And Yet Another FEM-Based Mode Solver for Dielectric Waveguides

TL;DR

This paper introduces an open-source FEM-based mode solver for dielectric waveguides that combines edge and nodal elements for accurate, efficient, and accessible modeling of hybrid modes, validated against commercial software.

Contribution

The authors develop a full-vector FEM mode solver using mixed Nedelec-Lagrange discretization, implemented in MATLAB and Python, emphasizing reproducibility and compatibility with cloud platforms.

Findings

Solver achieves less than 0.05% error compared to COMSOL.

Convergence studies confirm expected accuracy with mesh refinement.

Implementation is open-source and suitable for photonics research and education.

Abstract

We present a full-vector finite element method (FEM) mode solver for dielectric waveguides based on a mixed Nedelec-Lagrange discretization of Maxwell's curl equations in the frequency domain. The formulation combines edge elements for transverse field components with nodal elements for the longitudinal component, enabling accurate modeling of hybrid modes while effectively suppressing spurious solutions. The solver is implemented in both MATLAB and Python with an emphasis on reproducibility, computational efficiency, and accessibility, including compatibility with cloud-based platforms. Numerical validation is performed on representative waveguide structures, demonstrating excellent agreement with COMSOL Multiphysics, with relative errors below 0.05%. Convergence studies confirm the expected accuracy trends with mesh refinement, while highlighting the trade-off between computational cost and precision. The proposed implementation provides a flexible and reliable open-source tool for integrated photonics research and education.