Introduction to Photonics

1.1.1 Maxwell Equations......Page 9
1.1.2 Energy and Energy Flux of the Field......Page 11
1.1.3 Frequency Analysis......Page 12
1.2.1 Quantum Aspects of Light......Page 13
1.2.2 Field Operators......Page 14
1.2.3 Field Modes......Page 19
1.2.4 `Classical\' States of Light......Page 23
2.1.1 A Simple Model......Page 35
2.1.2 Exploiting Homogeneity......Page 37
2.1.3 Radiation off a Given Source......Page 40
2.2.1 Basic Equations......Page 42
2.2.2 Simple Reflection and Refraction......Page 44
2.2.3 Birefringent Media (Crystal Optics)......Page 51
2.3 Monochromatic Light Rays......Page 57
2.4 Group-Velocity Dispersion......Page 59
3.1 General Considerations......Page 61
3.1.1 Functionals of the Electric Field......Page 62
3.1.3 Perturbative Solution of Maxwell\'s Equations......Page 63
3.2.1 Phase Matching......Page 65
3.2.2 Three-Wave Mixing......Page 70
3.2.3 Four-Wave Mixing......Page 76
3.3.1 Quantized Radiation Inside Linear Media......Page 77
3.3.2 Nonlinear Perturbation......Page 79
3.3.3 Type-II Spontaneous Down Conversion......Page 81
4.1.1 Single Localized Detectors......Page 83
4.1.2 Independent Detectors......Page 85
4.2.1 Correlation Functions in General......Page 86
4.2.2 Correlation Functions of Single-Mode States......Page 88
4.3.2 Hanbury-Brown-Twiss Effect......Page 95
5.1 Criteria for Non-Classical Light......Page 99
5.2.1 General Action of Linear Optical Devices......Page 102
5.2.2 Classical Description of Lossless Beam Splitters......Page 103
5.2.3 Transformation of Photon Modes......Page 105
5.2.4 Mach-Zehnder Interferometer......Page 109
5.3.1 Single-Photon States and Quantum Cryptography......Page 111
5.3.2 Entangled Pairs of Photons......Page 114
5.3.3 Quantum Teleportation......Page 116
6.1.1 States and Observables in the Heisenberg Picture......Page 127
6.1.2 Time Evolution and Projective Measurements......Page 130
6.1.3 Time Dependent Perturbation Theory......Page 132
6.2.1 Composition of Distinguishable Systems......Page 133
6.2.2 Partial States......Page 134
6.2.3 Composition of Indistinguishable Systems......Page 135
6.3 Open Systems......Page 137
7.1.1 Naive Interaction Picture......Page 139
7.1.2 Electric Field Representation......Page 142
7.1.3 First Order Perturbation Theory......Page 144
7.2.1 Ionisation of One-Electron Atoms......Page 147
7.2.2 Simple Photodetectors......Page 150
8.1 The Exterior Electric Field Representation......Page 153
8.2 2-Level Systems......Page 154
8.2.1 Interpretation of the Bloch Vector......Page 157
8.2.2 Rotating Wave Approximation......Page 158
8.3.1 Population Trapping......Page 161
8.3.2 Electromagnetically Induced Transparency......Page 163
8.3.3 Change of Linear Susceptibility......Page 165
9.1.1 Quantized Radiation Field for Selected Modes......Page 171
9.1.2 Interaction of the Two-Level System with the Cavity Field......Page 172
A.1 Functional Taylor Expansion......Page 179
A.2.1 Scalar Particles in One Dimension......Page 181
A.2.2 Energy Eigenstates of the Harmonic Oscillator......Page 183
A.2.3 Coherent States......Page 186
A.3 Construction of Field Operators......Page 187
A.4 Dyson Series......Page 189
Bibliography......Page 191