Effective Medium Transformation: the Case of Stratified Magnetic Structures

Effective medium theory replaces a given fine-scale heterostructure with a homogeneous one in such a way that the physically measurable quantities, e.g. reaction fields and losses, remain approximately the same. This Letter shows that the very nature of the physical problem may change upon homogenization. A specific example is a stratified nonlinear magnetic and conducting medium, where a low frequency excitation induces eddy currents. It is shown that the appropriate coarse-scale (homogeneous) model is, counter intuitively, magnetostatic, with an effective complex valued BH curve whose real and imaginary parts represent active and reactive losses in the sample. Similar situations may arise in other physical and engineering applications, notably, in diffusion problems with boundary layers.