# Numerical simulation of a coupled system of Maxwell equations and a gas dynamic model

## TL;DR

This paper presents a numerical simulation method for plasmon dynamics in metallic nanostructures, combining Maxwell equations with a gas dynamic model including quantum effects, revealing insights into harmonic generation and resonance phenomena.

## Contribution

It introduces a coupled Maxwell-gas dynamic simulation framework with quantum pressure effects for plasmon behavior in nanostructures, advancing computational modeling capabilities.

## Key findings

- Quantum pressure term causes bulk plasmon resonance.
- Bound electrons influence high order harmonic generation.
- The numerical method accurately simulates nonlocal effects.

## Abstract

It is known that both linear and nonlinear optical phenomena can be produced when the plasmon in metallic nanostructures are excited by the external electromagnetic waves. In this work, a coupled system of Maxwell equations and a gas dynamic model including a quantum pressure term is employed to simulate the plasmon dynamics of free electron fluid in different metallic nanostructures using a discontinuous Galerkin method in two dimensions. Numerical benchmarks demonstrate that the proposed numerical method can simulate both the high order harmonic generation and the nonlocal effect from metallic nanostructures. Based on the switch-on-and-off investigation, we can conclude that the quantum pressure term in gas dynamics is responsible for the bulk plasmon resonance. In addition, for the dielectric-filled nano-cavity, a coupled effective polarization model is further adopted to investigate the optical behavior of bound electrons. Concerning the numerical setting in this work, a strengthened influence of bound electrons on the generation of high order harmonic waves has been observed.