Mathematics of Metamaterials

University Of Utah, Salt Lake City UT

Investigators

Abstract

Milton 0707978 Superlenses achieve resolution finer than convential lenses, and have some startling properties, such as making polarizable dipoles essentially invisible if they lie within a critical distance of the lens. This project improves our understanding of superlenses and invisibility, particularly for spherical superlenses, which not only superresolve but also magnify. It also seeks to characterize exotic electromagnetic behaviors that composite materials formed from constituent materials with extreme properties can exhibit in the quasistatic limit, where the wavelength of the time-harmonic radiation is much larger than the microstructure. The investigator also studies a new class of material named "massnetic materials." These have in their microstructure collections of spinning tops, each situated in a cavity in the body, and each weighted on one side by a mass that allows one to increase or decrease the spin of each top by appropriately oscillating the body. These materials should be able to store and release energy on the microscale. The investigator also explores new equations of elastodynamics, and studies novel microstructures with the unusual property that their average momentum depends not just on their overall velocity, but also on how they are deformed, i.e. on their strain. Metamaterials, i.e. composite materials with properties unachievable in ordinary materials, have attracted a great deal of interest and are beginning to revolutionize our understanding of materials and the properties they can exhibit. More technogical applications of these materials are now possible due to advances in our ability to tailor the microstructure of substances, for instance through nanotechnology. This project studies how composites can be constructed from high contrast materials to exhibit elastic and electromagnetic properties far richer than existing materials. In the defence, automotive, aerospace, electronics, and other manufacturing and telecommunication industries there is a constant need for new materials. The impact of such new materials is likely to be greatest when their properties are radically different from any material we know. The project could lead to the development of whole classes of radically different new materials with novel properties. Also it should give a much needed firm theoretical foundation to Pendry's work on spherical superlenses, and enhance our understanding of invisibility.