Techniques for determining the relative weights of spatial harmonics induced in truncated periodic structures such as metamaterials

In this paper we determine the weights of the spatial harmonics in a periodic structure, with quasi-periodicity along the propagation direction, by detailed analysis of the fields inside the unit-cells. We use both the Pronypsilas method and Fourier transform to extract the spectrum of the fields inside the unit cells along the propagation direction and compare the results obtained by each method. Two examples, one-dimensional dielectric layers and split-ring resonators with wires, are considered. The results show that the Fourier transform approach is more accurate and consistent in comparison to Pronypsilas method.