Study of Plasmonic Resonances on Platonic Solids

In this study we discuss the plasmonic subwavelength scattering resonances of five regular polyhedra, that is, the Platonic solids tetrahedron, hexahedron, octahedron, dodecahedron, and icosahedron. A brief discussion regarding their geometrical characteristics and the numerical method used in the study is given. All results are compared with the benchmark case of a sphere, in order to observe how the geometry of the solid affects the spectral characteristics. The principal finding is that the shift of the main dipole resonance exhibits a solid vertex hierarchical order; in other words, the position of the resonance correlates with the solid angle of the vertex of the given solid. This is in contrast with the hedra-hierarchical order found for the electrostatic dielectric response of these solids. These results can create new avenues for applications and devices that require plasmonic particles with on-demand functionalities.