  The utilization of periodic structures such as photonic crystals and
metasurfaces is common for light manipulation at nanoscales. One of the most
widely used computational approaches to consider them and design effective
optical devices is the Fourier modal method (FMM) based on Fourier
decomposition of electromagnetic fields. Nevertheless, calculating of periodic
structures with small inclusions is often a difficult task, since they induce
lots of high-$k_\parallel$ harmonics that should be taken into account. In this
paper, we consider small particle lattices with bases and construct their
scattering matrices via discrete dipole approximation (DDA). Afterwards, these
matrices are implemented in FMM for consideration of complicated layered
structures. We show the performance of the proposed hybrid approach by its
application to a lattice, which routes left and right circularly polarized
incident light to guided modes propagating in opposite directions. We also
demonstrate its precision by spectra comparison with finite element method
(FEM) calculations. The high speed and precision of this approach enable the
calculation of angle-dependent spectra with very high resolution in a
reasonable time, which allows resolving narrow lines unobservable by other
methods.
