Variational Schemes and Geometric Simulations for a Hydrodynamic-Electrodynamic Model of Surface Plasmon Polaritons

TL;DR

This paper develops variational numerical schemes based on discrete exterior calculus for simulating surface plasmon polaritons in a lossless free-electron gas, preserving key physical properties over long-term simulations.

Contribution

It introduces a novel variational discretization approach that maintains symplectic structure and gauge symmetry, improving simulation accuracy for surface plasmon polaritons.

Findings

Successfully reproduces dispersion relations of plasmons and polaritons.

Maintains bounded numerical errors in conserved quantities during long-term simulations.

Demonstrates improved numerical stability and physical fidelity over traditional methods.

Abstract

A class of variational schemes for the hydrodynamic-electrodynamic model of lossless free-electron gas in a quasineutral background is developed for high-quality simulations of surface plasmon polaritons. The Lagrangian density of lossless free-electron gas with a self-consistent electromagnetic field is established, and the dynamical equations with the associated constraints are obtained via a variational principle. Based on discrete exterior calculus, the action functional of this system is discretized and minimized to obtain the discrete dynamics. Newton-Raphson iteration and the biconjugate gradient stabilized method are equipped as a hybrid nonlinear-linear algebraic solver. Instead of discretizing the partial differential equations, the variational schemes have better numerical properties in secular simulations, as they preserve the discrete Lagrangian symplectic structure, gauge symmetry, and general energy-momentum density. Two numerical experiments were performed. The numerical results reproduce characteristic dispersion relations of bulk plasmons and surface plasmon polaritons, and the numerical errors of conserved quantities in all experiments are bounded by a small value after long-term simulations.