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Fourier modal method (FMM) proved itself as an effective technique for investigation of layered periodic structures. However, it fails to deal with arrays of small particles because of high gradients in a local field. In this paper, we demonstrate the capability of the method, which is based on the construction of scattering matrices of arrays of resonant nanoparticles semianalytically in discrete dipole approximation (DDA). This approach is much faster than conventional ones and therefore provides an opportunity for thorough consideration of various layered structures with small periodic inclusions in terms of the RCWA. The performance of the considered method is demonstrated on an example of plasmonic lattices embedded in a homogeneous ambience and placed inside and onto an optical waveguide. Localized surface plasmon resonances (LSPRs), lattice plasmon resonances (LPRs) and their hybridization with photonic guided modes are observed. High precision of this calculations is confirmed by comparison with finite element method (FEM).

Scattering-matrix analysis of nanoparticle lattices in dipole approximation