Сalculationplasmon resonances in the structure of a graphene rectangular resonator located above a homogeneous graphene sheet

A rigorous electromagnetic approach has been developed for the theoretical analysis of plasmon resonance excitation frequencies in a two-dimensionally confined structure consisting of a graphene square separated from a homogeneous graphene plane by a dielectric layer. The method is based on the formation of a system of integral equations for the components of the oscillating current in the graphene square. The integral equations are solved using the Galerkin method, which transforms the integral equations into a system of linear algebraic equations. Terahertz spectra of the plasmon resonance absorption cross sections in this structure are constructed. The excitation frequencies of "acoustic" and "optical" two-dimensional plasmons in this structure are found. Cases of a dielectric layer thin and thick compared to the plasmon wavelength are studied. Resonances corresponding to the excitation of mixed-parity plasmonsare detected.