Coupling mechanisms in nano-U dimers

Properties of split-ring metamaterials are governed by inter-element interactions. These interactions lead to slow eigenmodes of coupling, which, due to their short wavelengths, are ideal candidates for the design of near-field manipulating devices. In this paper we explore the electric and magnetic coupling mechanisms in nano-U and nano-SRR dimers comprising of two identical nano-resonators arranged axially and twisted relative to each other by an arbitrary angle. We study theoretically the couplings in a periodic chain of nano-dimers for the frequencies from 100 to 300 THz. In our analytical model, the electric and magnetic couplings can be expressed through the self and mutual terms for the magnetic and electric field energy. In addition, we incorporate the effect of kinetic inductance due to the inertia of the electrons (noticeable as element dimensions approach 100nm or smaller). The resulting dependence of the electric, magnetic and the total coupling constants on the twist angle within the dimer obtained analytically is shown to agree with numerical simulations (CST Microwave Studio). Our approach should enable an effective design of metamaterial structures with desired properties and would be a useful tool in developing THz range manipulating devices based on propagation of slow waves by virtue of coupling.