A vector finite element method with the high-order mixed-interpolation-type triangular elements for optical waveguiding problems

Abstract

A bstract-A vector finite element method with the high-order mixed.lnterpolation·type triangular elements is described tor the analysis ot optical waveguiding problems. It is a combination at linear edge elements tor transverse components of the electrk or magnetic field and quadl"8.lic nodal elements ror the axial one. The use ot mixed-interpolation.type elements provides a diret:t salulion ror propagation constants and avoids spurious solutions. This approach can yield more accurate results compared with the conventional approach using the lowest order mlxedInterpolation-type elements., namely, constant edge elements and linear nodal elements. The accuracy ot this approach is investi· gated by calculating the propagation characteristics or optical rib waveguides. Results obtained tor both E~ and SW polarizations are validated using benchmark results produced by established methods,IFFERENT types of the vector fin ite element method (VFEM) have been developed for the analysis of optical waveguiding problems. Of the various formu lations. the VFEM using fu ll vector electric or magnetic field is quite suitable for a wide range of practical complicated problems (1]-f I 3,!. This approach has been widely used for various optical waveguiding structures and recently has been utilized as the optical waveguide solver of CAD paCkages [14]. The most serious problem associated with this approach is the appearance of spurious solutions. The penalty function method [11-( I 4] has been used to cure this problem, but in this technique an arbitrary positive constant, called the penalty coefficient. is involved and the accuracy of solutions depends on its magnitude. Furthermore. in the ful! vectorial fonnulat ion the propagation constant is fi rst given as an input datum, and subsequently the operating wavelength is obtained as a solution. There is another serious problem in the full vectorial approach. As was made clear by Birman [15] and Binnan and Solomyak [16], such an approach is quite difficult for dealing with comer singulari ties and interface singularities so long as the conventional Lagrange interpolation polyno- , but the accuracy of the fi nite element analysis using the lowest order eleme nts is. in general. insufficient.In this paper, in order to provide more accurate numerical solutions and faster convergence in applications. a vector finite element method with the high-order mixed-interpolation-type triangular elements is form ulated in detai l. It is a combination of linear edge elements for transverse components of the electric or magnetic fie ld and quadratic nodal (conventional Lagrange) elements for the axial one. This approach can yield more accurate results compared with the conventional approach using the lowest order elements. The accuracy of this approach is investigated by calculati ng the propagation characteristics of optical rib waveguides. Resul ts obtained for both £'" and E" polarizations are validated using benchmark results produced by established methods.

Curvilinear hybrid edge/nodal elements with triangular shape for guided-wave problems

“…Especially, the hybrid edge/nodal elements with triangular shape are very useful for imposing the continuity of the tangential components of the electric and magnetic fields and for eliminating the nonphysical, spurious solutions. The hybrid elements developed so far [1]- [3] are, however, only for the waveguides with straight, rectilinear boundaries.…”

Measurement of the group dispersion of the fundamental mode of holey fiber by white-light spectral interferometry

“…2(a). A full-vector mode solver based on hybrid edge/nodal finite-element method (FEM) [16] was used to calculate the propagation constants of guided modes. In this approach, the following eigenequation is solved…”

Second zero dispersion wavelength measurement through soliton self-frequency shift compensation in suspended core fibre

“…Now, we put into practice our simple technique to determine the second ZDW of a 20-mlong suspended core fibre manufactured at Maria Curie-Sklodowska University, exhibiting a small silica core diameter estimated to 0.96 m (Fig.3a). We used a fully vectorial mode solver based on Finite Element Method in order to calculate dispersion characteristics of the fundamental mode (Fig.3c) [7]. SEM image of the fibre cross-section was numerically treated to accurately reproduce the image of the real fibre cross-section and calculations were based on a mesh composed of about 100 000 elements.…”