Geometry and Light The Science of Invisibility

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

The New copy of this book will include any supplemental materials advertised. Please check the title of the book to determine if it should include any access cards, study guides, lab manuals, CDs, etc.

The Used, Rental and eBook copies of this book are not guaranteed to include any supplemental materials. Typically, only the book itself is included. This is true even if the title states it includes any access cards, study guides, lab manuals, CDs, etc.