Lattice Boltzmann Method for Electromagnetic Wave Propagation

TL;DR

This paper introduces a novel Lattice Boltzmann method for solving Maxwell's equations, enabling efficient simulation of electromagnetic wave propagation in complex, heterogeneous media with high contrast in refractive index.

Contribution

A new LB formulation using pseudo-vector distributions that accurately reproduces Maxwell's equations and extends efficiently to 3D for complex media simulations.

Findings

Comparable accuracy to pseudo-spectral methods in 2D simulations

Effective extension to three dimensions

Suitable for parallel computation in complex geometries

Abstract

We present a new Lattice Boltzmann (LB) formulation to solve the Maxwell equations for electromagnetic (EM) waves propagating in a heterogeneous medium. By using a pseudo-vector discrete Boltzmann distribution, the scheme is shown to reproduce the continuum Maxwell equations. The technique compares well with a pseudo-spectral method at solving for two-dimensional wave propagation in a heterogeneous medium, which by design contains substantial contrasts in the refractive index. The extension to three dimensions follows naturally and, owing to the recognized efficiency of LB schemes for parallel computation in irregular geometries, it gives a powerful method to numerically simulate a wide range of problems involving EM wave propagation in complex media.