We propose a comparison of two approaches to model the periodic arrays of left-handed metamaterials (LHM) by field simulation in a single LHM-unit cell. First, an efficient scattering matrix analysis in time domain is able to produce broadband results in a single run. The set of transfer functions between a small number of input and output ports of the unit cell fully 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 discuss some consequences for a reliable extraction of effective material parameters of the LHM.
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