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

## TL;DR

This paper introduces a fast and accurate method combining discrete dipole approximation with RCWA to analyze optical properties of nanoparticle lattices, enabling detailed study of plasmonic resonances in layered structures.

## Contribution

It develops a novel approach integrating DDA with RCWA for efficient analysis of nanoparticle arrays, improving speed and accuracy over existing methods.

## Key findings

- Successfully models localized surface plasmon resonances.
- Accurately predicts lattice plasmon resonances and their hybridization.
- Demonstrates high accuracy and fast convergence compared to other computational methods.

## Abstract

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.