Plasmonic Metamaterials: Physical Background and Some Technological Applications

New technological frontiers appear every year, and few are as intriguing as the field of plasmonic metamaterials (PMMs). These uniquely designed materials use coherent electron oscillations to accomplish an astonishing array of tasks, and they present diverse opportunities in many scientific fields. This paper consists of an explanation of the scientific background of PMMs and some technological applications of these fascinating materials. The physics section addresses the foundational concepts necessary to understand the operation of PMMs, while the technology section addresses various applications, like precise biological and chemical sensors, cloaking devices for several frequency ranges, nanoscale photovoltaics, experimental optical computing components, and superlenses that can surpass the diffraction limit of conventional optics

Three-manifolds with many flat planes

We discuss the rigidity (or lack thereof) imposed by different notions of having an abundance of zero curvature planes on a complete Riemannian 3-manifold. We prove a rank rigidity theorem for complete 3-manifolds, showing that having higher rank is equivalent to having reducible universal covering. We also study 3-manifolds such that every tangent vector is contained in a flat plane, including examples with irreducible universal covering, and discuss the effect of finite volume and real-analiticity assumptions.Comment: LaTeX2e, 24 pages, 7 figures, revised version. To appear in Trans. Amer. Math. So