Numerical solution method of nonlinear guided modes with a finite difference complex axis beam propagation method

Author

Wijnands, Frank ; Hoekstra, Hugo J W M ; Krijnen, Gijs J M ; De Ridder, René M.

Author_Institution

Blackett Lab., Imperial Coll. of Sci., Technol. & Med., London, UK

Volume

31

Issue

5

fYear

1995

fDate

5/1/1995 12:00:00 AM

Firstpage

782

Lastpage

790

Abstract

A method to construct modal fields for an arbitrary one- or two-dimensional intensity dependent refractive index structure is described. An arbitrary starting field is propagated along an imaginary axis using the finite difference beam propagation method (FDBPM) based upon the slowly varying envelope approximation (SVEA). First the modes are found for the linear part of the refractive index structure. By suitably choosing the complex value of the propagation step, one mode is maximally increased in amplitude. After the nonlinearity has been put on, two methods are applied to find the modes for the nonlinear structure. One method is the same as the method used for the linear part, in the other method the propagation step is left unchanged. The applicability of the method is discussed and illustrated by a calculation on a waveguide with one-dimensional cross section having Kerr-type nonlinearity

Keywords

approximation theory; finite difference methods; optical Kerr effect; optical waveguide theory; refractive index; Kerr-type nonlinearity; arbitrary starting field; finite difference complex axis beam propagation method; imaginary axis; intensity dependent refractive index structure; modal fields; nonlinear guided modes; nonlinearity; numerical solution method; one-dimensional cross section; slowly varying envelope approximation; waveguide; Convergence; Difference equations; Eigenvalues and eigenfunctions; Finite difference methods; Fourier transforms; Matrices; Nonhomogeneous media; Refractive index; Slabs; Transmission line matrix methods;

fLanguage

English

Journal_Title

Quantum Electronics, IEEE Journal of

Publisher

ieee

ISSN

0018-9197

Type

jour

DOI

10.1109/3.375923

Filename

375923