Towards Digital Twins of Plasmonic Sensors: Constructing the Complex Numerical Model of a Plasmonic Sensor Based on Hexagonally Arranged Gold Nanoparticles

In this work, we aim to design the digital twin of a plasmonic sensor based on hexagonally arranged ellipsoidal gold nanoparticles fixed to a glass substrate. Based on electron microscopy images of three experimentally realized nanoparticle arrangement types, we constructed numerical models in environments based on finite element method (FEM) and boundary element method (BEM), namely COMSOL Multiphysics for FEM and the MNPBEM Matlab Toolbox for BEM. Models with nonperiodic and periodic boundary conditions with different unit cells were constructed to study the plasmonic behavior of both the single ellipsoidal particles and the hexagonal nanoparticle arrangements. The effect of the geometrical parameters, namely the interparticle distance, the nanoparticle diameter and thickness, on the resulting LSPR peak positions and bulk refractive index sensitivities were studied in detail, also taking into account the effect of the SiO(2) substrate (pillars) under the ellipsoidal particles. We have demonstrated that by optimizing the models, the LSPR peak positions (and sensitivities) can match the experimentally measured values within 1 nm (nm/RIU) precision. The comparison of simulation conditions and the detailed discussion of the effect of the geometrical parameters and used gold dielectric functions on the obtained sensitivities can be very beneficial for the optimization of plasmonic sensor constructions through numerical simulations.