  The polarization density of a broadband electrodynamic lattice-Boltzmann
method (ELBM) is generalized to represent frequency-dispersion of materials
interacting with electromagnetic waves. The frequency-dependent refractive
index and extinction coefficient are modeled using complex-conjugate
pole-residue pairs in an auxiliary-differential-equation (ADE). Electric and
magnetic fields are evaluated on a single lattice, ensuring a stable numerical
solution up to the Nyquist limit. The electric and magnetic fields from the
ELBM are compared with the electric and magnetic fields from the
finite-difference-time-domain (FDTD) method. Accurate transmittance of a 100 nm
silver slab is extracted from the transmitted power spectrum of a broadband
Dirac-delta wave-function for photon energies ranging from 0.125-5 eV. Given
this capability, the ELBM with an ADE is an accurate and computationally
efficient method for modeling broadband frequency-dispersion of materials.
