Analysis of single-cell modeling of periodic metamaterial structures

We propose a comparison of two approaches to analyze the periodic arrays of left-handed metamaterials by field simulations in a single unit cell. First, a scattering matrix analysis in time domain is able to produce broadband results. The set of transfer functions between a small number of input and output ports of the unit cell is able to describe its macroscopic behavior, where, however, the appearance of higher order modes is systematically neglected. As a reference result with respect to this issue, an eigenvalue analysis with periodic boundary conditions provides one point of the dispersion relation of the array per simulation run. We show how these results can be transformed into each other, and present a quantitative analysis of the impact of higher order modes on the effective array properties.