Geometry and Light: The Science of Invisibility
The science of invisibility combines two of physics' greatest concepts: Einstein's general relativity and Maxwell's principles of electromagnetism. Recent years have witnessed major breakthroughs in the area, and the authors of this volume — Ulf Leonhardt and Thomas Philbin of Scotland's University of St. Andrews — have been active in the transformation of invisibility from fiction into science. Their work on designing invisibility devices is based on modern metamaterials, inspired by Fermat's principle, analogies between mechanics and optics, and the geometry of curved space.
Suitable for graduate students and advanced undergraduates of engineering, physics, or mathematics, and scientific researchers of all types, this is the first authoritative textbook on invisibility and the science behind it. The book is two books in one: it introduces the mathematical foundations — differential geometry — for physicists and engineers, and it shows how concepts from general relativity become practically useful in electrical and optical engineering, not only for invisibility but also for perfect imaging and other fascinating topics. More than one hundred full-color illustrations and exercises with solutions complement the text.
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3–dimensional amplitude angle basis vectors Cartesian coordinates Christoffel symbols circle components conformal mapping Consider coordinate system coordinate transformation covariant derivative curvature curved space cylindrical polar dielectric tensors differential dipole dispersion relation distance electric field electromagnetic waves ellipses Euclidean Exercise expression Fermat’s principle Figure flat space formula function geodesic geometrical optics Hamilton’s equations hypersphere impedance–matched invisibility isotropic lens Leonhardt Levi–Civita tensor light rays line element Luneburg magnetic field matrix Maxwell’s equations Maxwell’s fish–eye medium metric tensor Möbius transformation momentum obtain one–form optical path length oscillation parallel transport parameter partial derivatives Penrose diagram permittivity phase physical space plane wave propagation radial radius ray trajectories refractive index refractive–index profile Riemann tensor rotation shows sin2 Snell’s law Solution spatial sphere stereographic projection surface symmetric transformation media vanishes vector field velocity virtual space wave equation wave vector zero