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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