Geometry and Light

Geometry and Light Contents Chapter 1 Prologue 1 Chapter 2 Fermat's Principle 7 1. Letters from Pierre de Fermat 7 2. Variational calculus 15 3. Newtonian analogy 20 4. Hamilton's equations 27 5. Optical conformal mapping 33 6. Transmutation 44 7. Spherical symmetry 48 8.   Tomography 58 9. From invisible spheres to perfect lenses 66 Chapter 3 Differential geometry 83 10. Coordinate transformations 83 11. The metric tensor 87 12. Vectors and bases 92 13. One-forms and general tensors 99 14. Vector products and the Levi-Civita tensor 103 15. The covariant derivative of a vector 107 16. Covariant derivatives of tensors and of the metric 115 17. Divergence, curl and Laplacian 119 18. Curvature   126 19. Geodesics 129 20. Parallel transport and covariant derivatives 133 21. Geodesic deviation and the Riemann tensor 136 22. Parallel transport around a closed loop 144 23. Conformally flat spaces 151 24. The hypersphere 155 25. Space-time geometry 161 Chapter 4 Maxwell's equations 165 26. Spatial geometrics and media 166 27. Planar media   170 28. Transformation media 173 29. Electromagnetic waves 175 30. Geometrical optics 186 31. Space-time geometries and media 199 Chapter 5 Geometries and media 205 32. Spatial transformation media 206 33. Perfect invisibility devices 210 34. Negative refraction and perfect lenses 216 35. Cloaking at a distance 221 36. Perfect imaging with positive refraction 227 37.   Moving media 239 38. Optical Aharonov-Bohm effect 246 39. Analogue of the event horizon 251 Appendix 261 Bibliography 265