Analysis of 2D hyperbolic metamaterial dispersion by elementary excitation coupling

Abstract

Hyperbolic metamaterials are examined for many applications thanks to the large density of states and extreme confinement of light they provide. For classical hyperbolic metal/dielectric multilayer structures, it was demon- strated that the properties originate from a specific coupling of the surface plasmon polaritons between the metal/dielectric interfaces. We show a similar analysis for 2D hyperbolic arrays of square (or rectangular) silver nanorods in a TiO2 host. In this case the properties derive from a specific coupling of the plasmons carried by the corners of the nanorods. The dispersion can be seen as the coupling of single rods for a through-metal connection of the corners, as the coupling of structures made of four semi-infinite metallic blocks separated by dielectric for a through-dielectric connection, or as the coupling of two semi-infinite rods for a through-metal and through-dielectric situation. For arrays of small square nanorods the elementary structure that explains the dispersion of the array is the single rod, and for arrays of large square nanorods it is four metallic corners. The medium size square nanorod case is more complicated, because the elementary structure can be one of the three basic designs, depending on the frequency and symmetry of the modes. Finally, we show that for arrays of rectangular nanorods the dispersion is explained by coupling of the two coupled rod structure. This work opens the way for a better understanding of a wide class of metamaterials via their elementary excitations.