems; iterative methods; matrix algebra; optical waveguide theory; optical waveguides; rectangular waveguides; refractive index; vectors; 3D paraxial wave equation; Fresnel equation; abrupt interfaces; conjugate gradient method; eigenvalues; eigenvectors; inverse iteration method; matrix equation; modal field construction; modal fields; optical waveguide theory; propagation equation; rectangular core cross section waveguides; semivectorial finite difference scheme; semivectorial mode solvers; standard eigenvalue equation; three-dimensional paraxial wave equation; two-dimensional refractive-index profile; Character generation; Eigenvalues and eigenfunctions; Electromagnetic waveguides; Finite difference methods; Optical propagation; Optical waveguides; Partial differential equations; Testing; Transmission line matrix methods; Two dimensional displays;

fLanguage

English

Journal_Title

Quantum Electronics, IEEE Journal of

Publisher

ieee

ISSN

0018-9197

Type

jour

DOI

10.1109/3.556005

Filename

556005