Orientation-averaged light scattering by nanoparticle clusters: far-field and near-field benchmarks of numerical cubature methods

The optical properties of nanoparticles can be substantially affected by their assembly in compact aggregates. This is a common situation notably for nanoparticles synthesised and self-assembled into rigid clusters in colloidal form, where they may be further characterised or used in spectroscopic applications. The theoretical description of such experiments generally requires averaging the optical response over all possible cluster orientations, as they randomly orient themselves over the course of a measurement. This averaging is often done numerically by simulating the optical response for several directions of incidence, using a spherical cubature method. The simulation time increases with the number of directions and can become prohibitive, yet few studies have examined the trade-off between averaging accuracy and computational cost. We benchmark seven commonly-used spherical cubature methods for both far-field and near-field optical responses for a few paradigmatic cluster geometries: dimers of nanospheres and of nanorods, and a helix. The relative error is rigorously evaluated in comparison to analytical results obtained with the superposition T-matrix method. Accurate orientation averaging is especially important for quantities relating to optical activity, the differential response to left and right circularly polarised light, and our example calculations include in particular far-field circular dichroism and near-field local degree of optical chirality.