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Ultrashort Laser Pulse Phenomena, 2nd Edition

by Jean-Claude Professor Diels, Jean-Claude Diels, Wolfgang Rudolph

September 2006

Intermediate to advanced

680 pages

22h 22m

English

Academic Press

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Front cover
Title page
Copyright page
Table of contents (1/2)
Table of contents (2/2)
Preface
Preface to the First Edition
Why Ultrashort Pulse Phenomena?
BIBLIOGRAPHY
1 Fundamentals
1.1. CHARACTERISTICS OF FEMTOSECOND LIGHT PULSES1.1.1. Complex Representation of the Electric Field

1.1.2. Power, Energy, and Related Quantities
1.1.3. Pulse Duration and Spectral Width
1.1.4. Wigner Distribution, Second-Order Moments, Uncertainty Relations (1/2)
1.1.4. Wigner Distribution, Second-Order Moments, Uncertainty Relations (2/2)
1.2. PULSE PROPAGATION
1.2.1. The Reduced Wave Equation
1.2.2. Retarded Frame of Reference
1.2.3. Dispersion
1.2.4. Gaussian Pulse Propagation
1.2.5. Complex Dielectric Constant
1.3. INTERACTION OF LIGHT PULSES WITH LINEAR OPTICAL ELEMENTS
1.4. GENERATION OF PHASE MODULATION
1.5. BEAM PROPAGATION
1.5.1. General
1.5.2. Analogy between Pulse and Beam Propagation
1.5.3. Analogy between Spatial and Temporal Imaging
1.6. NUMERICAL MODELING OF PULSE PROPAGATION
1.7. SPACE–TIME EFFECTS
1.8. PROBLEMS
BIBLIOGRAPHY
2 Femtosecond Optics
2.1. INTRODUCTION
2.2. WHITE LIGHT AND SHORT PULSE INTERFEROMETRY (1/2)
2.2. WHITE LIGHT AND SHORT PULSE INTERFEROMETRY (2/2)
2.3. DISPERSION OF INTERFEROMETRIC STRUCTURES
2.3.1. Mirror Dispersion
2.3.2. Fabry–Perot and Gires–Tournois Interferometer (1/2)
2.3.2. Fabry–Perot and Gires–Tournois Interferometer (2/2)
2.3.3. Chirped Mirrors
2.4. FOCUSING ELEMENTS
2.4.1. Singlet Lenses
2.4.2. Space–Time Distribution of the Pulse Intensity at the Focus of a Lens
2.4.3. Achromatic Doublets
2.4.4. Focusing Mirrors
2.5. ELEMENTS WITH ANGULAR DISPERSION
2.5.1. Introduction
2.5.2. Tilting of Pulse Fronts
2.5.3. GVD through Angular Dispersion—General
2.5.4. GVD of a Cavity Containing a Single Prism
2.5.5. Group Velocity Control with Pairs of Prisms (1/3)
2.5.5. Group Velocity Control with Pairs of Prisms (2/3)
2.5.5. Group Velocity Control with Pairs of Prisms (3/3)
2.5.6. GVD Introduced by Gratings
2.5.7. Grating Pairs for Pulse Compressors
2.5.8. Combination of Focusing and Angular Dispersive Elements
2.6. WAVE-OPTICAL DESCRIPTION OF ANGULAR DISPERSIVE ELEMENTS (1/2)
2.6. WAVE-OPTICAL DESCRIPTION OF ANGULAR DISPERSIVE ELEMENTS (2/2)
2.7. OPTICAL MATRICES FOR DISPERSIVE SYSTEMS (1/2)
2.7. OPTICAL MATRICES FOR DISPERSIVE SYSTEMS (2/2)
2.8. NUMERICAL APPROACHES
2.9. PROBLEMS
BIBLIOGRAPHY
3 Light–Matter Interaction
3.1. DENSITY MATRIX EQUATIONS (1/2)
3.1. DENSITY MATRIX EQUATIONS (2/2)
3.2. PULSE SHAPING WITH RESONANT PARTICLES
3.2.1. General
3.2.2. Pulses Much Longer Than the Phase Relaxation Time (τp >> T2)
3.2.3. Phase Modulation by Quasi-Resonant Interactions
3.2.4 Pulse Durations Comparable with or Longer Than the Phase Relaxation Time (τp ≥ T2)
3.3. NONLINEAR, NONRESONANT OPTICAL PROCESSES
3.3.1. General
3.3.2. Noninstantaneous Response
3.3.3. Pulse Propagation
3.4. SECOND HARMONIC GENERATION (SHG)
3.4.1. Type I Second Harmonic Generation (1/2)
3.4.1. Type I Second Harmonic Generation (2/2)
3.4.2. Second Harmonic Type II: Equations for Arbitrary Phase Mismatch and Conversion Efficiencies
3.4.3. Pulse Shaping in Second Harmonic Generation (Type II)
3.4.4. Group Velocity Control in SHG through Pulse Front Tilt
3.5. OPTICAL PARAMETRIC INTERACTION
3.5.1. Coupled Field Equations
3.5.2. Synchronous Pumping
3.5.3. Chirp Amplification
3.6. THIRD-ORDER SUSCEPTIBILITY
3.6.1. Fundamentals
3.6.2. Short Samples with Instantaneous Response
3.6.3. Short Samples and Noninstantaneous Response
3.6.4. Counter-Propagating Pulses and Third-Order Susceptibility
3.7. CONTINUUM GENERATION
3.8. SELF-FOCUSING
3.8.1. Critical Power
3.8.2. The Nonlinear Schrödinger Equation
3.9. BEAM TRAPPING AND FILAMENTS
3.9.1. Beam Trapping
3.9.2. Ultrashort Pulse Self-Focusing
3.10. PROBLEMS
BIBLIOGRAPHY (1/2)
BIBLIOGRAPHY (2/2)
4 Coherent Phenomena
4.1. FROM COHERENT TO INCOHERENT INTERACTIONS
4.2. COHERENT INTERACTIONS WITH TWO-LEVEL SYSTEMS
4.2.1. Maxwell-Bloch Equations
4.2.2. Rate Equations
4.2.3. Evolution Equations (1/2)
4.2.3. Evolution Equations (2/2)
4.2.4. Steady-State Pulses
4.3. MULTIPHOTON COHERENT INTERACTION
4.3.1. Introduction
4.3.2. Multiphoton Multilevel Transitions (1/3)
4.3.2. Multiphoton Multilevel Transitions (2/3)
4.3.2. Multiphoton Multilevel Transitions (3/3)
4.3.3. Simplifying a N-Level System to a Two-Level Transition
4.3.4. Four Photon Resonant Coherent Interaction (1/2)
4.3.4. Four Photon Resonant Coherent Interaction (2/2)
4.3.5. Miscellaneous Applications
4.4. PROBLEMS
BIBLIOGRAPHY
5 Ultrashort Sources I: Fundamentals
5.1. INTRODUCTION5.1.1. Superposition of Cavity Modes
5.1.2. Cavity Modes and Modes of a Mode-Locked Laser
5.1.3. The "Perfect” Mode-Locked Laser
5.1.4. The "Common” Mode-Locked Laser (1/2)
5.1.4. The "Common” Mode-Locked Laser (2/2)
5.1.5. Basic Elements and Operation of a fs Laser
5.2. CIRCULATING PULSE MODEL
5.2.1. General Round-Trip Model
5.2.2. Continuous Model
5.2.3. Elements of a Numerical Treatment
5.2.4. Elements of an Analytical Treatment
5.3. EVOLUTION OF THE PULSE ENERGY
5.3.1. Rate Equations for the Evolution of the Pulse Energy (1/2)
5.3.1. Rate Equations for the Evolution of the Pulse Energy (2/2)
5.3.2. Connection of the Model to Microscopic Parameters
5.4. PULSE SHAPING IN INTRACAVITY ELEMENTS
5.4.1. Saturation
5.4.2. Nonlinear Nonresonant Elements
5.4.3. Self-Lensing
5.4.4. Summary of Compression Mechanisms
5.4.5. Dispersion
5.5. CAVITIES
5.5.1. Cavity Modes and ABCD Matrix Analysis
5.5.2. Astigmatism and Its Compensation
5.5.3. Cavity with a Kerr Lens
5.6. PROBLEMS
BIBLIOGRAPHY
6 Ultrashort Sources II: Examples
6.1. SYNCHRONOUS MODE-LOCKING
6.2. HYBRID MODE-LOCKING
6.3. ADDITIVE PULSE MODE-LOCKING
6.3.1. Generalities
6.3.2. Analysis of APML
6.4. MODE-LOCKING BASED ON NONRESONANT NONLINEARITY
6.4.1. Nonlinear Mirror
6.4.2. Polarization Rotation
6.5. NEGATIVE FEEDBACK
6.6. SEMICONDUCTOR-BASED SATURABLE ABSORBERS
6.7. SOLID-STATE LASERS
6.7.1. Generalities
6.7.2. Ti:sapphire Laser
6.7.3. Cr:LiSAF, Cr:LiGAF, Cr:LiSGAF, and Alexandrite
6.7.4. Cr:Forsterite and Cr:Cunyite Lasers
6.7.5. YAG Lasers
6.7.6. Nd: YVO4 and Nd: YLF
6.8. SEMICONDUCTOR AND DYE LASERS
6.8.1. Dye Lasers
6.8.2. Semiconductor Lasers
6.9. FIBER LASERS
6.9.1. Introduction
6.9.2. Raman Soliton Fiber Lasers
6.9.3. Doped Fiber Lasers
6.9.4. Mode-Locking through Polarization Rotation
6.9.5. Figure-Eight Laser
BIBLIOGRAPHY (1/2)
BIBLIOGRAPHY (2/2)
7 Femtosecond Pulse Amplification
7.1. INTRODUCTION
7.2. FUNDAMENTALS
7.2.1. Gain Factor and Saturation
7.2.2. Shaping in Amplifiers
7.2.3. Amplified Spontaneous Emission (ASE)
7.3. NONLINEAR REFRACTIVE INDEX EFFECTS
7.3.1. General
7.3.2. Self-Focusing
7.3.3. Thermal Noise
7.3.4. Combined Pulse Amplification and Chirping
7.4. CHIRPED PULSE AMPLIFICATION (CPA)
7.5. AMPLIFIER DESIGN
7.5.1. Gain Media and Pump Pulses
7.5.2. Amplifier Configurations
7.5.3. Single-Stage, Multipass Amplifiers
7.5.4. Regenerative Amplifiers
7.5.5. Traveling Wave Amplification
7.6. OPTICAL PARAMETRIC CHIRPED PULSE AMPLIFICATION (OPCPA)
7.7. PROBLEMS
BIBLIOGRAPHY
8 Pulse Shaping
8.1. PULSE COMPRESSION8.1.1. General
8.1.2. The Fiber Compressor (1/3)
8.1.2. The Fiber Compressor (2/3)
8.1.2. The Fiber Compressor (3/3)
8.1.3. Pulse Compression Using Bulk Materials
8.2. SHAPING THROUGH SPECTRAL FILTERING
8.3. PROBLEMS
BIBLIOGRAPHY
9 Diagnostic Techniques
9.1. INTENSITY CORRELATIONS
9.1.1. General Properties9.1.2. The Intensity Autocorrelation
9.1.3. Intensity Correlations of Higher Order
9.2. INTERFEROMETRIC CORRELATIONS9.2.1. General Expression
9.2.2. Interferometric Autocorrelation
9.3. MEASUREMENT TECHNIQUES
9.3.1. Nonlinear Optical Processes for Measuring Femtosecond Pulse Correlations9.3.2. Recurrent Signals
9.3.3. Single Shot Measurements
9.4. PULSE AMPLITUDE AND PHASE RECONSTRUCTION
9.4.1. Introduction
9.4.2. Methods for Full-Field Characterization of Ultrashort Light Pulses
9.4.3. Retrieval from Correlation and Spectrum
9.4.4. Frequency Resolved Optical Gating (FROG)
9.4.5. Spectral Phase Interferometry for Direct Electric Field Reconstruction (SPIDER)
9.5. PROBLEMS
BIBLIOGRAPHY
10 Measurement Techniques of Femtosecond Spectroscopy
10.1. INTRODUCTION
10.2. DATA DECONVOLUTIONS
10.3. BEAM GEOMETRY AND TEMPORAL RESOLUTION
10.4. TRANSIENT ABSORPTION SPECTROSCOPY
10.5. TRANSIENT POLARIZATION ROTATION
10.6. TRANSIENT GRATING TECHNIQUES
10.6.1. General Technique
10.6.2. Degenerate Four Wave Mixing (DFWM)
10.7. FEMTOSECOND RESOLVED FLUORESCENCE
10.8. PHOTON ECHOES
10.9. ZERO AREA PULSE PROPAGATION
10.10. IMPULSIVE STIMULATED RAMAN SCATTERING
10.10.1. General Description
10.10.2. Detection
10.10.3. Theoretical Framework
10.10.4. Single Pulse Shaping Versus Mode- Locked Train
10.11. SELF-ACTION EXPERIMENTS
10.12. PROBLEMS
BIBLIOGRAPHY
11 Examples of Ultrafast Processes in Matter
11.1. INTRODUCTION
11.2. ULTRAFAST TRANSIENTS IN ATOMS
11.2.1. The Classical Limit of the Quantum Mechanical Atom11.2.2. The Radial Wave Packet
11.2.3. The Angularly Localized Wave Packet
11.3. ULTRAFAST PROCESSES IN MOLECULES
11.3.1. Observation of Molecular Vibrations
11.3.2. Chemical Reactions
11.3.3. Molecules in Solution
11.4. ULTRAFAST PROCESSES IN SOLID-STATE MATERIALS
11.4.1. Excitation Across the Band Gap
11.4.2. Excitons
11.4.3. Intraband Relaxation
11.4.4. Phonon Dynamics
11.4.5. Laser-Induced Surface Disordering
11.5. PRIMARY STEPS IN PHOTO–BIOLOGICAL REACTIONS
11.5.1. Femtosecond Isomerization of Rhodopsin
11.5.2. Photosynthesis
BIBLIOGRAPHY
12 Generation of Extreme Wavelengths
12.1. GENERATION OF TERAHERTZ (THz) RADIATION (1/2)
12.1. GENERATION OF TERAHERTZ (THz) RADIATION (2/2)
12.2. GENERATION OF ULTRAFAST X-RAY PULSES
12.2.1. Incoherent Bursts of X-Rays
12.2.2. High Harmonics (HH) and Attosecond Pulse Generation
12.3. GENERATION OF ULTRASHORT ACOUSTIC PULSES
12.4. GENERATION OF ULTRAFAST ELECTRIC PULSES
BIBLIOGRAPHY
13 Selected Applications
13.1. IMAGING13.1.1. Introduction
13.1.2. Range Gating with Ultrashort Pulses
13.1.3. Imaging through Scatterers
13.1.4. Prospects for Four-Dimensional Imaging
13.1.5. Microscopy
13.2. SOLITONS
13.2.1. Temporal Solitons
13.2.2. Spatial Solitons and Filaments
13.2.3. Spatial and Temporal Solitons
13.3. SENSORS BASED ON FS LASERS
13.3.1. Description of the Operation
13.3.2. Inertial Measurements (Rotation and Acceleration)
13.3.3. Measurement of Changes in Index (1/2)
13.3.3. Measurement of Changes in Index (2/2)
13.4. STABILIZED MODE-LOCKED LASERS FOR METROLOGY
13.4.1. Measurement of the Carrier to Envelope Offset (CEO)
13.4.2. Locking of fs Lasers to Stable Reference Cavities
13.5. PROBLEM
BIBLIOGRAPHY (1/2)
BIBLIOGRAPHY (2/2)
Appendix A The Uncertainty Principle
Appendix B Phase Shifts on Transmission and Reflection
B.1. THE SYMMETRICAL INTERFACE
B.2. COATED INTERFACE BETWEEN TWO DIFFERENT DIELECTRICS
Appendix C Slowly Evolving Wave Approximation
BIBLIOGRAPHY
Appendix D Four-Photon Coherent Interaction
BIBLIOGRAPHY
Appendix E Kerr Lensing in a Cavity
E.1. ELEMENTARY KERR LENSING MODEL
E.2. EXAMPLE OF A NONLINEAR CAVITY AND GAUSSIAN BEAM ANALYSIS
Appendix F Abbreviations for Dyes
List of Symbols
Index (1/2)
Index (2/2)

Content preview from Ultrashort Laser Pulse Phenomena, 2nd Edition

94 Femtosecond Optics

2.5. ELEMENTS WITH ANGULAR DISPERSION

2.5.1. Introduction

Besides focusing elements there are various other optical components which

modify the temporal characteristics of ultrashort light pulses through a change

of their spatial propagation characteristics.

Even a simple prism can provide food for thought in fs experiments. Let us

consider an expanded parallel beam of short light pulses incident on a prism,

and diffracted by the angle β = β(), as sketched in Figure 2.17. As discussed

in Chapter 1, a Gaussian beam with beam waist w

self-diffracts by an angle

of approximately θ = λ/πw

. In the case of a short pulse (or white light), ...

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Ultrashort Laser Pulse Phenomena, 2nd Edition

by Jean-Claude Professor Diels, Jean-Claude Diels, Wolfgang Rudolph

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