This article discusses electromagnetic properties of volumetric metamaterial samples with essentially discrete structure, that is, assembled as a periodic array of electromagnetic resonators. We develop an efficient numerical procedure for precise calculation of quasistatic electromagnetic response so that samples containing several million meta-atoms can be analyzed. We demonstrate that, contrary to common belief, even million-“atoms” samples with sharp edges are still quite different from uniform (“homogenized”) materials, and their properties are critically sensitive to their shape and boundary structure. We compare our results with calculations based on the discrete dipole approximation as well as with an integral model for continuous particles, and analyze distinctions and similarities between the different approaches. In particular, discrete metamaterials present themselves as a stringent platform for assessing continuous models developed for finite objects with sharp edges. Overall, the reported results should be important for understanding mesoscopic systems with strongly interacting elements.

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• Dielectric properties
• Mesoscopics
• Metamaterials
• Numerical techniques