Mathematical Modeling of Interaction of THz Waves with Multilayer 2D Arrays of Graphene Nanoribbon Elements

The numerical techniques to solve the 3D diffraction boundary problems for multilayer 2D arrays of graphene nanoribbon elements are developed. The rigorous mathematical models are based on the solution of the Maxwell`s equations with electrodynamic boundary conditions simultaneously with a model of the graphene surface conductivity determined from the Kubo formula. The mathematical modeling involves three specific methods. The reflection, transmittance coefficients and losses of periodic 2D arrays of graphene ribbon elements based on multilayered substrates, depending on the frequency and angle of incidence for different geometry and values of the chemical potential were calculated in the THz frequency range. The results show that the performances of graphene nanoribbon arrays THz absorbers, tuned by the external bias electric field, can also be controlled by modifying the 2D array geometry and areal density, through changing the periodicity, the size and the configuration of the graphene ribbon elements.