This paper is concerned with the numerical solution to a three-dimensional coefficient inverse problem for buried objects with multi-frequency experimental data. The measured data, which are associated with a single direction of an incident plane wave, are backscatter data for targets buried in a sandbox. These raw scattering data were collected using a microwave scattering facility at the University of North Carolina at Charlotte. We develop a data preprocessing procedure and exploit a newly developed globally convergent inversion method for solving the inverse problem with these preprocessed data. It is shown that dielectric constants of the buried targets as well as their locations are reconstructed with a very good accuracy. We also prove a new analytical result which rigorously justifies an important step of the so-called “data propagation” procedure.

Metamaterials are artificially structured materials that provide new electronic or optical properties. They encompass electronic superlattices and photonic crystals, as well as composites having no properties attributable to phase coherence. This paper examines the role of phase coherency in terms of the applicability of the random phase approximation in determining unusual properties in metamaterials. The focus is on the understanding of fundamental principles to provide a different and hopefully more profound appreciation of this rapidly growing field. Fabrication of wavelength scale and subwavelength scale structures becomes increasingly difficult as dimensions are reduced for higher-frequency applications. Natural materials can rely in principle on distinct atom types for their bulk properties, with their neighbors playing a role in defining those bulk properties. Metamaterials suffer from degrees of disorder arising from fabrication tolerances that bring uncertainty to the ‘artificial atomic’ properties as well as nearest-neighbor locations.

Surface plasmon modes in structures of metal-insulator-metal (MIM), insulator-insulator-metal (IIM) and insulator-metal-insulator (IMI) are studied theoretically for both lossless and lossy cases. Causality dictates which solutions of Maxwell’s equations we accept for these structures. We find that for both lossless and lossy cases, the negative index modes and positive index modes are independent and should be treated separately. For the lossless case, our results differ from some published papers. By studying in detail the lossy case, we demonstrate how the curves should look like.