viii CONTENTS 2.4 Solid-State Laser Mode-Locking Using the Optical Kerr Effect,57 2.4.1 Nonlinear Refractive Index Changes,57 2.4.2 Self-Amplitude Modulation,Self-Phase Modulation,and Group Velocity Dispersion,58 2.4.3 Additive Pulse Mode-Locking,60 2.4.4 Kerr Lens Mode-Locking,64 2.4.5 Mode-Locking Solutions,75 2.4.6 Initiation of Mode-Locking,81 Problems,83 3 Ultrafast-pulse Measurement Methods 85 3.1 Terminology and Definitions,85 3.2 Electric Field Autocorrelation Measurements and the Power Spectrum,88 3.3 Electric Field Cross-Correlation Measurements and Spectral Interferometry,91 3.3.1 Electric Field Cross-Correlation.92 3.3.2 Spectral Interferometry,93 3.3.3 Application:Optical Coherence Tomography,96 3.4 Intensity Correlation Measurements,99 3.4.1 Correlation Measurements Using Second-Harmonic Generation,99 3.4.2 Experimental Procedures,108 3.4.3 Correlation Measurements Using Two-Photon absorption,110 3.4.4 Higher-Order Correlation Techniques,111 3.5 Chirped Pulses and Measurements in the Time-Frequency Domain,112 3.6 Frequency-Resolved Optical Gating,118 3.6.1 Polarization-Gating FROG.119 3.6.2 Self-Diffraction FROG.122 3.6.3 Second-Harmonic-Generation FROG,124 3.6.4 Frequency-Resolved Optical Gating Using Temporal Phase Modulation,125 3.6.5 Signal Recovery from FROG Traces,126 3.7 Pulse Measurements Based on Frequency Filtering.130 3.7.1 Single-Slit Approaches,131 3.7.2 Double-Slit Approach,134 3.8 Self-Referencing Interferometry,135 3.8.1 Time-Domain Interferometry of Chirped Pulses,135 3.8.2 Self-Referencing Spectral Interferometry,137 3.9 Characterization of Noise and Jitter,139 Problems,144 4 Dispersion and Dispersion Compensation 147 4.1 Group Velocity Dispersion,147 4.1.1 Group Velocity Definition and General Dispersion Relations,147 4.1.2 General Aspects of Material Dispersion,151 4.2 Temporal Dispersion Based on Angular Dispersion,155 4.2.1 Relation Between Angular and Temporal Dispersion,155 4.2.2 Angular Dispersion and Tilted Intensity Fronts,159 4.3 Dispersion of Grating Pairs,161viii CONTENTS 2.4 Solid-State Laser Mode-Locking Using the Optical Kerr Effect, 57 2.4.1 Nonlinear Refractive Index Changes, 57 2.4.2 Self-Amplitude Modulation, Self-Phase Modulation, and Group Velocity Dispersion, 58 2.4.3 Additive Pulse Mode-Locking, 60 2.4.4 Kerr Lens Mode-Locking, 64 2.4.5 Mode-Locking Solutions, 75 2.4.6 Initiation of Mode-Locking, 81 Problems, 83 3 Ultrafast-pulse Measurement Methods 85 3.1 Terminology and Definitions, 85 3.2 Electric Field Autocorrelation Measurements and the Power Spectrum, 88 3.3 Electric Field Cross-Correlation Measurements and Spectral Interferometry, 91 3.3.1 Electric Field Cross-Correlation, 92 3.3.2 Spectral Interferometry, 93 3.3.3 Application: Optical Coherence Tomography, 96 3.4 Intensity Correlation Measurements, 99 3.4.1 Correlation Measurements Using Second-Harmonic Generation, 99 3.4.2 Experimental Procedures, 108 3.4.3 Correlation Measurements Using Two-Photon absorption, 110 3.4.4 Higher-Order Correlation Techniques, 111 3.5 Chirped Pulses and Measurements in the Time–Frequency Domain, 112 3.6 Frequency-Resolved Optical Gating, 118 3.6.1 Polarization-Gating FROG, 119 3.6.2 Self-Diffraction FROG, 122 3.6.3 Second-Harmonic-Generation FROG, 124 3.6.4 Frequency-Resolved Optical Gating Using Temporal Phase Modulation, 125 3.6.5 Signal Recovery from FROG Traces, 126 3.7 Pulse Measurements Based on Frequency Filtering, 130 3.7.1 Single-Slit Approaches, 131 3.7.2 Double-Slit Approach, 134 3.8 Self-Referencing Interferometry, 135 3.8.1 Time-Domain Interferometry of Chirped Pulses, 135 3.8.2 Self-Referencing Spectral Interferometry, 137 3.9 Characterization of Noise and Jitter, 139 Problems, 144 4 Dispersion and Dispersion Compensation 147 4.1 Group Velocity Dispersion, 147 4.1.1 Group Velocity Definition and General Dispersion Relations, 147 4.1.2 General Aspects of Material Dispersion, 151 4.2 Temporal Dispersion Based on Angular Dispersion, 155 4.2.1 Relation Between Angular and Temporal Dispersion, 155 4.2.2 Angular Dispersion and Tilted Intensity Fronts, 159 4.3 Dispersion of Grating Pairs, 161