Ultrafast Optics Andrew M. Weiner Wiley Series in Pure and Applied Optics Glenn D. Boreman, Series Editor

Andrew M. Weiner is the Scifres Family Distinguished Professor of Electrical and Computer Engineering at Purdue University. Professor Weiner is the coeditor of two conference proceedings and has published six book chapters, over 200 journal articles, and over 350 conference papers. His research focuses on ultrafast optical signal processing, high-speed optical communications, and ultrabroadband radio-frequency photonics. He is especially well known for pioneering the field of femtosecond pulse shaping, for which he has received numerous awards.

Preface	p. xiii
Introduction and Review	p. 1
Introduction to Ultrashort Laser Pulses	p. 1
Brief Review of Electromagnetics	p. 4
Maxwell's Equations	p. 4
The Wave Equation and Plane Waves	p. 6
Poynting's Vector and Power Flow	p. 8
Review of Laser Essentials	p. 10
Steady-State Laser Operation	p. 10
Gain and Gain Saturation in Four-Level Atoms	p. 15
Gaussian Beams and Transverse Laser Modes	p. 17
Introduction to Ultrashort Pulse Generation Through Mode-Locking	p. 22
Fourier Series and Fourier Transforms	p. 25
Analytical Aspects	p. 25
Computational Aspects	p. 28
Problems	p. 30
Principles of Mode-Locking	p. 32
Processes Involved in Mode-Locking	p. 32
Active Mode-Locking	p. 33
Time-Domain Treatment	p. 34
Frequency-Domain Treatment	p. 40
Variations of Active Mode-Locking	p. 43
Passive Mode-Locking Using Saturable Absorbers	p. 44
Saturation Model	p. 47
Slow Saturable Absorber Mode-Locking	p. 50
Fast Saturable Absorber Mode-Locking	p. 54
Solid-State Laser Model-Locking Using the Optical Kerr Effect	p. 57
Nonlinear Refractive Index Changes	p. 57
Self-Amplitude Modulation, Self-Phase Modulation, and Group Velocity Dispersion	p. 58
Additive Pulse Mode-Locking	p. 60
Kerr Lens Mode-Locking	p. 64
Mode-Locking Solutions	p. 75
Initiation of Mode-Locking	p. 81
Problems	p. 83
Ultrafast-pulse Measurement Methods	p. 85
Terminology and Definitions	p. 85
Electric Field Autocorrelation Measurements and the Power Spectrum	p. 88
Electric Field Cross-Correlation Measurements and Spectral Interferometry	p. 91
Electric Field Cross-Correlation	p. 92
Spectral Interferometry	p. 93
Application: Optical Coherence Tomography	p. 96
Intensity Correlation Measurements	p. 99
Correlation Measurements Using Second-Harmonic Generation	p. 99
Experimental Procedures	p. 108
Correlation Measurements Using Two-Photon absorption	p. 110
Higher-Order Correlation Techniques	p. 111
Chirped Pulses and Measurements in the Time-Frequency Domain	p. 112
Frequency-Resolved Optical Gating	p. 118
Polarization-Gating FROG	p. 119
Self-Diffraction FROG	p. 122
Second-Harmonic-Generation FROG	p. 124
Frequency-Resolved Optical Gating Using Temporal Phase Modulation	p. 125
Signal Recovery from FROG Traces	p. 126
Pulse Measurements Based on Frequency Filtering	p. 130
Single-Slit Approaches	p. 131
Double-Slit Approach	p. 134
Self-Referencing Interferometry	p. 135
Time-Domain Interferometry of Chirped Pulses	p. 135
Self-Referencing Spectral Interferometry	p. 135
Characterization of Noise and Jitter	p. 139
Problems	p. 144
Dispersion and Dispersion Compensation	p. 147
Group Velocity Dispersion	p. 147
Group Velocity Definition and General Dispersion Relations	p. 147
General Aspects of Material Dispersion	p. 151
Temporal Dispersion Based on Angular Dispersion	p. 155
Relation Between Angular and Temporal Dispersion	p. 155
Angular Dispersion and Tilted Intensity Fronts	p. 159
Dispersion of Grating Pairs	p. 161
Dispersion of Prism Pairs	p. 166
Dispersive Properties of Lenses	p. 173
Dispersion of Mirror Structures	p. 177
The Gires-Tournois Interferometer	p. 178
Quarter-Wave Stack High Reflectors	p. 180
Chirped Mirrors	p. 182
Measurements of Group Velocity Dispersion	p. 186
Interferometric Methods	p. 187
Frequency-Domain Intracavity Dispersion Measurements	p. 190
Appendix	p. 191
Frequency-Dependent Phase Due to Propagation Through a Slab: Alternative Derivation	p. 191
Impedance Method for Analysis of Dielectric Mirror Stacks	p. 192
Problems	p. 195
Ultrafast Nonlinear Optics: Second Order	p. 198
Introduction to Nonlinear Optics	p. 198
The Forced Wave Equation	p. 201
Frequency-Domain Formulation	p. 202
Time-Domain Formulation	p. 203
Summary of Continuous-Wave Second-Harmonic Generation	p. 204
Effect of Phase Matching	p. 207
Phase Matching in Birefringent Media	p. 209
Focusing Effects in Continuous-Wave SHG	p. 215
Second-Harmonic Generation with Pulses	p. 220
SHG in the Quasi-Continuous-Wave Limit	p. 220
Ultrashort-Pulse SHG	p. 221
Quasi-Phase Matching	p. 228
Effect of Group Velocity Walk-off on SHG-Based Pulse Measurements	p. 233
Three-Wave Interactions	p. 237
Sum Frequency Generation	p. 240
Difference Frequency Generation	p. 244
Optical Parametric Amplification	p. 245
Appendix	p. 253
Spatial Walk-off and Pulse Fronts in Anisotropic Media	p. 253
Velocity Matching in Broadband Noncollinear Three-Wave Mixing	p. 254
Problems	p. 256
Ultrafast Nonlinear Optics: Third Order	p. 258
Propagation Equation for Nonlinear Refractive Index Media	p. 258
Plane Waves in Uniform Media	p. 260
Nonlinear Propagation in Waveguides	p. 261
Optical Fiber Types	p. 264
The Nonlinear Schröet;dinger Equation	p. 266
Self-Phase Modulation	p. 270
Dispersionless Self-Phase Modulation	p. 270
Dispersionless Self-Phase Modulation with Loss	p. 273
Self-Phase Modulation with Normal Dispersion	p. 274
Cross-Phase Modulation	p. 275
Pulse Compression	p. 276
Modulational Instability	p. 283
Solitons	p. 286
Higher-Order Propagation Effects	p. 291
Nonlinear Envelope Equation in Uniform Media	p. 292
Nonlinear Envelope Equation in Waveguides	p. 295
Delayed Nonlinear Response and the Raman Effect	p. 296
Self-Steepening	p. 306
Space-Time Focusing	p. 308
Continuum Generation	p. 310
Problems	p. 313
Mode-Locking: Selected Advanced Topics	p. 316
Soliton Fiber Lasers: Artificial Fast Saturable Absorbers	p. 316
The Figure-Eight Laser	p. 317
Energy Quantization	p. 322
Soliton Sidebands	p. 324
Soliton Mode-Locking: Active Modulation and Slow Saturable Absorbers	p. 328
Harmonically Mode-Locked Soliton Fiber Lasers	p. 328
The Net Gain Window in Soliton Mode-Locking	p. 330
Stretched Pulse Mode-Locking	p. 337
Stretched Pulse Mode-Locked Fiber Laser	p. 337
Dispersion-Managed Solitons	p. 340
Theoretical Issues	p. 342
Mode-Locked Lasers in the Few-Cycle Regime	p. 344
Mode-Locked Frequency Combs	p. 347
Comb Basics	p. 347
Measurement Techniques	p. 350
Stabilization of Frequency Combs	p. 354
Applications	p. 356
Problems	p. 360
Manipulation of Ultrashort Pulses	p. 362
Fourier Transform Pulse Shaping	p. 362
Examples of Pulse Shaping Using Fixed Masks	p. 364
Programmable Pulse Shaping	p. 369
Pulse-Shaping Theory	p. 376
Other Pulse-Shaping Techniques	p. 386
Direct Space-to-Time Pulse Shaping	p. 386
Acousto-optic Dispersive Filters	p. 390
Chirp Processing and Time Lenses	p. 394
Space-Time Duality	p. 394
Chirp Processing	p. 397
Time Lens Processing	p. 399
Ultrashort-Pulse Amplification	p. 405
Amplification Basics	p. 406
Special Issues in Femtosecond Amplifiers	p. 411
Appendix	p. 416
Fresnel Diffraction and Fourier Transform Property of a Lens	p. 416
Wave Optics Model of a Grating	p. 418
Problems	p. 420
Ultrafast Time-Resolved Spectroscopy	p. 422
Introduction to Ultrafast Spectroscopy	p. 422
Degenerate Pump-Probe Transmission Measurements	p. 426
Co-polarized Fields: Scalar Treatment	p. 426
Vector Fields and Orientational Effects	p. 431
Nondegenerate and Spectrally Resolved Pump-Probe: Case Studies	p. 439
Femtosecond Pump-Probe Studies of Dye Molecules	p. 440
Femtosecond Pump-Probe Studies of GaAs	p. 444
Basic Quantum Mechanics for Coherent Short-Pulse Spectroscopies	p. 451
Some Basic Quantum Mechanics	p. 451
The Density Matrix	p. 456
Wave Packets	p. 460
Example: Semiconductor Quantum Wells	p. 461
Molecules	p. 462
Dephasing Phenomena	p. 469
Linear Spectroscopies	p. 469
Models of Dephasing	p. 475
Measurement of Dephasing Using Transient Gratings	p. 481
Two-Dimensional Spectroscopy	p. 494
Impulsive Stimulated Raman Scattering	p. 499
Problems	p. 505
Terahertz Time-Domain Electromagnetics	p. 507
Ultrafast Electromagnetics: Transmission Lines	p. 507
Photoconductive Generation and Sampling	p. 507
Electro-optic Sampling	p. 513
Ultrafast Electromagnetics: Terahertz Beams	p. 516
Generation and Measurement of Terahertz Pulses	p. 517
Terahertz Spectroscopy and Imaging	p. 527
Problems	p. 531
References	p. 533
Index	p. 563
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