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Abstract
We have investigated the electromagnetic properties of arbitrarily-shaped three-dimensional concentrators based on the field-transformation theory for the first time. Up to now, many researchers are inclined to investigate the characteristics of the two dimensional optical-transformation devices instead of the three-dimensional (3D) ones due to the huge simulation burden for the commercial electromagnetic softwares. The field transformation theory has provided us a smart and powerful way to study such 3D problems. Analytical expressions for the fields and power flows inside the concentrators have been presented accurately, which have never been considered before. As examples, the spherical and cubic concentrators are discussed in more details. The study shows that the magnification of fields and power-flow densities inside the central parts of concentrators is only dependent upon the spatial compression ratio in the transformation equations, which gives a theoretical proof to the numerical simulations.