Theory of Nonlinear Propagation of High Harmonics Generated in a Gaseous Medium (Springer Theses)

__Theory of Nonlinear Propagation of High Harmonics Generated in a Gaseous Medium__ establishes the theoretical tools to study High-Order Harmonic Generation (HHG) by intense ultrafast infrared lasers in atoms and molecules. The macroscopic propagation of both laser and high-harmonic fields is taken into account by solving Maxwell's wave equations, while the single-atom or single-molecule response is treated with a quantitative rescattering theory by solving the time-dependent Schrödinger equation. This book demonstrates for the first time that observed experimental HHG spectra of atoms and molecules can be accurately reproduced theoretically when precise experimental conditions are known. The macroscopic HHG can be expressed as a product of a macroscopic wave packet and a photorecombination cross section, where the former depends on laser and experimental conditions while the latter is the property of target atoms or molecules. The factorization makes it possible to retrieve microscopically atomic or molecular structure information from the measured macroscopic HHG spectra. This book also investigates other important issues about HHG, such as contributions from multiple molecular orbitals, the minimum in the HHG spectrum, the spatial mode of laser beams, and the generation of an isolated attosecond pulse. Additionally, this book presents the photoelectron angular distribution of aligned molecules ionized by the HHG light. Supervisor’s Foreword 8 Acknowledgments 10 Contents 12 1 Introduction to High-Order Harmonic Generation 16 1.1 Background 16 1.2 Single-Atom Response 18 1.2.1 Three-Step Model 18 1.2.2 Wavelength Scaling and Attochirp 22 1.3 Macroscopic Propagation Effects 24 1.3.1 Phase Matching Conditions 24 1.3.2 Absorption Effect 26 1.3.3 Spatiotemporal Dynamics of Laser Pulse 28 1.4 Applications of High-Order Harmonic Generation 29 1.4.1 Generation of APT and IAP 29 1.4.2 Probing Electronic Structure and Dynamics 30 1.4.3 Single-Photon Ionization of Aligned Molecules 32 1.5 Thesis Outline 33 References 33 2 Theoretical Tools 39 2.1 Introduction 39 2.2 Time-Dependent Schrödinger Equation 40 2.2.1 Semiclassical Theory 40 2.2.2 Strong-Field Approximation 42 2.2.3 Quantitative Rescattering Theory 45 2.3 Maxwell's Wave Equation 48 2.3.1 Fundamental Laser Field in an Atomic Target 48 2.3.2 High-Harmonic Field of an Atomic Target 50 2.3.3 High-Harmonic Field of Aligned Molecules 51 2.4 Far-Field Harmonic Emission 54 References 55 3 Medium Propagation Effects in High-Order Harmonic Generation of Ar 59 3.1 Introduction 59 3.2 Macroscopic HHG Spectra: QRS Versus TDSE 60 3.2.1 Strength of High Harmonics 61 3.2.2 Phase of High Harmonics 63 3.3 Macroscopic HHG Spectra: Theory Versus Experiment 64 3.4 Disappearance of Cooper Minimum in the HHG Spectrum of Ar 65 3.5 Macroscopic Wave Packet 67 3.5.1 Independence of Macroscopic Wave Packet on Targets 67 3.5.2 Separation of Target Structure Information from HHG Spectra 68 3.5.3 Dependence of Macroscopic Wave Packet on Experimental Conditions 69 3.6 Wavelength Scaling of Harmonic Efficiency 70 3.7 Conclusion 73 References 74 4 Comparison of High-Order Harmonic Generation of Ar Using a Truncated Bessel or a Gaussian Beam 76 4.1 Introduction 76 4.2 Simulations of HHG Spectra of Ar 77 4.2.1 780-nm Few-Cycle Laser 77 4.2.2 1800-nm Few-Cycle Laser 80 4.3 Phase Matching Conditions at Low Gas Pressure 80 4.3.1 Phase Matching Map at Low Gas Pressure 81 4.3.2 Dependence of Harmonic Yield on Gas-Jet Position 83 4.4 Gas Pressure Induced Phase Mismatch 86 4.5 Conclusion 87 References 88 5 Generation of an Isolated Attosecond Pulse in the Far Field by Spatial Filtering with an Intense Few-Cycle Mid-infrared Laser 90 5.1 Introduction 90 5.2 Macroscopic HHG Spectra of Xe Using an 1825-nm Few-Cycle Laser 91 5.2.1 Photorecombination Dipole Moment of Xe in the QRS Theory 91 5.2.2 Macroscopic HHG Spectra of Xe at Low and High Intensities 92 5.3 Spatiotemporal Evolution of Fundamental Laser Field 93 5.4 Time-Frequency Representation of High Harmonics 94 5.4.1 Wavelet Analysis of Attosecond Pulses 94 5.4.2 Time-Frequency Analysis of High Harmonics in Near and Far Fields 96 5.5 Spectral and Spatial Filtering in the Generation of Attosecond Pulses 99 5.6 CEP Dependence of Isolated Attosecond Pulses 101 5.7 Comparison Between QRS and SFA in Modeling Propagation Effects 102 5.8 Conclusion 103 References 104 6 Effects of Macroscopic Propagation and Multiple Molecular Orbitals on the High-Order Harmonic Generation of Aligned N2 and CO2 Molecules 106 6.1 Introduction 106 6.2 HOMO Contribution in HHG of Random and Aligned N2 108 6.2.1 Macroscopic HHG Spectra: Theory Versus Experiment 108 6.2.2 Separation of PR Transition Dipole from HHG Spectra 110 6.3 Intensity Dependence of Multiple Orbital Contributions in HHG of Aligned N2 111 6.3.1 Macroscopic HHG Spectra: Theory Versus Experiment 111 6.3.2 Single Orbital (HOMO) Contribution at Low Laser Intensity 113 6.3.3 Multiple Orbital (HOMO and HOMO-1) Contributions at Higher Laser Intensity 113 6.4 Shape Resonance in Photoionization and HHG of N2 115 6.4.1 PICSs and Phases from HOMO and HOMO-1 Orbitals 115 6.4.2 Shape Resonance in HHG of Aligned N2 117 6.5 Contributions of Multiple Molecular Orbitals in HHG of Aligned CO2 118 6.5.1 Macroscopic HHG Spectra: Theory Versus Experiment 118 6.5.2 Origin of Minimum in the HHG Spectrum of Aligned CO2 120 6.6 Major Factors that Influence the Positions of Minima in HHG Spectra 122 6.6.1 Progression of Harmonic Minimum Versus Laser Intensity 122 6.6.2 Other Factors Influencing Precise Positions of HHG Minima 123 6.7 Conclusion 126 References 127 7 Photoelectron Angular Distributions in Single-Photon Ionization of Aligned N2 and CO2 Molecules Using XUV Light 131 7.1 Introduction 131 7.2 Connection Between Photoionization and HHG 132 7.3 Total Photoionization Yield from Aligned N2 and CO2 134 7.3.1 Single-Photon Ionization Yield of Aligned N2: Theory Versus Experiment 134 7.3.2 Single-Photon Ionization Yield of Aligned CO2: Theory Versus Eexperiment 136 7.4 Photoelectron Angular Distributions (PADs) of Fixed-in-Space N2 in the Laboratory Frame 137 7.5 PADs of Transiently Aligned N2 in the Laboratory Frame 138 7.5.1 PADs at Low Degree of Alignment 138 7.5.2 PADs at High Degree of Alignment 139 7.6 Photon Energy Dependence of PADs for Aligned N2 140 7.7 PADs of Transiently Aligned CO2 in the Laboratory Frame 141 7.7.1 PADs of Fixed-in-space CO2 141 7.7.2 PADs of Aligned CO2 142 7.8 Conclusion 143 References 144 8 Summary 146 References 148 Appendix AAbbreviations 150 Appendix BTheory of Alignment for Linear Molecules 152 Appendix CPhotorecombination Transition Dipole 154 References 160 Appendix DSpatial Mode of Laser Beam: Gaussian BeamVersus Truncated Bessel Beam 161 Curriculum Vitae 169 Theory of Nonlinear Propagation of High Harmonics Generated in a Gaseous Medium establishes the theoretical tools to study High-Order Harmonic Generation (HHG) by intense ultrafast infrared lasers in atoms and molecules. The macroscopic propagation of both laser and high-harmonic fields is taken into account by solving Maxwell's wave equations, while the single-atom or single-molecule response is treated with a quantitative rescattering theory by solving the time-dependent Schrd inger equation. This book demonstrates for the first time that observed experimental HHG spectra of atoms and molecules can be accurately reproduced theoretically when precise experimental conditions are known. The macroscopic HHG can be expressed as a product of a macroscopic wave packet and a photorecombination cross section, where the former depends on laser and experimental conditions while the latter is the property of target atoms or molecules. The factorization makes it possible to retrieve microscopically atomic or molecular structure information from the measured macroscopic HHG spectra. This book also investigates other important issues about HHG, such as contributions from multiple molecular orbitals, the minimum in the HHG spectrum, the spatial mode of laser beams, and the generation of an isolated attosecond pulse. Additionally, this book presents the photoelectron angular distribution of aligned molecules ionized by the HHG light Front Matter....Pages i-xiv Introduction to High-Order Harmonic Generation....Pages 1-23 Theoretical Tools....Pages 25-44 Medium Propagation Effects in High-Order Harmonic Generation of Ar....Pages 45-61 Comparison of High-Order Harmonic Generation of Ar Using a Truncated Bessel or a Gaussian Beam....Pages 63-76 Generation of an Isolated Attosecond Pulse in the Far Field by Spatial Filtering with an Intense Few-Cycle Mid-infrared Laser....Pages 77-92 Effects of Macroscopic Propagation and Multiple Molecular Orbitals on the High-Order Harmonic Generation of Aligned N $$_2$$ and CO $$_2$$ Molecules....Pages 93-117 Photoelectron Angular Distributions in Single-Photon Ionization of Aligned N $$_2$$ 2 and CO $$_2$$ 2 Molecules Using XUV Light....Pages 119-133 Summary....Pages 135-138 Back Matter....Pages 139-159