A Reliable Lattice-Boltzmann Solver for Electrodynamics: New Applications in Non-linear Media

Hereby we summarize a recently developed 3D lattice-Boltzmann method for the simulation of Maxwell equations in materials, and we illustrate its performance by computing the time evolution of electromagnetic flelds inside a non-linear dielectric medium. The model allows for both dielectrics and conductors with realistic parameters and has computed the most diverse electromagnetic problems (including micro-strips and antennas), all with 2% accuracy. Preliminary tests showed that it is one order of magnitude faster than the original flnite-difierence time-domain scheme formulated by Yee to reach the same accuracy. To illustrate the power of the new solver, we simulate the time evolution of a cylindrical electromagnetic wave through a non-linear and non-dispersive medium and the resonant modes of a cylindrical cavity fllled with that medium. Our results are in excellent agreement with the analytic solutions by E. Y. Petrov and A. V. Kudrin for the same cases. The model constitutes, therefore, a valuable alternative to compute electromagnetic flelds, even in non-linear media.