Geometry and Light: The Science of Invisibility
Suitable for advanced undergraduate and graduate students of engineering, physics, and mathematics and scientific researchers of all types, this is the first authoritative text on invisibility and the science behind it. It introduces the mathematical foundations of differential geometry and demonstrates practical applications from general relativity to electrical and optical engineering. More than 100 full-color illustrations, plus exercises with solutions. 2010 edition.
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Suitable for advanced undergraduate and graduate students of engineering, physics, and mathematics and scientific researchers of all types, this is the first authoritative text on invisibility and the science behind it. More than 100 full-color illustrations, plus exercises with solutions. 2010 edition.
Chapter 1 Prologue 1Chapter 2 Fermat's principle 71 Letters from Pierre de Fermat 72 Variational calculus 153 Newtonian analogy 204 Hamilton's equations 275 Optical conformal mapping 336 Transmutation 447 Spherical symmetry 488 Tomography 589 From invisible spheres to perfect lenses 66Chapter 3 Differential geometry 8310 Coordinate transformations 8311 The metric tensor 8712 Vectors and bases 9213 One-forms and general tensors 9914 Vector products and the Levi-Civita tensor 10315 The covariant derivative of a vector 10716 Covariant derivatives of tensors and of the metric 11517 Divergence, curl and Laplacian 11918 Curvature 12619 Geodesies 12920 Parallel transport and covariant derivatives 13321 Geodesic deviation and the Riemann tensor 13622 Parallel transport around a closed loop 14423 Conformally flat spaces 15124 The hypersphere 15525 Space-time geometry 161Chapter 4 Maxwell's equations 16526 Spatial geometries and media 16627 Planar media 17028 Transformation media 17329 Electromagnetic waves 17530 Geometrical optics 18631 Space-time geometries and media 199Chapter 5 Geometries and media 20532 Spatial transformation media 20633 Perfect invisibility devices 21034 Negative refraction and perfect lenses 21635 Cloaking at a distance 22136 Perfect imaging with positive refraction 22737 Moving media 23938 Optical Aharonov-Bohm effect 24639 Analogue of the event horizon 251Appendix 261Bibliography 265
