Ultrafast Optics

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 xiii1 Introduction and Review 11.1 Introduction to Ultrashort Laser Pulses 11.2 Brief Review of Electromagnetics 41.2.1 Maxwell’s Equations 41.2.2 The Wave Equation and Plane Waves 61.2.3 Poynting’s Vector and Power Flow 81.3 Review of Laser Essentials 101.3.1 Steady-State Laser Operation 101.3.2 Gain and Gain Saturation in Four-Level Atoms 151.3.3 Gaussian Beams and Transverse Laser Modes 171.4 Introduction to Ultrashort Pulse Generation Through Mode-Locking 221.5 Fourier Series and Fourier Transforms 251.5.1 Analytical Aspects 251.5.2 Computational Aspects 28Problems 302 Principles of Mode-Locking 322.1 Processes Involved in Mode-Locking 322.2 Active Mode-Locking 332.2.1 Time-Domain Treatment 342.2.2 Frequency-Domain Treatment 402.2.3 Variations of Active Mode-Locking 432.3 Passive Mode-Locking Using Saturable Absorbers 442.3.1 Saturation Model 472.3.2 Slow Saturable Absorber Mode-Locking 502.3.3 Fast Saturable Absorber Mode-Locking 542.4 Solid-State Laser Mode-Locking Using the Optical Kerr Effect 572.4.1 Nonlinear Refractive Index Changes 572.4.2 Self-Amplitude Modulation Self-Phase Modulation and Group Velocity Dispersion 582.4.3 Additive Pulse Mode-Locking 602.4.4 Kerr Lens Mode-Locking 642.4.5 Mode-Locking Solutions 752.4.6 Initiation of Mode-Locking 81Problems 833 Ultrafast-pulse Measurement Methods 853.1 Terminology and Definitions 853.2 Electric Field Autocorrelation Measurements and the Power Spectrum 883.3 Electric Field Cross-Correlation Measurements and Spectral Interferometry 913.3.1 Electric Field Cross-Correlation 923.3.2 Spectral Interferometry 933.3.3 Application: Optical Coherence Tomography 963.4 Intensity Correlation Measurements 993.4.1 Correlation Measurements Using Second-Harmonic Generation 993.4.2 Experimental Procedures 1083.4.3 Correlation Measurements Using Two-Photon absorption 1103.4.4 Higher-Order Correlation Techniques 1113.5 Chirped Pulses and Measurements in the Time–Frequency Domain 1123.6 Frequency-Resolved Optical Gating 1183.6.1 Polarization-Gating FROG 1193.6.2 Self-Diffraction FROG 1223.6.3 Second-Harmonic-Generation FROG 1243.6.4 Frequency-Resolved Optical Gating Using Temporal Phase Modulation 1253.6.5 Signal Recovery from FROG Traces 1263.7 Pulse Measurements Based on Frequency Filtering 1303.7.1 Single-Slit Approaches 1313.7.2 Double-Slit Approach 1343.8 Self-Referencing Interferometry 1353.8.1 Time-Domain Interferometry of Chirped Pulses 1353.8.2 Self-Referencing Spectral Interferometry 1373.9 Characterization of Noise and Jitter 139Problems 1444 Dispersion and Dispersion Compensation 1474.1 Group Velocity Dispersion 1474.1.1 Group Velocity Definition and General Dispersion Relations 1474.1.2 General Aspects of Material Dispersion 1514.2 Temporal Dispersion Based on Angular Dispersion 1554.2.1 Relation Between Angular and Temporal Dispersion 1554.2.2 Angular Dispersion and Tilted Intensity Fronts 1594.3 Dispersion of Grating Pairs 1614.4 Dispersion of Prism Pairs 1664.5 Dispersive Properties of Lenses 1734.6 Dispersion of Mirror Structures 1774.6.1 The Gires–Tournois Interferometer 1784.6.2 Quarter-Wave Stack High Reflectors 1804.6.3 Chirped Mirrors 1824.7 Measurements of Group Velocity Dispersion 1864.7.1 Interferometric Methods 1874.7.2 Frequency-Domain Intracavity Dispersion Measurements 1904.8 Appendix 1914.8.1 Frequency-Dependent Phase Due to Propagation Through a Slab: Alternative Derivation 1914.8.2 Impedance Method for Analysis of Dielectric Mirror Stacks 192Problems 1955 Ultrafast Nonlinear Optics: Second Order 1985.1 Introduction to Nonlinear Optics 1985.2 The Forced Wave Equation 2015.2.1 Frequency-Domain Formulation 2025.2.2 Time-Domain Formulation 2035.3 Summary of Continuous-Wave Second-Harmonic Generation 2045.3.1 Effect of Phase Matching 2075.3.2 Phase Matching in Birefringent Media 2095.3.3 Focusing Effects in Continuous-Wave SHG 2155.4 Second-Harmonic Generation with Pulses 2205.4.1 SHG in the Quasi-Continuous-Wave Limit 2205.4.2 Ultrashort-Pulse SHG 2215.4.3 Quasi-Phase Matching 2285.4.4 Effect of Group Velocity Walk-off on SHG-Based Pulse Measurements 2335.5 Three-Wave Interactions 2375.5.1 Sum Frequency Generation 2405.5.2 Difference Frequency Generation 2445.5.3 Optical Parametric Amplification 2455.6 Appendix 2535.6.1 Spatial Walk-off and Pulse Fronts in Anisotropic Media 2535.6.2 Velocity Matching in Broadband Noncollinear Three-WaveMixing 254Problems 2566 Ultrafast Nonlinear Optics: Third Order 2586.1 Propagation Equation for Nonlinear Refractive Index Media 2586.1.1 Plane Waves in Uniform Media 2606.1.2 Nonlinear Propagation in Waveguides 2616.1.3 Optical Fiber Types 2646.2 The Nonlinear Schr¨odinger Equation 2666.3 Self-Phase Modulation 2706.3.1 Dispersionless Self-Phase Modulation 2706.3.2 Dispersionless Self-Phase Modulation with Loss 2736.3.3 Self-Phase Modulation with Normal Dispersion 2746.3.4 Cross-Phase Modulation 2756.4 Pulse Compression 2766.5 Modulational Instability 2836.6 Solitons 2866.7 Higher-Order Propagation Effects 2916.7.1 Nonlinear Envelope Equation in Uniform Media 2926.7.2 Nonlinear Envelope Equation in Waveguides 2956.7.3 Delayed Nonlinear Response and the Raman Effect 2966.7.4 Self-Steepening 3066.7.5 Space–Time Focusing 3086.8 Continuum Generation 310Problems 3137 Mode-Locking: Selected Advanced Topics 3167.1 Soliton Fiber Lasers: Artificial Fast Saturable Absorbers 3167.1.1 The Figure-Eight Laser 3177.1.2 Energy Quantization 3227.1.3 Soliton Sidebands 3247.2 Soliton Mode-Locking: Active Modulation and Slow Saturable Absorbers 3287.2.1 Harmonically Mode-Locked Soliton Fiber Lasers 3287.2.2 The Net Gain Window in Soliton Mode-Locking 3307.3 Stretched Pulse Mode-Locking 3377.3.1 Stretched Pulse Mode-Locked Fiber Laser 3377.3.2 Dispersion-Managed Solitons 3407.3.3 Theoretical Issues 3427.4 Mode-Locked Lasers in the Few-Cycle Regime 3447.5 Mode-Locked Frequency Combs 3477.5.1 Comb Basics 3477.5.2 Measurement Techniques 3507.5.3 Stabilization of Frequency Combs 3547.5.4 Applications 356Problems 3608 Manipulation of Ultrashort Pulses 3628.1 Fourier Transform Pulse Shaping 3628.1.1 Examples of Pulse Shaping Using Fixed Masks 3648.1.2 Programmable Pulse Shaping 3698.1.3 Pulse-Shaping Theory 3768.2 Other Pulse-Shaping Techniques 3868.2.1 Direct Space-to-Time Pulse Shaping 3868.2.2 Acousto-optic Dispersive Filters 3908.3 Chirp Processing and Time Lenses 3948.3.1 Space–Time Duality 3948.3.2 Chirp Processing 3978.3.3 Time Lens Processing 3998.4 Ultrashort-Pulse Amplification 4058.4.1 Amplification Basics 4068.4.2 Special Issues in Femtosecond Amplifiers 4118.5 Appendix 4168.5.1 Fresnel Diffraction and Fourier Transform Property of a Lens 4168.5.2 Wave Optics Model of a Grating 418Problems 4209 Ultrafast Time-Resolved Spectroscopy 4229.1 Introduction to Ultrafast Spectroscopy 4229.2 Degenerate Pump–Probe Transmission Measurements 4269.2.1 Co-polarized Fields: Scalar Treatment 4269.2.2 Vector Fields and Orientational Effects 4319.3 Nondegenerate and Spectrally Resolved Pump–Probe: Case Studies 4399.3.1 Femtosecond Pump–Probe Studies of Dye Molecules 4409.3.2 Femtosecond Pump–Probe Studies of GaAs 4449.4 Basic Quantum Mechanics for Coherent Short-Pulse Spectroscopies 4519.4.1 Some Basic Quantum Mechanics 4519.4.2 The Density Matrix 4569.5 Wave Packets 4609.5.1 Example: Semiconductor Quantum Wells 4619.5.2 Molecules 4629.6 Dephasing Phenomena 4699.6.1 Linear Spectroscopies 4699.6.2 Models of Dephasing 4759.6.3 Measurement of Dephasing Using Transient Gratings 4819.6.4 Two-Dimensional Spectroscopy 4949.7 Impulsive Stimulated Raman Scattering 499Problems 50510 Terahertz Time-Domain Electromagnetics 50710.1 Ultrafast Electromagnetics: Transmission Lines 50710.1.1 Photoconductive Generation and Sampling 50710.1.2 Electro-optic Sampling 51310.2 Ultrafast Electromagnetics: Terahertz Beams 51610.2.1 Generation and Measurement of Terahertz Pulses 51710.2.2 Terahertz Spectroscopy and Imaging 527Problems 531References 533Index 563