Effect of Geometric Parameters of Metallic Nanoprisms on the Plasmonic Resonance Wavelength

We study the effect of geometric dimensions on the optical properties of equilateral triangular gold and silver nanoprisms with rounded corners. An analytical expression for calculating the spectral characteristics of the main longitudinal plasmonic resonance of such nanoprisms is obtained. As variables, the expression includes the nanoprism dimensions, its composition, and the permittivity of the surrounding environment. Our results demonstrate that the extinction cross sections can be adequately described by this expression for nanoprisms with edge lengths up to a few hundred nanometers. We show that the scattering of free electrons from the metal/environment interface in metallic nanoprisms can be described with the help of the size-dependent dielectric function. Using a simple relation, we evaluate the necessary effective size parameter, which allows one to achieve a good agreement with experimental data. The results obtained are of interest for solving a number of fundamental problems in nanophotonics and nanoplasmonics, as well as for applications in the development of next-generation optoelectronic devices.