Variational Simulations for Hydrodynamics Model of the Surface Plasmon Polaritons

A variational integrator for the hydrodynamics model of free electron gas in quasi-neutrality background is developed for high-quality simulations of the surface plasmon polaritons. The Lagrangian density of electron gas with self-consistent electromagnetic field is established and the action of this system is discretized and minimized to obtain the discrete dynamics law. Instead of discretizing the differential equations, the variational integrator has better numerical properties in secular simulations, as it conserves the discrete Lagrangian structure and the general energy-momentum density. The numerical results reproduce characteristic dispersion relations of surface plasmon polaritons.