Dielectric function and the absorption cross-section of the metal-graphene nanocylinders of the finite length

The behavior of the diagonal components of the dielectric tensor and the behavior of the absorption cross-section in the different frequency ranges for the composite cylindrical nanostructures “metallic core – graphene shell” have been studied. In order to obtain the calculation formulas one uses the relations for the longitudinal and transverse components of the dielectric tensors for metallic core and graphene shell, which are determined by Drude model and Cubo model correspondingly. The consideration is carried out in the frameworks of “equivalent” elongated spheroid approach, according to which the defining dimensional parameter is effective aspect ratio, calculated from the condition of the equality of the corresponding axial inertia moments for two-layer cylinder and the “equivalent” elongated spheroid. The numerical results have been obtained for the nanocylinders with the cores of different metals, different radius and with the different number of graphene layers. The variation of amplitude and the variation of the location of extremes of the real and imaginary parts of the transverse component of the dielectric tensor under the increase in radius of the metallic core and the thickness of the graphene shell have been analyzed. It has been shown that the variation of the radius of the core has the significantly greater influence on the properties of the polarizability resonances and absorption cross-section than the variation of the number of graphene layers. The reasons of the presence of two maxima of the absorption cross-section for the metal-graphene cylinders which differ in both amplitude and width and located in infrared, violet and near ultraviolet parts of the spectrum and their relation with the surface plasmonic resonances in the metallic core and with the terahertz plasmons of graphene have been found. The factors which have an effect on amplitude and on the shift of the maxima of the absorption cross-section have been found. The reasons of the different width of maxima, which are located in the different spectral intervals, have been determined.