of frequency ω, electric field polarization E 0 , wavevector k = k k, wavenumber k = |k| = √ ε f µ f ω, and propagation direction k. As described in Methods, we use MPM to determine each particle's induced dipole moment p i (ω) and quadrupole moment Q i (ω), from which we construct the total electric field E(x, ω). We consider the quasistatic limit, where the wavelength of incident light is much larger than the nanoparticle radius, and p i and Q i can be inferred from Laplace's equation for electrostatics. Additionally, we consider only two truncation approximations in the moment expansion of a particle's total polarization response: We characterize the nanoparticle ensemble's far-field optical response through its extinction spectrum, quantified by the effective extinction cross-section per nanoparticle volume,