1 Introduction 1
1.1 "Traditional"Nonlinear Optics-Extreme Nonlinear Optics 1
1.2 How to Read this Book? 6
2 Selected Aspects of Few-Cycle Laser Pulses and Nonlinear Optics 9
2.1 Maxwell Equations 9
2.2 The Light Intensity 10
2.3 Electric Field in a Laser Resonator 11
2.4 A Brief Look at Phenomenological Nonlinear Optics 19
2.5 Even-Harmonic Generation and Inversion Symmetry 21
2.6 Principle of Measuring the Carrier-Envelope Frequency 23
3 The Lorentz Oscillator Model and Beyond 27
3.1 Linear Optics:Revisiting the Lorentz Oscillator Model 27
3.2 Two-Level Systems and Rabi Energy 29
3.3 Carrier-Wave Rabi Flopping 33
3.4 Frequency Doubling with Inversion Symmetry 38
3.5 Quantum Interference of Multiphoton Absorption 41
3.6 High Harmonics from Two-Level Systems 46
3.6.1 The"Static-Field Approximation" 51
3.6.2 The"Square-Wave Approximation" 53
3.6.3 The Dressed Two-Level System:Floquet States 57
4 The Drude Free-Electron Model and Beyond 61
4.1 Linear Optics:The Drude Model 61
4.2 Electron Wave Packets Driven by Light 63
4.2.1 Semiclassical Considerations 63
4.2.2 Quantum-Mechanical Treatment:Dressed Electrons 64
4.3 Crystal Electrons 71
4.3.1 Static-Field Case 71
4.3.2 High Harmonics from Carrier-Wave Bloch Oscillations 72
4.4 Extreme Nonlinear Optics of Relativistic Electrons 75
4.4.1 Second-Harmonic Generation and Photon Drag 78
4.4.2 Nonperturbative Regime 81
4.5 Extreme Nonlinear Optics of Dirac Electrons 86
4.6 Unruh Radiation 91
5 Lorentz Becomes Drude:Bound-Unbound Transitions 93
5.1 High-Harmonic Generation:Phenomenological Approach 93
5.2 The Keldysh Parameter 96
5.3 Field Ionization of Atoms 99
5.4 High-Harmonic Generation 104
5.4.1 Three-Step Scenario and Cutoff 105
5.5 Application to Photoemission from Metal Surfaces 109
6 Accounting for Propagation Effects 113
6.1 Numerical Solution of the Nonlinear Maxwell Equations 113
6.2 Slowly Varying Envelope Approximation 116
6.3 Gouy Phase and Carrier-Envelope Phase 117
6.4 Reshaping ofthe Amplitude Spectrum 123
7 Extreme Nonlinear Optics of Semiconductors and Isolators 129
7.1 Carrier-Wave Rabi Flopping 132
7.1.1 Experiment 134
7.1.2 Theory 139
7.1.3 Dependence on the Carrier-Envelope Phase 147
7.1.4 Semiconductor Bloch Equations 150
7.2 "THG in the Disguise of SHG" 152
7.3 Dynamic Franz-Keldysh Effect 161
7.4 Photon Drag or Dynamic Hall Effect 166
7.5 Conical Second-Harmonic Generation 169
8 Extreme Nonlinear Optics of Atoms and Electrons 173
8.1 High-Harmonic Generation From Atoms 173
8.1.1 Gas Jets 174
8.1.2 Hollow Waveguides 177
8.1.3 Quasi Phase-Matching in Modulated Capillaries 179
8.1.4 Dependence on the Carrier-Envelope Phase 180
8.2 Relativistic Nonlinear Thomson Scattering 183
Solutions 187
Symbols 205
References 209
Index 219