Title :
A modified finite-element method for dielectric waveguides using an asymptotically correct approximation on infinite elements
Author_Institution :
Swedish Defence Res. Establ., Linkoping, Sweden
fDate :
2/1/1991 12:00:00 AM
Abstract :
A modified finite-element method for the propagation analysis of such dielectric waveguides as optical fibers and integrated optical waveguides is presented. Possible applications include nondissipative structures of arbitrary anisotropic media with, in some cases, inhomogeneous exterior regions. The method is based on the full vectorial finite-element formulation, which is known to be without spurious solutions. With this formulation all appropriate boundary and interelement conditions on both tangential and normal components are a priori satisfied. For the unbounded, exterior region a novel type of asymptotically correct approximation on infinite elements is proposed that simultaneously, for each mode and frequency, locally adapts the rate of radial decay to the transversal wavenumbers. The linearity of the original finite-element method has been retained by using β/k0 as a parameter, which results in a sparse generalized eigenvalue problem. Numerical examples including both optical fibers and integrated optical waveguides, isotropic as well as anisotropic, have been analyzed to confirm the validity of the method. The observed correspondence with analytical solutions has been excellent. For some examples a special near-field wavenumber has been added to preserve a high accuracy close to cutoff
Keywords :
dielectric waveguides; eigenvalues and eigenfunctions; finite element analysis; guided light propagation; integrated optics; optical fibres; optical waveguide theory; arbitrary anisotropic media; asymptotically correct approximation; dielectric waveguides; finite-element method; full vectorial finite-element formulation; infinite elements; inhomogeneous exterior regions; integrated optical waveguides; isotropic waveguides; modified FEM; nondissipative structures; optical fibers; propagation analysis; sparse generalized eigenvalue problem; Anisotropic magnetoresistance; Dielectrics; Finite element methods; Frequency; Geometrical optics; Integrated optics; Nonhomogeneous media; Optical fibers; Optical propagation; Optical waveguides;
Journal_Title :
Microwave Theory and Techniques, IEEE Transactions on