Various Optimization Problems of Electromagnetic Power Absorption in Homogeneous and Heterogeneous Phantoms

Over the last decade, problems related to electromagnetic power absorption by human bodies or phantoms have been motivating a large scientific and technical effort. In many situations, the ultimate goal is to characterize and get as close as possible to the minimum or maximum value of a fraction of the total dissipated power (TDP) in a given volume. As is well known in mathematics, to find an optimum of a function can be a very tough question, whose complexity strongly depends on the constraints imposed, and the number of variables. Considering this point, the following paper gives a brief review of some optimization problems involving radiating sources and phantoms, and tries to highlight their complexity. The particular situation of a two-dimensional (2-D) source, radiating close to homogeneous or two-layer cylindrical phantoms, is analyzed. Thanks to an equivalent junction model derived from a modal-based approach, the sources minimizing and maximizing the TDP in these phantoms are obtained, as well as the sources giving the maximal or minimal difference between the TDP in two chosen phantoms. Finally, the obtained results are discussed, and shortly extrapolated to the problem of specific absorption rate (SAR) due to wireless devices