Bent optical waveguide finite element analysis with a 3D envelope Maxwell model

TL;DR

This paper introduces a novel numerical method using an envelope Maxwell model with DPG discretization to accurately analyze optical field losses in 3D bent waveguides, including complex geometries like coiled fibers.

Contribution

It develops a boundary value problem approach with adaptive meshing and PMLs for precise 3D bent waveguide loss analysis, achieving stable convergence previously unreported.

Findings

Successfully verified against semi-analytical bent slab waveguide results.

Demonstrated stable convergence to loss values for 3D coiled optical fibers.

Enabled extraction of mode confinement losses in complex geometries.

Abstract

With the goal of accurately extracting the optical field losses in a three-dimensional (3D), circularly coiled waveguide (e.g., bent optical fiber), this effort presents the numerical methodologies that are implemented for an envelope Maxwell model that propagates electromagnetic fields as an entirely boundary value problem. Our unique modeling approach includes an ultraweak variational formulation of the envelope Maxwell model in the curved geometry of the bending, which is discretized by the discontinuous Petrov-Galerkin (DPG) method, which permits residual-driven mesh and polynomial-order adaptivity. This also, then, requires a unique approach for constructing perfectly matched layers (PMLs) as absorbing boundary conditions in both the direction of optical field propagation and in the tangential directions, where unguided energy escapes the waveguide. Our coiled waveguide modeling technology extracts the mode confinement losses from the propagation of the coherent optical field through the bent waveguide. We verify our simulations against the semi-analytical results from the analogous bent slab waveguide problem, and we successfully demonstrate stable convergence to loss values for the 3D coiled optical fiber problem, which has never been done previously for our specific modeling approach.