FDTD for Hydrodynamic Electron Fluid Maxwell Equations

Yingxue Zhao,Jinjie Liu

doi:10.3390/photonics2020459

Abstract

In this work, we develop a numerical method for solving the three dimensional hydrodynamic electron fluid Maxwell equations that describe the electron gas dynamics driven by an external electromagnetic wave excitation. Our numerical approach is based on the Finite-Difference Time-Domain (FDTD) method for solving the Maxwell’s equations and an explicit central finite difference method for solving the hydrodynamic electron fluid equations containing both electron density and current equations. Numerical results show good agreement with the experiment of studying the second-harmonic generation (SHG) from metallic split-ring resonator (SRR).

Highlights

Maxwell’s equations are a set of partial differential equations governing the electromagnetic (EM)waves [1]
Experiments have shown that strong nonlinear response such as the second-harmonic wave can be generated from Split-Ring Resonator (SRR) [3,4,5,6]
Since the current density J is defined at the same location as E in space and at the same location as H in time, our numerical method requires all components of J to be interpolated at cell corners

Summary

Introduction

Maxwell’s equations are a set of partial differential equations governing the electromagnetic (EM). Among many methods for solving Maxwell’s equations, the Finite-Difference Time-Domain (FDTD). In [8], a nonlinear Drude model is developed and solved by a time-splitting finite difference method. In [11], the discontinuous Galerkin time domain method and the hydrodynamic Maxwell-plasma model are applied to simulate the linear and nonlinear optical response from SRR arrays. We numerically study the solution of the hydrodynamic electron fluid Maxwell equations by solving the electron density and momentum equations using an explicit finite difference hyperbolic. We apply our model to simulate the nonlinear optical responses such as second-harmonic generation (SHG) from metallic nanoparticles and the numerical results yield good agreement with the experimental results published in [3,4,5]

Numerical Model of Hydrodynamic Electron Fluid Maxwell Equations

Numerical Simulation of SHG from SRR

Conclusions