Fourier modal method for the description of nanoparticle lattices in the dipole approximation

Rigorous coupled-wave analysis (RCWA) is a very effective tool for 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 paper, we implement the 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 demonstrate the performance of the proposed method by considering plasmonic lattices embedded in a homogeneous ambience and placed inside and onto an optical waveguide. Both 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 comparison with the finite element method (FEM) and RCWA calculations correspondingly.