Ultrashort_Laser_Pulse_Phenomena_Fundamentals_Tech.pdf
- 1. See discussions, stats, and author profiles for this publication at: https://www.researchgate.net/publication/266908536 Ultrashort Laser Pulse Phenomena Fundamentals, Techniques, and Applications an a Femtosecond Time Scale Second Edition Article · January 1996 CITATIONS 239 READS 3,709 2 authors, including: Jean-Claude Diels University of New Mexico 467 PUBLICATIONS 5,962 CITATIONS SEE PROFILE All content following this page was uploaded by Jean-Claude Diels on 21 June 2016. The user has requested enhancement of the downloaded file.
- 2. Ultrashort Laser Pulse Phenomena Fundamentals, Techniques, and Applications an a Femtosecond Time Scale Second Edition JEAN-CLAUDE DIELS Department of Physics and Astronomy University of New Mexico Albuquerque, NM WOLFGANG RUDOLPH Department of Physics and Astronomy University of New Mexico Albuquerque, NM AMSTERDAM • BOSTON • HEIDELBERG • LONDON NEW YORK • OXFORD • PARIS • SAN DIEGO SAN FRANCISCO • SINGAPORE • SYDNEY • TOKYO ELSEVIER Academic Press is an immint of Elsevier
- 3. Contents 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
- 4. vi Contents 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 (i, » 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 (rp > 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
- 5. Contents vii 3.4. Second Harmonie Generation (SHG) 172 3.4.1. Type I Second Harmonie Generation 173 3.4.2. Second Harmonie Type II: Equations for Arbitrary Phase Mismatch and Conversion Efficiencies 180 3.4.3. Pulse Shaping in Second Harmonie 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 Schrödinger 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
- 6. viii Contents 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
- 7. Contents ix 6.4. Mode-Locking Based an 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
- 8. x Contents 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
- 9. Contents xi 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
- 10. xii Contents 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 B Phase Shifts on Transmission and Reflection 625 B.1. The Symmetrical Interface 625 B.2. Coated Interface between Two Different Dielectrics 626 Appendix C Slowly Evolving Wave Approximation 629
- 11. Contents xiii 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 View publication stats