On the Fundamental Limitations of Artificial Magnetic Materials

Fundamental limitations are presented on the performance of artificial magnetic materials based on the geometrical and physical characteristics of the inclusions comprising the medium. The permeability and magnetic susceptibility of the medium are formulated in terms of newly defined geometrical and physical parameters. Based on the Lorentzian form of the effective permeability function of the medium, it is shown that the flatness of the permeability function is limited by the desired operational bandwidth. Also, by applying a specific circuit-based model for inclusions, geometric invariant fundamental constraints are derived. It is shown that inclusions with larger surface area result in higher value of permeability. Next, the magnetic loss tangent in the medium is expressed as a function of the newly defined geometrical and physical parameters. It is found that there is a tradeoff between increasing the permeability and decreasing the loss on the one hand and reducing dispersion, on the other hand.