Finite and Boundary Element Methods for Simulating Optical Properties of Plasmonic Nanostructures

In this study, a numerical investigation was done on the optical properties of silver nanostructures using the boundary element method (BEM) and finite element method (FEM). The BEM simulation was done using a freely available code called MNBEM in MATLAB with minor modifications. The FEM simulation was done by Comsol Multiphysics, a commercial software package. Silver nanostructures in the sphere, rod, and triangle geometries and the presence of different polarization angles were compared between these two methods. According to the obtained results, the absorption cross-sections for both BEM and FEM were consistent with their actual optical properties. For instance, both longitudinal and transverse resonance modes were observed in the case of nanorods, and all three in–plane dipole, in–plane quadrupole, and out–plane quadrupole plasmon resonances were observed successfully obtained for triangular nanostructures. Although both BEM and FEM results were similar to each other (from the number and position of the peaks in the final spectra), this similarity was decreased as the anisotropy was increased in the structure. For example, nearly 40 nm difference was observed between the BEM and FEM results in the triangular nanostructures, even though the trends and shape of the peaks were similar. It was revealed that specific points should be considered in the discretization process (especially the corner fillets) to close the gap in the obtained results from BEM and FEM. According to the obtained results, BEM significantly reduces the computational cost and time by discretizing only the boundary of the domain. A self-written software was developed to predict the optical cross-section of a plasmonic-ensemble consisting of spherical, rod-shaped, and triangular nanostructures, which can be used in different disciplines such as plasmon-enhanced solar cells, plasmon-enhanced photocatalysis, and plasmon-enhanced fluorescence.Graphical Abstract