A homogenization model is applied to describe the wave interaction with finite three-dimensional metamaterial objects composed of periodic arrays of magnetodielectric spheres and is validated with full-wave numerical simulations. The homogenization is based on a dipolar model of the inclusions, which is shown to hold even in the case of densely packed arrays once weak forms of spatial dispersion and the full dynamic array coupling are taken into account. The numerical simulations are based on a fast surface-integral equation solver that enables the analysis of scattering from complex piecewise homogeneous objects. We validate the homogenization model by considering electrically large disk- and cube-shaped arrays and quantify the accuracy of the transition from an array of spheres to a homogeneous object as a function of the array size. Simulation results show that the fields scattered from large arrays with up to one thousand spheres and equivalent homogeneous objects agree well, not only far away from the arrays but also near them.
We introduce the Slepian transverse vector spher ical harmonics (TVSH). Unlike the classical TVSH, they are orthogonal over a given truncated spherical surface and the orthogonality constants can be computed. We apply the Slepian TVSH to the problem of reconstructing the far field from spatially truncated near-field samples and show that the far field can be reconstructed accurately over the entire angular sector where the near-field samples are available.
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