Adaptive finite element simulations of waveguide configurations involving parallel 2D material sheets
This work provides a numerical tool for accurately simulating coupled surface plasmon polaritons in 2D material waveguides, which is important for designing nanophotonic devices.
The authors developed an adaptive finite-element method for computing energy transmission in waveguide structures with two parallel 2D material sheets, achieving reliable and efficient numerical solutions validated against analytic solutions.
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.