  Rigorous coupled-wave analysis (RCWA) is a very effective tool for the
studying optical properties of multilayered vertically invariant periodic
structures. However, it fails to deal with arrays of small particles because of
high gradients in a local field. In this thesis, we implement discrete dipole
approximation (DDA) for the construction of scattering matrices of arrays of
resonant nanoparticles. This strongly speeds up the calculations and therefore
provides an opportunity for thorough consideration of various layered
structures with small periodic inclusions in terms of the RCWA. We study in
detail three main stages of the method: calculation of polarizability tensor of
a single nanoparticle, effective polarizability of this particle in a lattice
and corresponding scattering matrix of the layer for further integration in the
conventional RCWA approach. We demonstrate the performance of the proposed
method by considering plasmonic lattices embedded in a homogeneous ambiance and
placed inside and onto optical waveguides and compare our results with
experimental papers. Such phenomena as localized surface plasmon resonances
(LSPRs) and lattice plasmon resonances (LPRs) are observed as well as their
hybridization with photonic guided modes. High accuracy and fast convergence of
our approach are shown by a comparison with other computational approaches.
Typical limits of applicability of our approximate method are determined by an
exploration of the dependence of its error on the parameters of the structure.
