Light propagation and effective parameters of nanowire based metamaterials: An analytical approach

An alternative way to determine the dispersion relation and the effective material parameters is presented. The introduced model can be applied to treat the double wire as well as the split ring resonator geometry, while the first one is presented in this paper. The approach combines the electric and magnetic multipole expansion of a single structure to describe the propagation properties of the respective effective medium. The electron dynamics in the composite structure is described by a coupled harmonic oscillator. Thus all higher order multipoles can be calculated explicitly and the macroscopic Maxwell equations can be solved self consistent for electromagnetic plane waves. A final comparison to numerically obtained parameters validates the applicability of the model.