Attosecond and XUV Physics: Ultrafast Dynamics and Spectroscopy

This book provides fundamental knowledge in the fields of attosecond science and free electron lasers, based on the insight that the further development of both disciplines can greatly benefit from mutual exposure and interaction between the two communities. 
With respect to the interaction of high intensity lasers with matter, it covers ultrafast lasers, high-harmonic generation, attosecond pulse generation and characterization. Other chapters review strong-field physics, free electron lasers and experimental instrumentation.
Written in an easy accessible style, the book is aimed at graduate and postgraduate students so as to support the scientific training of early stage researchers in this emerging field. Special emphasis is placed on the practical approach of building experiments, allowing young researchers to develop a wide range of scientific skills in order to accelerate the development of spectroscopic techniques and their implementation in scientific experiments. 
The editors are managers of a research network devoted to the education of young scientists, and this book idea is based on a summer school organized by the ATTOFEL network. 

List of Contributors XIII

1 Attosecond and XUV Physics: Ultrafast Dynamics and Spectroscopy 1
Marc Vrakking

1.1 Introduction 1

1.2 The Emergence of Attosecond Science 2

1.2.1 Attosecond Pulse Trains and Isolated Attosecond Pulses 3

1.2.2 Characterization of Attosecond Laser Pulses 4

1.2.3 Experimental Challenges in Attosecond Science 5

1.2.4 Attosecond Science as a Driver for Technological Developments 6

1.3 Applications of Attosecond Laser Pulses 7

1.4 Ultrafast Science Using XUV/X-ray Free Electron Lasers 9

1.5 The Interplay between Experiment and Theory 11

1.6 Conclusion and Outlook 12

References 13

Part One Laser Techniques 17

2 Ultrafast Laser Oscillators and Amplifiers 19
Uwe Morgner

2.1 Introduction 19

2.2 Mode-Locking and Few-Cycle Pulse Generation 20

2.3 High-Energy Oscillators 23

2.4 Laser Amplifiers 25

References 29

3 Ultrashort Pulse Characterization 37
Adam S. Wyatt

3.1 Motivation: Why Ultrafast Metrology? 37

3.1.1 Ultrafast Science: High-Speed Photography in the Extreme 38

3.2 Formal Description of Ultrashort Pulses 42

3.2.1 Sampling Theorem 45

3.2.2 Chronocyclic Representation of Ultrafast Pulses 46

3.2.3 Space-Time Coupling 46

3.2.4 Accuracy, Precision and Consistency 49

3.3 Linear Filter Analysis 51

3.4 Ultrafast Metrology in the Visible to Infrared 53

3.4.1 Temporal Correlations 53

3.4.2 Spectrography 55

3.4.3 Sonography 60

3.4.4 Tomography 60

3.4.5 Interferometry 63

3.5 Ultrafast Metrology in the Extreme Ultraviolet 73

3.5.1 Complete Characterization of Ultrashort XUV Pulses via Photoionization Spectroscopy 75

3.5.2 XUV Interferometry 81

3.6 Summary 85

References 85

4 Carrier Envelope Phase Stabilization 95
Vincent Crozatier

4.1 Introduction 95

4.2 CEP Fundamentals 96

4.2.1 Time Domain Representation 96

4.2.2 Frequency Domain Representation 97

4.3 Stabilization Loop Fundamentals 99

4.3.1 The Noisy Source 99

4.3.2 Noise Detection 100

4.3.3 Open-Loop Noise Analysis 101

4.3.4 Feedback 102

4.3.5 Closed-Loop Noise Analysis 103

4.4 CEP in Oscillators 104

4.4.1 Oscillators Peculiarities 105

4.4.2 CEP Detection 107

4.4.3 Actuation 110

4.5 CEP in Amplifiers 115

4.5.1 Amplifier Peculiarities 116

4.5.2 CEP Detection 119

4.5.3 Actuation 123

4.5.4 Feedback Results 124

4.5.5 Parametric Amplification 126

4.6 Conclusion 129

References 129

5 Towards Tabletop X-Ray Lasers 135
Philippe Zeitoun, Eduardo Oliva, Thi Thu Thuy Le, Stéphane Sebban, Marta Fajardo, David Ros, and Pedro Velarde

5.1 Context and Objectives 135

5.2 Choice of Plasma-Based Soft X-Ray Amplifier 137

5.2.1 Basic Aspects of High Harmonic Amplification 138

5.2.2 Basic Aspects of Plasma Amplifiers 140

5.3 2D Fluid Modeling and 3D Ray Trace 141

5.3.1 ARWEN Code 142

5.3.2 Model to Obtain 2D Maps of Atomic Data 143

5.4 The Bloch–Maxwell Treatment 149

5.5 Stretched Seed Amplification 157

5.6 Conclusion 170

References 171

Part Two Theoretical Methods 177

6 Ionization in Strong Low-Frequency Fields 179
Misha Ivanov

6.1 Preliminaries 179

6.2 Speculative Thoughts 179

6.3 Basic Formalism 181

6.3.1 Hamiltonians and Gauges 181

6.3.2 Formal Solutions 182

6.4 The Strong-Field Approximation 184

6.4.1 The Volkov Propagator and the Classical Connection 185

6.4.2 Transition Amplitudes in the SFA 186

6.5 Strong-Field Ionization: Exponential vs. Power Law 189

6.5.1 The Saddle Point Approximation and the Classical Connection 190

6.6 Semiclassical Picture of High Harmonic Generation 195

6.7 Conclusion 198

References 199

7 Multielectron High Harmonic Generation: Simple Man on a Complex Plane 201
Olga Smirnova and Misha Ivanov

7.1 Introduction 201

7.2 The Simple Man Model of High Harmonic Generation (HHG) 203

7.3 Formal Approach for One-Electron Systems 205

7.4 The Lewenstein Model: Saddle Point Equations for HHG 209

7.5 Analysis of the Complex Trajectories 214

7.6 Factorization of the HHG Dipole: Simple Man on a Complex Plane 221

7.6.1 Factorization of the HHG Dipole in the Frequency Domain 222

7.6.2 Factorization of the HHG Dipole in the Time Domain 224

7.7 The Photoelectron Model of HHG: The Improved Simple Man 227

7.8 The Multichannel Model of HHG: Tackling Multielectron Systems 231

7.9 Outlook 238

7.10 Appendix A: Supplementary Derivations 241

7.11 Appendix B: The Saddle PointMethod 242

7.11.1 Integrals on the Real Axis 243

7.11.2 Stationary Phase Method 248

7.12 Appendix C: Treating the Cutoff Region: Regularization of Divergent Stationary Phase Solutions 250

7.13 Appendix D: Finding Saddle Points for the Lewenstein Model 251

References 253

8 Time-Dependent Schrödinger Equation 257
Armin Scrinzi

8.1 Atoms and Molecules in Laser Fields 258

8.2 Solving the TDSE 259

8.2.1 Discretization of the TDSE 260

8.2.2 Finite Elements 263

8.2.3 Scaling with Laser Parameters 265

8.3 Time Propagation 266

8.3.1 Runge–Kutta Methods 267

8.3.2 Krylov Subspace Methods 268

8.3.3 Split-Step Methods 269

8.4 Absorption of Outgoing Flux 269

8.4.1 Absorption for a One-Dimensional TDSE 270

8.5 Observables 272

8.5.1 Ionization and Excitation 272

8.5.2 Harmonic Response 274

8.5.3 Photoelectron Spectra 275

8.6 Two-Electron Systems 278

8.6.1 Very Large-Scale Grid-Based Approaches 278

8.6.2 Basis and Pseudospectral Approaches 278

8.7 Few-Electron Systems 282

8.7.1 MCTDHF: Multiconfiguration Time-Dependent Hartree–Fock 283

8.7.2 Dynamical Multielectron Effects in High Harmonic Generation 285

8.8 Nuclear Motion 287

References 290

9 Angular Distributions in Molecular Photoionization 293
Robert R. Lucchese and Danielle Dowek

9.1 Introduction 293

9.2 One-Photon Photoionization in the Molecular Frame 297

9.3 Methods for Computing Cross-Sections 302

9.4 Post-orientation MFPADs 304

9.4.1 MFPADs for Linear Molecules in the Axial Recoil Approximation 304

9.4.2 MFPADs forNonlinearMolecules in the Axial Recoil Approximation 306

9.4.3 Breakdown of the Axial Recoil Approximation Due to Rotation 308

9.4.4 Breakdown of the Axial Recoil Approximation Due to Vibrational Motion 309

9.4.5 Electron Frame Photoelectron Angular Distributions 309

9.5 MFPADs from Concurrent Orientation in Multiphoton Ionization 310

9.6 Pre-orientation or Alignment, Impulsive Alignment 314

9.7 Conclusions 315

References 315

Part Three High Harmonic Generation and Attosecond Pulses 321

10 High-Order Harmonic Generation and Attosecond Light Pulses: An Introduction 323
Anne L’Huillier

10.1 Early Work, 1987–1993 323

10.2 Three-Step Model, 1993–1994 325

10.3 Trajectories and Phase Matching, 1995–2000 328

10.4 Attosecond Pulses 2001 331

10.5 Conclusion 332

References 335

11 Strong-Field Interactions at Long Wavelengths 339
Manuel Kremer, Cosmin I. Blaga, Anthony D. DiChiara, Stephen B. Schoun, Pierre Agostini, and Louis F. DiMauro

11.1 Theoretical Background 340

11.1.1 Keldysh Picture of Ionization in Strong Fields 340

11.1.2 Classical Perspectives on Postionization Dynamics 341

11.1.3 High-Harmonic Generation 342

11.1.4 Wavelength Scaling of High-Harmonic Cutoff and Attochirp 342

11.1.5 In-situ and RABBITT Technique 344

11.2 Mid-IR Sources and Beamlines at OSU 346

11.2.1 2-μm Source 346

11.2.2 3.6-μm Source 347

11.2.3 OSU Attosecond Beamline 347

11.3 Strong-Field Ionization: The Single-Atom Response 348

11.4 High-Harmonic Generation 350

11.4.1 Harmonic Cutoff and Harmonic Yield 350

11.4.2 Attochirp 352

11.4.3 In-situ Phase Measurement 352

11.4.4 RABBITT Method 355

11.5 Conclusions and Future Perspectives 356

References 356

12 Attosecond Dynamics in Atoms 361
Giuseppe Sansone, Francesca Calegari, Matteo Lucchini, and Mauro Nisoli

12.1 Introduction 361

12.2 Single-Electron Atom: Hydrogen 362

12.3 Two-Electron Atom: Helium 365

12.3.1 ElectronicWave Packets 366

12.3.2 Autoionization: Fano Profile 371

12.3.3 Two-Photon Double Ionization 373

12.4 Multielectron Systems 380

12.4.1 Neon: Dynamics of Shake-Up States 381

12.4.2 Neon: Delay in Photoemission 384

12.4.3 Argon: Fano Resonance 386

12.4.4 Krypton: Auger Decay 388

12.4.5 Krypton: Charge Oscillation 390

12.4.6 Xenon: Cascaded Auger Decay 391

References 393

13 Application of Attosecond Pulses to Molecules 395
Franck Lépine

13.1 Attosecond Dynamics in Molecules 395

13.2 State-of-the-Art Experiments Using Attosecond Pulses 397

13.2.1 Ion Spectroscopy 398

13.2.2 Electron Spectroscopy 402

13.2.3 Photo Absorption 404

13.3 Theoretical Work 405

13.3.1 Electron Dynamics in Small Molecules 405

13.3.2 Electron Dynamics in Large Molecules 406

13.4 Perspectives 413

13.4.1 Molecular Alignment and Orientation 413

13.4.2 Electron Delocalization between DNA Group Junction 414

13.4.3 Similar Dynamics in Water and Ice 416

13.4.4 More 416

13.5 Conclusion 416

References 417

14 Attosecond Nanophysics 421
Frederik Süßmann, Sarah L. Stebbings, Sergey Zherebtsov, Soo Hoon Chew, Mark I. Stockman, Eckart Rühl, Ulf Kleineberg, Thomas Fennel, and Matthias F. Kling

14.1 Introduction 421

14.2 Attosecond Light-Field Control of Electron Emission and Acceleration from Nanoparticles 425

14.2.1 Imaging of the Electron Emission from Isolated Nanoparticles 426

14.2.2 Microscopic Analysis of the Electron Emission 429

14.3 Few-Cycle Pump-Probe Analysis of Cluster Plasmons 433

14.3.1 Basics of Spectral Interferometry 433

14.3.2 Oscillator Model Results for Excitation with Gaussian Pulses 435

14.3.3 Spectral Interferometry Analysis of Plasmons in Small Sodium Clusters 437

14.4 Measurements of Plasmonic Fields with Attosecond Time Resolution 439

14.4.1 Attosecond Nanoplasmonic Streaking 439

14.4.2 The Regimes of APS Spectroscopy 441

14.4.3 APS Spectroscopy of Collective Electron Dynamics in Isolated Nanoparticles 442

14.4.4 Attosecond Nanoscope 444

14.4.5 Experimental Implementation of the Attosecond Nanoscope 446

14.5 Nanoplasmonic Field-Enhanced XUV Generation 449

14.5.1 Tailoring of Nanoplasmonic Field Enhancement for HHG 450

14.5.2 Generation of Single Attosecond XUV Pulses in Nano-HHG 452

14.6 Conclusions and Outlook 454

References 455

Part Four Ultra Intense X-Ray Free Electron Laser Experiments 463

15 Strong-Field Interactions at EUV and X-Ray Wavelengths 465
Artem Rudenko

15.1 Introduction 465

15.2 Experimental Background 467

15.2.1 What Is a “Strong” Field? 467

15.2.2 Basic Parameters of Intense High-Frequency Radiation Sources 469

15.2.3 Detection Systems 471

15.3 Atoms and Molecules under Intense EUV Light 473

15.3.1 Two-Photon Single Ionization of Helium 473

15.3.2 Few-Photon Double Ionization of Helium and Neon 476

15.3.3 Multiple Ionization of Atoms 485

15.3.4 EUV-Induced Fragmentation of Simple Molecules 487

15.4 EUV Pump–EUV Probe Experiments 493

15.4.1 Split-and-Delay Arrangements and Characterization of the EUV Pulses 493

15.4.2 Nuclear Wave Packet Imaging in Diatomic Molecules 495

15.4.3 Isomerization Dynamics of Acetylene Cations 498

15.5 Experiments in the X-Ray Domain 499

15.5.1 Multiple Ionization of Heavy Atoms: Role of Resonant Excitations 500

15.5.2 Multiphoton Ionization of Molecules Containing High-Z Atoms 506

15.6 Summary and Outlook 510

References 512

16 Ultraintense X-Ray Interactions at the Linac Coherent Light Source 529
Linda Young

16.1 Introduction 529

16.1.1 Comparison of Ultrafast, Ultraintense Optical, and X-Ray Lasers 531

16.1.2 X-Ray Atom Interactions 533

16.2 Atomic and Molecular Response to Ultraintense X-Ray Pulses 536

16.2.1 Nonresonant High-Intensity X-Ray Phenomena 537

16.2.2 Resonant High-Intensity X-Ray Phenomena 540

16.3 Ultrafast X-Ray Probes of Dynamics 543

16.4 Characterization of LCLS Pulses 544

16.5 Outlook 546

References 549

17 Coherent Diffractive Imaging 557
Willem Boutu, Betrand Carré, and Hamed Merdji

17.1 Introduction 557

17.2 Far-Field Diffraction 559

17.2.1 Optical Point of View 559

17.2.2 Born Approximation 561

17.2.3 Resolution 562

17.2.4 Comments on the Approximations 564

17.3 Source Requirements 565

17.3.1 Coherence 565

17.3.2 Signal-to-Noise Ratio 568

17.3.3 Dose 569

17.3.4 Different XUV Sources Comparison 572

17.4 Solving the Phase Problem 572

17.4.1 Oversampling Method 572

17.4.2 Basics on Iterative Phasing Algorithms 574

17.4.3 Implementations of Phase Retrieval Algorithms 577

17.5 Holography 583

17.5.1 Fourier Transform Holography 583

17.5.2 HERALDO 587

17.6 Conclusions 590

References 592

Index 599