Helmholtz–Galerkin Regularizing Technique for the Analysis of the THz-Range Surface-Plasmon-Mode Resonances of a Graphene Microdisk Stack

The aim of this paper is the accurate and efficient analysis of the surface-plasmon-mode resonances of a graphene microdisk stack in the terahertz range. By means of suitable generalized boundary conditions and Fourier series expansion, the problem is formulated in terms of sets of one-dimensional integral equations in the vector Hankel transform domain for the harmonics of the surface current densities. In virtue of the Helmholtz decomposition, the unknowns are replaced by the corresponding surface curl-free and divergence-free contributions. An approximate solution is achieved by means of the Galerkin method. The proper selection of expansion functions reconstructing the physical behavior of the surface current densities leads to a fast-converging Fredholm second-kind matrix equation, whose elements are accurately and efficiently evaluated by means of a suitable analytical procedure in the complex plane. It is shown that the surface-plasmon mode resonance frequencies upshift by increasing the number of disks and by decreasing the distance between the disks, and that new resonances can arise for small with respect to the radius distances between the disks, resembling the dipole-mode resonances of the dielectric disk, while, for larger distances, the surface-plasmon-mode resonances can split.