Dispersion relation and self-collimation frequency of spoof surface plasmon using tight binding model

The analytical dispersion relation of spoof surface plasmon (SSP) is known only in the low-frequency limit and thus cannot be used to describe various practically important characteristics of SSP in the high-frequency limit (such as multimodal nature, anisotropic propagation, self-collimation). In this article, we consider a square lattice of holes made on a perfect electric conductor and derive a closed form expression of the SSP dispersion relation in the high-frequency limit using a tight binding model. Instead of using prior knowledge of the band diagram along the entire first Brillouin zone (BZ) edge, we analytically determine the hopping parameters by using the eigenfrequencies only at the three high-symmetry points of the square lattice. Using this dispersion relation, we derive an expression for the self-collimation frequency of SSP. We show that this analytical formulation is also applicable to dielectric photonic crystals and can be used to predict the frequencies corresponding to centimetre-scale supercollimation and second band self-collimation in these structures. Finally, we show that our analytical results are in agreement with the simulation results for both SSP and photonic crystals.