Finite element analysis of 2-D dielectric waveguides with Helmholtz vector equations and virtual exterior elements

This paper reports a finite-element-method formulation, which is based on the Helmholtz vector equations in terms of transverse electrical field components to characterize two-dimensional dielectric waveguides with an arbitrary continuous permittivity profile. A virtual exterior element iteration technique is associated with the finite-element analysis to process the remote boundary condition. This technique achieves both excellent computational efficiency and accuracy when studying the dielectric propagation constants and cutoff frequencies. The spurious-infection-free modal electrical field can be obtained directly. Numerical results of circular optical fibers with the parabolic permitivity profile are presented to show the validity of this technique.