Nonlinear Optical Technology From The Beginning

Comprehensive resources describing today?s Nonlinear Optics (NLO) technology, its applications, and concepts behind the technology

Taking shape at the unique interdisciplinary engineering school at Dartmouth College, Nonlinear Optical Technology explores the importance of NLO in terms of how it permeates a vast number of applications such as fiber optics, biomedicine, sensors (especially Internet of Things), microscopy, spectroscopy, and machining, under the assumption engineers of all stripes may end up working in technical areas impacted by Nonlinear Optics (NLO) and would benefit from learning about the field.

Each section follows a set format, beginning by describing some exciting new technology made possible by NLO. This part is followed by a description of the background information necessary for students to understand the basic NLO concepts for that application. The author occasionally includes personal experiences as a pioneer in this field where it provides additional understanding and motivation. Each section ends with a description of other developments in technology that use the same NLO concept.

Bringing together disparate topics in NLO under a straight-forward rubric based on applications, Nonlinear Optical Technology includes information on:

• Extending lasers (with NLO technology), covering new colors (harmonic generation, stimulated raman, and stimulated brillouin) and pulsed lasers (saturable absorption and ultra-high harmonic generation)
• Information technology, covering telecommunications (fiber optics NLO and photonic NLO) and data storage (NLO in nanostructures and photonic crystals)
• Sensors, covering distributed sensing (brillouin scattering in fibers) and localized sensors (NLO in photonics)
• Materials interaction, covering machining (nonlinear absorption), spectroscopy (four-wave mixing), and microscopy (two-photon absorption)

Serving as a comprehensive standalone resource on the subject for engineers and students without requiring pre-knowledge of advanced concepts, Nonlinear Optical Technology is an essential resource for those in fields that intersect with NLO applications and integration, as well as anyone who wishes to self-teach NLO concepts in general.

Preface xxi

Acronyms xxiii

Introduction: Why Nonlinear Optics? xxvii

Summary 1: What is Nonlinear Optics Technology? S1

Summary 2: Second-Order Nonlinearity S5

Summary 3: Third-Order Nonlinearity S24

Summary 4: Nonlinear Scattering and Loss S47

Part I Technical Chapters on Second-Order Nonlinearity 1

1 Second Harmonic Generation 3

1.1 Introduction 3

1.2 Second Harmonic Generation at the Beginning 3

1.3 How Do We Begin? 5

1.4 Approaches to Second Harmonic Generation 8

1.5 Electromagnetic Response to Dielectric 11

1.6 Nonlinear Static Field 13

1.7 Second Harmonic Has No Inversion Symmetry 14

1.8 Photon Picture of SHG 15

1.9 Nonlinear Optics (a Look Ahead) 16

1.10 Applications: SHG at Interfaces 17

1.11 Discussion 22

2 Generating Second Harmonic Efficiently 23

2.1 Introduction 23

2.2 Traveling Waves for SHG 25

2.3 Phase-Matched Growth of Intensity 28

2.4 SHG from Crystal Under Refractive-Index Mismatch 32

2.5 When SH Power Diminishes Due to Phase Mismatch, Where Does It Go? 36

2.6 Phase-Matched Depleted Pump 37

2.7 SH Intensity with Phase Mismatch and Depleted Pump 39

2.8 Applications of SHG 40

2.9 Sum and Difference Frequency Generation 44

2.10 Optical Field Rectification 45

2.11 Review 47

3 Extending Coherence Lengths 49

3.1 Introduction 49

3.2 How Important Is Matching Phases? 51

3.3 Experimental Demonstration of SHG With/Without PM 53

3.4 Anisotropic Crystals 59

3.5 Anisotropic Crystals for SHG Phase Matching 62

3.6 Quasi-Phase Matching 66

3.7 Challenge of Alternating SHG Domains 71

3.8 Periodically-Poled Lithium Niobate (PPLN) 73

3.9 Gaussian Beam Diffraction 77

3.10 Resonators for Enhanced SHG: Fabry-Perot Interferometer 82

3.11 Cavity Enhancement in Green Laser Pointer 85

4 Optical Parametric Amplification 87

4.1 Optical Parametric Amplifier: Tunable Source of Coherent Light 87

4.2 Optical Parametric Amplifiers: Engineering Perspective 92

4.3 Amplification by Parametric Nonlinearities 95

4.4 OPA as Reverse of Difference Frequency Generation 99

4.5 Understanding Parametric Oscillators 100

4.6 Operating an OPO System 104

4.7 OPO Is OPA in Optical Cavity 107

4.8 Relate Electric Field and Intensity to Photon Density 109

4.9 Understanding Degenerate Oscillators and Amplifiers 111

4.10 Practical Applications of OPOs 116

Part II Technical Chapters on Third-Order Nonlinearity 119

5 Third-Order Nonlinearity 121

5.1 Introduction to Third-order Nonlinearity x3 121

5.2 Third-Harmonic Generation 121

5.3 Higher Order Nonlinearities in Pressurized Gases 125

5.4 High-Harmonic Generation Experimental Results 127

5.5 Toward Commercialization 130

5.6 Analyzing fs Pulses: Frequency Resolved Optical Gate 132

5.7 Chirped-Pulse Amplification Systems 134

5.8 Race to Achieve the Highest Intensity 137

5.9 Next Chapter 138

6 Nonlinear Index and Pulses 139

6.1 Intensity-Induced Refractive Index Change 139

6.2 Impact of Phase Delay Due to Δn 143

6.3 Solitons: Temporal Pulse Shape Never Changes 146

6.4 Self-intensity-Modulated Phase 148

6.5 Frequency Shift Equals Time Slope of Changing Phase 152

6.6 XPM: Cross-phase Modulation 159

6.7 XPM to Transfer Phase Information 166

6.8 Applications of Lossless Quantum Information Transfer 167

6.9 Next Chapter 169

7 Spatial Nonlinear Index 171

7.1 Introduction 171

7.2 Self-trapping in the Spatial Domain by Nonlinear Index 171

7.3 Spatial Solitons 175

7.4 Derivation of 1D Spatial Soliton Wave Equation 177

7.5 Self-focusing with Power Higher than Critical 181

7.6 Experimental Improvements 185

7.7 Nonlinear Fabry-Perot Etalon: Optical Bistability 186

7.8 Measuring Nonlinear Coefficients: Z-scan Technique 190

7.9 Kerr Lens Mode-locking 191

7.10 Next Chapter 192

8 Coherent Wave-Mixing 193

8.1 Introduction 193

8.2 Lateral Grating from Two-wave Mixing 195

8.3 Bragg Gratings 202

8.4 Pulsed Gratings 204

8.5 Four-wave-Mixing 206

8.6 Four-wave Mixing Backward Waves 210

8.7 Spatial Analysis to Find Fourth Wave D in χ(3) 211

8.8 Time-dependence of E3 and E4 213

8.9 Phase Conjugation (Changing Sign of Phase) 214

8.10 Fiber Optical Parametric Amplification 216

8.11 Four Wave Mixing as Four-photon Scattering 221

8.12 Next Chapter 224

Part III Technical Chapters on Nonlinear Optical Scattering and Loss 225

9 Stimulated Raman Scattering 227

9.1 Introduction 227

9.2 Spontaneous Raman Scattering 229

9.3 Introduction to Stimulated Raman Scattering 233

9.4 Understanding Stokes Generation 236

9.5 Stokes Generates Coherent Molecular Vibrations 240

9.6 Anti-Stokes Waves 243

9.7 Raman Laser 246

9.8 Applications: SRS Optical Nonlinearity is Both Useful and Detrimental 251

9.9 Raman SRS Fiber Amplifiers 252

9.10 High-power Raman Lasers in Special Fibers 255

9.11 Photonic Raman Lasers 255

9.12 Stimulated Raman Spectroscopy 259

9.13 Review: Short List of Main Uses for SRS 262

10 Stimulated Brillouin Scattering 265

10.1 Spontaneous Brillouin Scattering 265

10.2 Spontaneous or Parametric Brillouin Scattering 269

10.3 Stimulated Brillouin Scattering 270

10.4 SBS as Stokes Power Amplifier 275

10.5 Historical Background 279

10.6 Phase Conjugation and SBS Reflection 283

10.7 Brillouin Fiber Lasers 289

10.8 Brillouin Fiber Sensors 291

10.9 Photonic Brillouin Ring Laser 293

10.10 Prospective SBS Applications 296

11 Nonlinear Absorption 299

11.1 Nonlinear Absorption 299

11.2 Two-photon Absorption 300

11.3 Saturable Absorption 308

11.4 Rate Equation for Absorption Transition 309

11.5 Solve for Saturable Absorption 311

11.6 Application: Creating Pulsing Lasers 312

11.7 Classes of Pulsed Lasers 314

11.8 Final Thoughts 317

Appendix A Light Beams in Transparent Media 319

Appendix B Optical Materials and Light Fields 345

Appendix C Understanding Resonators 373

Appendix D Waveguides to Avoid Diffraction 385

Problem Assignments 399

Index 415

Elsa M. Garmire, PhD, is a Fellow of IEEE, the Optical Society, the American Physical Society, and the Society of Women Engineers. She was elected to the National Academy of Engineering and the National Academy of Inventors. From 1995 to 2016, she taught interdisciplinary engineering courses as Sydney Junkins Professor at the Thayer School of Engineering at Dartmouth College. She has served on multiple National Research Council Committees and specialized in Nonlinear Optics (NLO) at MIT.