Tuning the electromagnetic density spectral function in a graphene–dielectric micro-cavity

Abstract

This work focuses on the study of the electromagnetic density spectral function (DSF) near a graphene–dielectric cavity. The cavity is formed in the space confined by the base of a dielectric micro-cube and a planar graphene sheet covering a dielectric substrate. The size and refractive index of the micro-cube, the constitutive parameters of graphene, and the gap between the dielectric cube and the graphene sheet determine the modifications to the DSF. We have developed a method based on the coupled dipole approximation (CDA), incorporating the surface Green’s tensor to account for the scattering processes with the graphene substrate, thereby rigorously modeling the electromagnetic problem. Our results reveal three well-distinguishable peaks in the DSF spectrum, which are attributed to the isolated micro-cube, the graphene substrate, and their mutual interaction. Specific parameters allow for the selective tuning of an individual peak’s properties, with minimal crosstalk to other spectral features. Using simple physical arguments related to the kinetic characteristics of surface plasmons (SPs) on graphene, we explain the key dependencies on constitutive and geometrical parameters.