On the Convergence and Accuracy of Numerical Mode Computations of Surface Plasmon Waveguides

Abstract

Two-dimensional surface plasmon-polariton waveguides must generally be analysed using numerical methods. However, accurate analysis is challenging due to large permittivity contrasts and to strong localisation of mode fields, especially near corners where they tend to diverge. These difficulties impact the convergence of numerical methods, yet understanding convergence is essential if accuracy is to be claimed. The convergence and accuracy of two vectorial numerical methods commonly used, the method of lines and the finite element method, were assessed by computing the propagation constant of modes supported by the metal slab, the metal stripe and the 90 metal corner. A discretisation strategy that yields smooth monotonic convergence is demonstrated for both methods. More accurate results are then extrapolated from the convergence histories and anticipated errors (relative to extrapolated results) are computed. Both methods yield similar anticipated errors for a comparable discretisation spacing, with the finite element method yielding slightly lower errors but the method of lines requiring less computational effort. Convergence was slower for highly confined modes, particularly those having fields localised near corners. Convergence to within an anticipated error of ±2% was readily achieved with both methods, except for the attenuation of modes that are highly confined to corners which remained in error by 10 to 20%. However, the percentage difference between the extrapolated results computed from both methods ranged from 3 75 to 0 012%. The convergence and accuracy of the methods of lines for curves was also investigated, and it was found that the absorbing boundary condition used along the radiating side of the curve introduces errors that can further limit the accuracy of the computations.

A Slot-Based Surface Plasmon-Polariton Waveguide With Long-Range Propagation and Superconfinement

“…1(a) comes from [25]. It has the symmetric insulator-metal-insulator (IMI) configuration featuring a thin metal film of relative permittivity 1 and thickness t being embedded in a dielectric background of relative permittivity 2 , which extends infinitely on both sides of the film.…”

“…In the past, several numerical methods have been developed to analyze the SPP propagation characteristics, including the method of lines (MoL), the finite element method (FEM), the finite difference method (FDM), the finite difference time domain (FDTD) method, etc. [25], [26]. However, these conventional methods still face great challenges since SPP waveguides possess peculiar configuration and field distributions, especially the intensive mode field concentration and variation in nanoscale regions near the metal.…”

Dynamics of coupled plasmon polariton wave packets excited at a subwavelength slit in optically thin metal films

“…So far, most of the theoretical analyses of coupled SPP modes in thin metal films have been carried out with an analytical approach solving for the momentum dependent eigenmodes for specific metal/dielectric structures 16,[23][24][25] More recently, numerical methods have also been developed, most of which, however, were also limited to solving for the eigenmodes. [26][27][28][29][30][31][32][33] Simulations of SPP-related systems with ultrashort pulse excitation have been few, 34,35 and to the authors' knowledge none has been applied to the coupled SPP modes in thin metal films. Considering the femtosecond scale lifetimes of SPPs, a detailed understanding of the dynamics of the coupled SPP excitation and propagation is essential for applications in, e.g., coherent control of ultrafast plamonics.…”

Simulation of complex plasmonic circuits including bends

“…Over the past ten years, tremendous developments have occurred in the field of surface plasmon polaritons (SPPs)-propagating electromagnetic waves at a dielectric-metal interface [1][2][3][4][5][6][7]. The strong confinement and local field enhancement associated with SPPs enables them to resolve spatial detail beyond the diffraction limit.…”