Preface ........................................................ xv
Preface to the First Edition ................................. xvii
Chapter 1 Fundamentals .......................................... 1
1.1 Characteristics of Femtosecond Light Pulses ................ 1
1.1.1 Complex Representation of the Electric Field ........ 1
1.1.2 Power, Energy, and Related Quantities ............... 6
1.1.3 Pulse Duration and Spectral Width ................... 9
1.1.4 Wigner Distribution, Second-Order Moments,
Uncertainty Relations .............................. 12
1.2 Pulse Propagation ......................................... 20
1.2.1 The Reduced Wave Equation .......................... 21
1.2.2 Retarded Frame of Reference ........................ 26
1.2.3 Dispersion ......................................... 30
1.2.4 Gaussian Pulse Propagation ......................... 33
1.2.5 Complex Dielectric Constant ........................ 38
1.3 Interaction of Light Pulses with Linear Optical
Elements .................................................. 42
1.4 Generation of Phase Modulation ............................ 44
1.5 Beam Propagation .......................................... 46
1.5.1 General ............................................ 46
1.5.2 Analogy between Pulse and Beam Propagation ......... 49
1.5.3 Analogy between Spatial and Temporal Imaging ....... 50
1.6 Numerical Modeling of Pulse Propagation ................... 53
1.7 Space-Time Effects ........................................ 56
1.8 Problems .................................................. 57
Bibliography .............................................. 58
Chapter 2 Femtosecond Optics .................................. 61
2.1 Introduction .............................................. 61
2.2 White Light and Short Pulse Interferometry ................ 64
2.3 Dispersion of Interferometric Structures .................. 70
2.3.1 Mirror Dispersion .................................. 70
2.3.2 Fabry-Perot and Gires-Tournois Interferometer ...... 73
2.3.3 Chirped Mirrors .................................... 80
2.4 Focusing Elements ......................................... 82
2.4.1 Singlet Lenses ..................................... 82
2.4.2 Space-Time Distribution of the Pulse Intensity
at the Focus of a Lens ............................. 86
2.4.3 Achromatic Doublets ................................ 91
2.4.4 Focusing Mirrors ................................... 92
2.5 Elements with Angular Dispersion .......................... 94
2.5.1 Introduction ....................................... 94
2.5.2 Tilting of Pulse Fronts ............................ 95
2.5.3 GVD through Angular Dispersion—General ............ 100
2.5.4 GVD of a Cavity Containing a Single Prism ......... 102
2.5.5 Group Velocity Control with Pairs of Prisms ....... 105
2.5.6 GVD Introduced by Gratings ........................ 117
2.5.7 Grating Pairs for Pulse Compressors ............... 120
2.5.8 Combination of Focusing and Angular Dispersive
Elements .......................................... 122
2.6 Wave-Optical Description of Angular Dispersive
Elements ................................................. 124
2.7 Optical Matrices for Dispersive Systems ............. 130
2.8 Numerical Approaches ................................ 136
2.9 Problems ............................................ 136
Bibliography ............................................. 140
Chapter 3 Light-Matter Interaction ........................... 143
3.1 Density Matrix Equations ................................. 144
3.2 Pulse Shaping with Resonant Particles .................... 154
3.2.1 General ........................................... 154
3.2.2 Pulses Much Longer Than the Phase Relaxation
Time (τp ≫ T2) .................................... 156
3.2.3 Phase Modulation by Quasi-Resonant Interactions ... 161
3.2.4 Pulse Durations Comparable with or Longer Than
the Phase Relaxation Time (τp ≥ T2) ............... 165
3.3 Nonlinear, Nonresonant Optical Processes ................. 166
3.3.1 General ........................................... 166
3.3.2 Noninstantaneous Response ......................... 168
3.3.3 Pulse Propagation ................................. 170
3.4 Second Harmonic Generation (SHG) ......................... 172
3.4.1 Type I Second Harmonic Generation ................. 173
3.4.2 Second Harmonic Type II: Equations for Arbitrary
Phase Mismatch and Conversion Efficiencies ........ 180
3.4.3 Pulse Shaping in Second Harmonic Generation
(Type II) ......................................... 183
3.4.4 Group Velocity Control in SHG through Pulse
Front Tilt ........................................ 185
3.5 Optical Parametric Interaction ........................... 188
3.5.1 Coupled Field Equations ........................... 188
3.5.2 Synchronous Pumping ............................... 190
3.5.3 Chirp Amplification ............................... 190
3.6 Third-Order Susceptibility ............................... 192
3.6.1 Fundamentals ...................................... 192
3.6.2 Short Samples with Instantaneous Response ......... 195
3.6.3 Short Samples and Noninstantaneous Response ....... 197
3.6.4 Counter-Propagating Pulses and Third-Order
Susceptibility .................................... 199
3.7 Continuum Generation ..................................... 202
3.8 Self-Focusing ............................................ 205
3.8.1 Critical Power .................................... 205
3.8.2 The Nonlinear Schrodinger Equation ................ 208
3.9 Beam Trapping and Filaments .............................. 209
3.9.1 Beam Trapping ..................................... 209
3.9.2 Ultrashort Pulse Self-Focusing .................... 212
3.10 Problems ................................................. 213
Bibliography ............................................. 215
Chapter 4 Coherent Phenomena ................................. 221
4.1 From Coherent to Incoherent Interactions ................. 221
4.2 Coherent Interactions with Two-Level Systems ............. 225
4.2.1 Maxwell-Bloch Equations ........................... 225
4.2.2 Rate Equations .................................... 229
4.2.3 Evolution Equations ............................... 230
4.2.4 Steady-State Pulses ............................... 239
4.3 Multiphoton Coherent Interaction ......................... 243
4.3.1 Introduction ...................................... 243
4.3.2 Multiphoton Multilevel Transitions ................ 245
4.3.3 Simplifying a N-Level System to a Two-Level
Transition ........................................ 258
4.3.4 Four Photon Resonant Coherent Interaction ......... 262
4.3.5 Miscellaneous Applications ........................ 268
4.4. Problems ................................................. 272
Bibliography .................................................. 273
Chapter 5 Ultrashort Sources I: Fundamentals ................. 277
5.1 Introduction ............................................. 277
5.1.1 Superposition of Cavity Modes ..................... 277
5.1.2 Cavity Modes and Modes of a Mode-Locked Laser ..... 280
5.1.3 The "Perfect" Mode-Locked Laser ................... 283
5.1.4 The "Common" Mode-Locked Laser .................... 285
5.1.5 Basic Elements and Operation of a fs Laser ........ 291
5.2 Circulating Pulse Model .................................. 293
5.2.1 General Round-Trip Model .......................... 293
5.2.2 Continuous Model .................................. 295
5.2.3 Elements of a Numerical Treatment ................. 298
5.2.4 Elements of an Analytical Treatment ............... 300
5.3 Evolution of the Pulse Energy ............................ 303
5.3.1 Rate Equations for the Evolution of the Pulse
Energy ............................................ 304
5.3.2 Connection of the Model to Microscopic
Parameters ........................................ 311
5.4 Pulse Shaping in Intracavity Elements .................... 314
5.4.1 Saturation ........................................ 315
5.4.2 Nonlinear Nonresonant Elements .................... 317
5.4.3 Self-Lensing ...................................... 320
5.4.4 Summary of Compression Mechanisms ................. 323
5.4.5 Dispersion ........................................ 323
5.5 Cavities ................................................. 325
5.5.1 Cavity Modes and ABCD Matrix Analysis ............. 325
5.5.2 Astigmatism and Its Compensation .................. 328
5.5.3 Cavity with a Kerr Lens ........................... 332
5.6 Problems ................................................. 335
Bibliography ............................................. 337
Chapter 6 Ultrashort Sources II: Examples .................... 341
6.1 Synchronous Mode-Locking ................................. 341
6.2 Hybrid Mode-Locking ...................................... 345
6.3 Additive Pulse Mode-Locking .............................. 346
6.3.1 Generalities ...................................... 346
6.3.2 Analysis of APML .................................. 348
6.4 Mode-Locking Based on Nonresonant Nonlinearity ........... 349
6.4.1 Nonlinear Mirror .................................. 349
6.4.2 Polarization Rotation ............................. 351
6.5 Negative Feedback ........................................ 352
6.6 Semiconductor-Based Saturable Absorbers .................. 356
6.7 Solid-State Lasers ....................................... 358
6.7.1 Generalities ...................................... 358
6.7.2 Ti:sapphire Laser ................................. 360
6.7.3 Cr:LiSAF, Cr:LiGAF, Cr:LiSGAF, and Alexandrite .... 364
6.7.4 Cr:Forsterite and Cr:Cunyite Lasers ............... 366
6.7.5 YAG Lasers ........................................ 367
6.7.6 Nd:YVO4 and Nd:YLF ................................ 370
6.8 Semiconductor and Dye Lasers ............................. 371
6.8.1 Dye Lasers ........................................ 371
6.8.2 Semiconductor Lasers .............................. 374
6.9 Fiber Lasers ............................................. 378
6.9.1 Introduction ...................................... 378
6.9.2 Raman Soliton Fiber Lasers ........................ 379
6.9.3 Doped Fiber Lasers ................................ 380
6.9.4 Mode-Locking through Polarization Rotation ........ 381
6.9.5 Figure-Eight Laser ................................ 384
Bibliography .................................................. 386
Chapter 7 Femtosecond Pulse Amplification ................... 395
7.1 Introduction ............................................. 395
7.2 Fundamentals ............................................. 396
7.2.1 Gain Factor and Saturation ........................ 396
7.2.2 Shaping in Amplifiers ............................. 400
7.2.3 Amplified Spontaneous Emission (ASE) .............. 404
7.3 Nonlinear Refractive Index Effects ....................... 406
7.3.1 General ........................................... 406
7.3.2 Self-Focusing ..................................... 409
7.3.3 Thermal Noise ..................................... 410
7.3.4 Combined Pulse Amplification and Chirping ......... 411
7.4 Chirped Pulse Amplification (CPA) ........................ 412
7.5 Amplifier Design ......................................... 414
7.5.1 Gain Media and Pump Pulses ........................ 414
7.5.2 Amplifier Configurations .......................... 416
7.5.3 Single-Stage, Multipass Amplifiers ................ 418
7.5.4 Regenerative Amplifiers ........................... 421
7.5.5 Traveling Wave Amplification ...................... 422
7.6 Optical Parametric Chirped Pulse Amplification (OPCPA) ... 426
7.7 Problems ................................................. 427
Bibliography ............................................. 429
Chapter 8 Pulse Shaping ...................................... 433
8.1 Pulse Compression ........................................ 433
8.1.1 General ........................................... 433
8.1.2 The Fiber Compressor .............................. 437
8.1.3 Pulse Compression Using Bulk Materials ............ 450
8.2 Shaping through Spectral Filtering ....................... 451
8.3 Problems ............................................ 454
Bibliography .................................................. 455
Chapter 9 Diagnostic Techniques .............................. 457
9.1 Intensity Correlations ................................... 458
9.1.1 General Properties ................................ 458
9.1.2 The Intensity Autocorrelation ..................... 458
9.1.3 Intensity Correlations of Higher Order ............ 459
9.2 Interferometric Correlations ............................. 459
9.2.1 General Expression ................................ 459
9.2.2 Interferometric Autocorrelation 462
9.3 Measurement Techniques ................................... 466
9.3.1 Nonlinear Optical Processes for Measuring
Femtosecond Pulse Correlations .................... 466
9.3.2 Recurrent Signals ................................. 466
9.3.3 Single Shot Measurements .......................... 468
9.4 Pulse Amplitude and Phase Reconstruction ................. 473
9.4.1 Introduction ...................................... 473
9.4.2 Methods for Full-Field Characterization of
Ultrashort Light Pulses ........................... 474
9.4.3 Retrieval from Correlation and Spectrum ........... 477
9.4.4 Frequency Resolved Optical Gating (FROG) .......... 480
9.4.5 Spectral Phase Interferometry for Direct
Electric Field Reconstruction (SPIDER) ................... 484
9.5 Problems ................................................. 485
Bibliography ............................................. 486
Chapter 10 Measurement Techniques of Femtosecond
Spectroscopy ....................................... 491
10.1 Introduction ............................................. 491
10.2 Data Deconvolutions ...................................... 493
10.3 Beam Geometry and Temporal Resolution .................... 494
10.4 Transient Absorption Spectroscopy ........................ 497
10.5 Transient Polarization Rotation .......................... 500
10.6 Transient Grating Techniques ............................. 503
10.6.1 General Technique ................................. 503
10.6.2 Degenerate Four Wave Mixing (DFWM) ................ 506
10.7 Femtosecond Resolved Fluorescence ........................ 509
10.8 Photon Echoes ............................................ 512
10.9 Zero Area Pulse Propagation .............................. 515
10.10 Impulsive Stimulated Raman Scattering ................... 518
10.10.1 General Description .............................. 518
10.10.2 Detection ........................................ 520
10.10.3 Theoretical Framework ............................ 522
10.10.4 Single Pulse Shaping Versus Mode-Locked Train .... 524
10.11 Self-Action Experiments ................................. 526
10.12 Problems ................................................ 528
Bibliography .................................................. 529
Chapter 11 Examples of Ultrafast Processes in Matter ......... 531
11.1 Introduction ............................................. 531
11.2 Ultrafast Transients in Atoms ............................ 532
11.2.1 The Classical Limit of the Quantum Mechanical
Atom .............................................. 532
11.2.2 The Radial Wave Packet ............................ 532
11.2.3 The Angularly Localized Wave Packet ............... 534
11.3 Ultrafast Processes in Molecules ......................... 536
11.3.1 Observation of Molecular Vibrations ............... 536
11.3.2 Chemical Reactions ................................ 540
11.3.3 Molecules in Solution ............................. 543
11.4 Ultrafast Processes in Solid-State Materials ............. 544
11.4.1 Excitation across the Band Gap .................... 544
11.4.2 Excitons .......................................... 545
11.4.3 Intraband Relaxation .............................. 545
11.4.4 Phonon Dynamics ................................... 547
11.4.5 Laser-Induced Surface Disordering ................. 549
11.5 Primary Steps in Photo-Biological Reactions .............. 550
11.5.1 Femtosecond Isomerization of Rhodopsin ............ 550
11.5.2 Photosynthesis .................................... 551
Bibliography ............................................. 553
Chapter 12 Generation of Extreme Wavelengths .................. 557
12.1 Generation of Terahertz (THz) Radiation .................. 558
12.2 Generation of Ultrafast X-Ray Pulses ..................... 565
12.2.1 Incoherent Bursts of X-Rays ....................... 565
12.2.2 High Harmonics (HH) and Attosecond Pulse
Generation ........................................ 566
12.3 Generation of Ultrashort Acoustic Pulses ................. 568
12.4 Generation of Ultrafast Electric Pulses .................. 571
Bibliography .................................................. 575
Chapter 13 Selected Applications .............................. 579
13.1 Imaging .................................................. 579
13.1.1 Introduction ...................................... 579
13.1.2 Range Gating with Ultrashort Pulses ............... 580
13.1.3 Imaging through Scatterers ........................ 583
13.1.4 Prospects for Four-Dimensional Imaging ............ 585
13.1.5 Microscopy ........................................ 586
13.2 Solitons ................................................. 590
13.2.1 Temporal Solitons ................................. 590
13.2.2 Spatial Solitons and Filaments .................... 592
13.2.3 Spatial and Temporal Solitons ..................... 597
13.3 Sensors Based on fs Lasers ............................... 598
13.3.1 Description of the Operation ...................... 598
13.3.2 Inertial Measurements (Rotation and
Acceleration) ..................................... 601
13.3.3 Measurement of Changes in Index ................... 603
13.4 Stabilized Mode-Locked Lasers for Metrology .............. 609
13.4.1 Measurement of the Carrier to Envelope Offset
(CEO) ............................................. 610
13.4.2 Locking of fs Lasers to Stable \ Reference
Cavities .......................................... 614
13.5 Problem .................................................. 616
Bibliography ............................................. 617
Appendix A The Uncertainty Principle ......................... 623
Appendix В Phase Shifts on Transmission and Reflection ....... 625
B.l The Symmetrical Interface ......................... 625
B.2 Coated Interface between Two Different
Dielectrics ....................................... 626
Appendix С Slowly Evolving Wave Approximation ................ 629
Appendix D Four-Photon Coherent Interaction .................. 633
Appendix E Kerr Lensing in a Cavity .......................... 637
E.1 Elementary Kerr Lensing Model ..................... 637
E.2 Example of a Nonlinear Cavity and Gaussian Beam
Analysis .......................................... 638
Appendix F Abbreviations for Dyes ............................ 643
List of Symbols ............................................... 645
Index ......................................................... 647
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