Adaptive finite element simulations of waveguide configurations involving parallel 2D material sheets

TL;DR

This paper develops an adaptive finite element method to accurately simulate electromagnetic wave propagation and energy transmission in waveguides with two parallel 2D material sheets, validated by analytical solutions.

Contribution

It introduces a goal-oriented adaptive finite element approach with error estimation for modeling coupled surface plasmon polaritons in layered 2D materials.

Findings

Validated numerical method against analytical solutions.

Effective local grid refinement improves accuracy.

Accurate determination of optimal spacing for waveguide design.

Abstract

We discuss analytically and numerically the propagation and energy transmission of electromagnetic waves caused by the coupling of surface plasmon polaritons (SPPs) between two spatially separated layers of 2D materials, such as graphene, at subwavelength distances. We construct an adaptive finite-element method to compute the ratio of energy transmitted within these waveguide structures reliably and efficiently. At its heart, the method is built upon a goal-oriented a posteriori error estimation with the dual-weighted residual method (DWR). Further, we derive analytic solutions of the two-layer system, compare those to (known) single-layer configurations, and compare and validate our numerical findings by comparing numerical and analytical values for optimal spacing of the two-layer configuration. Additional aspects of our numerical treatment, such as local grid refinement, and the utilization of perfectly matched layers (PMLs) are examined in detail.