x CONTENTS 6.3.3 Self-Phase Modulation with Normal Dispersion,274 6.3.4 Cross-Phase Modulation,275 6.4 Pulse Compression,276 6.5 Modulational Instability,283 6.6 Solitons.286 6.7 Higher-Order Propagation Effects,291 6.7.1 Nonlinear Envelope Equation in Uniform Media,292 6.7.2 Nonlinear Envelope Equation in Waveguides,295 6.7.3 Delayed Nonlinear Response and the Raman Effect,296 6.7.4 Self-Steepening,306 6.7.5 Space-Time Focusing,308 6.8 Continuum Generation,310 Problems.313 7 Mode-Locking:Selected Advanced Topics 316 7.1 Soliton Fiber Lasers:Artificial Fast Saturable Absorbers,316 7.1.1 The Figure-Eight Laser,317 7.1.2 Energy Quantization,322 7.1.3 Soliton Sidebands,324 7.2 Soliton Mode-Locking:Active Modulation and Slow Saturable Absorbers,328 7.2.1 Harmonically Mode-Locked Soliton Fiber Lasers,328 7.2.2 The Net Gain Window in Soliton Mode-Locking.330 7.3 Stretched Pulse Mode-Locking.337 7.3.1 Stretched Pulse Mode-Locked Fiber Laser.337 7.3.2 Dispersion-Managed Solitons,340 7.3.3 Theoretical Issues.342 7.4 Mode-Locked Lasers in the Few-Cycle Regime,344 7.5 Mode-Locked Frequency Combs,347 7.5.1 Comb Basics.347 7.5.2 Measurement Techniques,350 7.5.3 Stabilization of Frequency Combs,354 7.5.4 Applications,356 Problems,360 8 Manipulation of Ultrashort Pulses 362 8.1 Fourier Transform Pulse Shaping,362 8.1.1 Examples of Pulse Shaping Using Fixed Masks,364 8.1.2 Programmable Pulse Shaping,369 8.1.3 Pulse-Shaping Theory,376 8.2 Other Pulse-Shaping Techniques,386 8.2.1 Direct Space-to-Time Pulse Shaping,386 8.2.2 Acousto-optic Dispersive Filters.390 8.3 Chirp Processing and Time Lenses,394 8.3.1 Space-Time Duality,394 8.3.2 Chirp Processing.397 8.3.3 Time Lens Processing,399x CONTENTS 6.3.3 Self-Phase Modulation with Normal Dispersion, 274 6.3.4 Cross-Phase Modulation, 275 6.4 Pulse Compression, 276 6.5 Modulational Instability, 283 6.6 Solitons, 286 6.7 Higher-Order Propagation Effects, 291 6.7.1 Nonlinear Envelope Equation in Uniform Media, 292 6.7.2 Nonlinear Envelope Equation in Waveguides, 295 6.7.3 Delayed Nonlinear Response and the Raman Effect, 296 6.7.4 Self-Steepening, 306 6.7.5 Space–Time Focusing, 308 6.8 Continuum Generation, 310 Problems, 313 7 Mode-Locking: Selected Advanced Topics 316 7.1 Soliton Fiber Lasers: Artificial Fast Saturable Absorbers, 316 7.1.1 The Figure-Eight Laser, 317 7.1.2 Energy Quantization, 322 7.1.3 Soliton Sidebands, 324 7.2 Soliton Mode-Locking: Active Modulation and Slow Saturable Absorbers, 328 7.2.1 Harmonically Mode-Locked Soliton Fiber Lasers, 328 7.2.2 The Net Gain Window in Soliton Mode-Locking, 330 7.3 Stretched Pulse Mode-Locking, 337 7.3.1 Stretched Pulse Mode-Locked Fiber Laser, 337 7.3.2 Dispersion-Managed Solitons, 340 7.3.3 Theoretical Issues, 342 7.4 Mode-Locked Lasers in the Few-Cycle Regime, 344 7.5 Mode-Locked Frequency Combs, 347 7.5.1 Comb Basics, 347 7.5.2 Measurement Techniques, 350 7.5.3 Stabilization of Frequency Combs, 354 7.5.4 Applications, 356 Problems, 360 8 Manipulation of Ultrashort Pulses 362 8.1 Fourier Transform Pulse Shaping, 362 8.1.1 Examples of Pulse Shaping Using Fixed Masks, 364 8.1.2 Programmable Pulse Shaping, 369 8.1.3 Pulse-Shaping Theory, 376 8.2 Other Pulse-Shaping Techniques, 386 8.2.1 Direct Space-to-Time Pulse Shaping, 386 8.2.2 Acousto-optic Dispersive Filters, 390 8.3 Chirp Processing and Time Lenses, 394 8.3.1 Space–Time Duality, 394 8.3.2 Chirp Processing, 397 8.3.3 Time Lens Processing, 399