  We introduce a numerical method that enables efficient modelling of light
scattering by large, disordered ensembles of non-spherical particles
incorporated in stratified media, including when the particles are in close
vicinity to each other, to planar interfaces and/or to localized light sources.
The method consists in finding a small set of fictitious polarizable elements
-- or numerical dipoles -- that quantitatively reproduces the field scattered
by an individual particle for any excitation and at an arbitrary distance from
the particle surface. The set of numerical dipoles is described by a global
polarizability matrix that is determined numerically by solving an inverse
problem relying on fullwave simulations. The latter are classical and may be
performed with any Maxwell's equations solver. Spatial non-locality is an
important feature of the numerical dipoles set, providing additional degrees of
freedom compared to classical coupled dipoles to reconstruct complex scattered
fields. Once the polarizability matrix describing scattering by an individual
particle is determined, the multiple scattering problem by ensembles of such
particles in stratified media can be solved using a Green tensor formalism and
only few numerical dipoles, thereby with a low physical memory usage, even for
dense systems in close vicinity to interfaces. The performance of the method is
studied with the example of large high-aspect-ratio high-index dielectric
cylinders. The method is easy to implement and may offer new possibilities for
the study of complex nanostructured surfaces, which are becoming widespread in
emerging photonic technologies.
