Mie plasmon-polariton modes in a 2D photonic crystal composed by superconducting cylindrical hollow rods

At present work we study the physical properties of localized surface plasmon-polariton modes (Mie plasmons) in a two-dimensional photonic crystal composed by high temperature superconducting cylindrical hollow rods. Numerical calculations were performed by means of the finite difference time-domain (FDTD) technique by considering Drude-lorentz dispersive hollow rods with an inner and outer radii R$_{1}=$0.2$a$ and R$_{2}=$0.3$a$ respectively, where $a$ corresponds to the lattice parameter. Additionally, we have calculated the field profiles for some specific modes at $\Gamma$ and X band edges within the first Brillouin zone. On the other hand, in the present work we show the conditions for Mie resonances in a single hollow rod and these results were compared with the corresponding slight dispersive modes in the case of a 2D photonic crystal.