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More About This Title Shaping Light in Nonlinear Optical Fibers
English
This book is a contemporary overview of selected topics in fiber optics. It focuses on the latest research results on light wave manipulation using nonlinear optical fibers, with the aim of capturing some of the most innovative developments on this topic. The book’s scope covers both fundamentals and applications from both theoretical and experimental perspectives, with topics including linear and nonlinear effects, pulse propagation phenomena and pulse shaping, solitons and rogue waves, novel optical fibers, supercontinuum generation, polarization management, optical signal processing, fiber lasers, optical wave turbulence, light propagation in disordered fiber media, and slow and fast light. With contributions from leading-edge scientists in the field of nonlinear photonics and fiber optics, they offer an overview of the latest advances in their own research area. The listing of recent research papers at the end of each chapter is useful for researchers using the book as a reference. As the book addresses fundamental and practical photonics problems, it will also be of interest to, and benefit, broader academic communities, including areas such as nonlinear science, applied mathematics and physics, and optical engineering. It offers the reader a wide and critical overview of the state-of-the-art within this practical – as well as fundamentally important and interesting – area of modern science, providing a useful reference which will encourage further research and advances in the field.
English
Edited by
Sonia Boscolo, Aston Institute of Photonic Technologies, Aston University, Birmingham, UK
Christophe Finot, Laboratoire Interdisciplinaire Carnot de Bourgogne, CNRS-Université de Bourgogne, Dijon, France
English
Contents
List of Contributors xiii
Preface xvii
1 Modulation Instability, Four-Wave Mixing and their Applications 1
Tobias Hansson, Alessandro Tonello, Stefano Trillo, and Stefan Wabnitz
1.1 Introduction 1
1.2 Modulation Instability 2
1.2.1 Linear and Nonlinear Theory of MI 2
1.2.2 Polarization MI (PMI) in Birefringent Fibers 7
1.2.3 Collective MI of Four-Wave-Mixing 9
1.2.4 Induced MI Dynamics, Rogue Waves, and Optimal Parametric
Amplification 11
1.2.5 High-Order Induced MI 13
1.2.6 MI Recurrence Break-Up and Noise 14
1.3 Four-Wave Mixing Dynamics 17
1.3.1 FWM Processes with Two Pumps 17
1.3.2 Bragg Scattering FWM 18
1.3.3 Applications of BS-FWM to Quantum Frequency Conversion 20
1.4 Fiber Cavity MI and FWM 20
1.4.1 Dynamics of MI in a Passive Fiber Cavity 20
1.4.2 Parametric Resonances and Period Doubling Phenomena 23
1.4.3 FWM in a Fiber Cavity for Optical Buffer Applications 25
References 27
2 Phase-Sensitive Amplification and Regeneration 35
Francesca Parmigiani
2.1 Introduction to Phase-Sensitive Amplifiers 35
2.2 Operation Principles and Realization of Phase-Sensitive Parametric
Devices 36
2.3 One-Mode Parametric Processes 40
2.4 Two-Mode Parametric Processes 54
2.5 Four-Mode Parametric Processes 56
2.6 Conclusion 58
Acknowledgments 59
References 60
3 Novel Nonlinear Optical Phenomena in Gas-Filled Hollow-Core Photonic
Crystal Fibers 65
Mohammed F. Saleh and Fabio Biancalana
3.1 Introduction 65
3.2 Nonlinear Pulse Propagation in Guided Kerr Media 66
3.3 Ionization Effects in Gas-Filled HC-PCFs 67
3.3.1 Short Pulse Evolution 68
3.3.2 Long-Pulse Evolution 72
3.4 Raman Effects in Gas-Filled HC-PCFs 76
3.4.1 Density Matrix Theory 76
3.4.2 Strong Probe Evolution 82
3.5 Interplay Between Ionization and Raman Effects in Gas-Filled HC-PCFs 85
3.6 Conclusion 89
Acknowledgments 89
References 89
4 Modulation Instability in Periodically Modulated Fibers 95
Arnaud Mussot, Matteo Conforti, and Alexandre Kudlinski
4.1 Introduction 95
4.2 Basic Theory of Modulation Instability in Periodically Modulated
Waveguides 96
4.2.1 Piecewise Constant Dispersion 100
4.3 Fabrication of Periodically Modulated Photonic Crystal Fibers 101
4.3.1 Fabrication Principles 101
4.3.2 Typical Example 101
4.4 Experimental Results 104
4.4.1 Experimental Setup 104
4.4.2 First Observation of Multiple Simultaneous MI Side Bands in
Periodically Modulated Fibers 104
4.4.3 Impact of the Curvature of the Dispersion 105
4.4.4 Other Modulation Formats 107
4.5 Conclusion 111
Acknowledgments 111
References 111
5 Pulse Generation and Shaping Using Fiber Nonlinearities 115
Christophe Finot and Sonia Boscolo
5.1 Introduction 115
5.2 Picosecond Pulse Propagation in Optical Fibers 116
5.3 Pulse Compression and Ultrahigh-Repetition-Rate Pulse
Train Generation 117
5.3.1 Pulse Compression 117
5.3.2 High-Repetition-Rate Sources 121
5.4 Generation of Specialized Temporal Waveforms 124
5.4.1 Pulse Evolution in the Normal Regime of Dispersion 124
5.4.2 Generation of Parabolic Pulses 125
5.4.3 Generation of Triangular and Rectangular Pulses 127
5.5 Spectral Shaping 128
5.5.1 Spectral Compression 129
5.5.2 Generation of Frequency-Tunable Pulses 132
5.5.3 Supercontinuum Generation 133
5.6 Conclusion 137
Acknowledgments 138
References 138
6 Nonlinear-Dispersive Similaritons of Passive Fibers: Applications in
Ultrafast Optics 147
Levon Mouradian and Alain Barth´el´emy
6.1 Introduction 147
6.2 Spectron and Dispersive Fourier Transformation 150
6.3 Nonlinear-Dispersive Similariton 15 1
6.3.1 Spectronic Nature of NL-D Similariton: Analytical Consideration 152
6.3.2 Physical Pattern of Generation of NL-D Similariton, Its Character and
Peculiarities on the Basis of Numerical Studies 153
6.3.3 Experimental Study of NL-D Similariton by Spectral Interferometry
(and also Chirp Measurements by Spectrometer and Autocorrelator) 155
6.3.4 Bandwidth and Duration of NL-D Similariton 158
6.3.5 Wideband NL-D Similariton 159
6.4 Time Lens and NL-D Similariton 160
6.4.1 Concept of Time Lens: Pulse Compression—Temporal Focusing, and
Spectral Compression—“Temporal Beam” Collimation/Spectral
Focusing 160
6.4.2 Femtosecond Pulse Compression 161
6.4.3 Classic and “All-Fiber” Spectral Compression 163
6.4.4 Spectral Self-Compression: Spectral Analogue of Soliton-Effect
Compression 165
6.4.5 Aberration-Free Spectral Compression with a Similariton-Induced
Time Lens 167
6.4.6 Frequency Tuning Along with Spectral Compression in
Similariton-Induced Time Lens 168
6.5 Similariton for Femtosecond Pulse Imaging and Characterization 172
6.5.1 Fourier Conversion and Spectrotemporal Imaging in
SPM/XPM-Induced Time Lens 173
6.5.2 Aberration-Free Fourier Conversion and Spectrotemporal Imaging in
Similariton-Induced Time Lens: Femtosecond Optical Oscilloscope 177
6.5.3 Similariton-Based Self-Referencing Spectral Interferometry 181
6.5.4 Simple Similaritonic Technique for Measurement of Femtosecond
Pulse Duration, an Alternative to the Autocorrelator 185
6.5.5 Reverse Problem of NL-D Similariton Generation 187
6.5.6 Pulse Train Shaped by Similaritons’ Superposition 188
6.6 Conclusion 190
References 191
7 Applications of Nonlinear Optical Fibers and Solitons in Biophotonics
And Microscopy 199
Esben R. Andresen and Herv´e Rigneault
7.1 Introduction 199
7.2 Soliton Generation 200
7.2.1 Fundamental Solitons 200
7.2.2 A Sidenote on Dispersive Wave Generation 202
7.2.3 Spatial Properties of PCF Output 204
7.3 TPEF Microscopy 204
7.4 SHG Microscopy 205
7.5 Coherent Raman Scattering 206
7.6 MCARS Microscopy 207
7.7 ps-CARS Microscopy 210
7.8 SRS Microscopy 211
7.9 Pump-Probe Microscopy 213
7.10 Increasing the Soliton Energy 215
7.10.1 SC-PBG Fibers 216
7.10.2 Multiple Soliton Generation 217
7.11 Conclusion 218
References 218
8 Self-Organization of Polarization State in Optical Fibers 225
Julien Fatome and Massimiliano Guasoni
8.1 Introduction 225
8.2 Principle of Operation 227
8.3 Experimental Setup 229
8.4 Theoretical Description 230
8.5 Bistability Regime and Related Applications 234
8.6 Alignment Regime 238
8.7 Chaotic Regime and All-Optical Scrambling for WDM Applications 241
8.8 Future Perspectives: Towards an All-Optical Modal Control in Fibers 247
8.9 Conclusion 250
Acknowledgments 251
References 251
9 All-Optical Pulse Shaping in the Sub-Picosecond Regime Based on Fiber
Grating Devices 257
Maria R. Fern´andez-Ruiz, Alejandro Carballar, Reza Ashrafi, Sophie LaRochelle,
and Jos´e Aza˜na
9.1 Introduction 257
9.2 Non-Fiber-Grating-Based Optical Pulse Shaping Techniques 258
9.3 Motivation of Fiber-Grating Based Optical Pulse Shaping 260
9.3.1 Fiber Bragg Gratings (FBGs) 264
9.3.2 Long Period Gratings (LPGs) 267
9.4 Recent Work on Fiber Gratings-Based Optical Pulse Shapers:
Reaching the Sub-Picosecond Regime 268
9.4.1 Recent Findings on FBGs 268
9.4.2 Recent Findings on LPGs 276
9.5 Advances towards Reconfigurable Schemes 284
9.6 Conclusion 285
References 285
10 Rogue Breather Structures in Nonlinear Systems with an Emphasis on
Optical Fibers as Testbeds 293
Bertrand Kibler
10.1 Introduction 293
10.2 Optical Rogue Waves as Nonlinear Schr¨odinger Breathers 295
10.2.1 First-Order Breathers 295
10.2.2 Second-Order Breathers 301
10.3 Linear-Nonlinear Wave Shaping as Rogue Wave Generator 303
10.3.1 Experimental Configurations 304
10.3.2 Impact of Initial Conditions 306
10.3.3 Higher-Order Modulation Instability 308
10.3.4 Impact of Linear Fiber Losses 309
10.3.5 Noise and Turbulence 311
10.4 Experimental Demonstrations 311
10.4.1 Peregrine Breather 312
10.4.2 Periodic First-Order Breathers 313
10.4.3 Higher-Order Breathers 315
10.5 Conclusion 317
Acknowledgments 318
References 318
11 Wave-Breaking and Dispersive Shock Wave Phenomena in Optical Fibers 325
Stefano Trillo and Matteo Conforti
11.1 Introduction 325
11.2 Gradient Catastrophe and Classical Shock Waves 326
11.2.1 Regularization Mechanisms 327
11.3 Shock Formation in Optical Fibers 329
11.3.1 Mechanisms of Wave-Breaking in the Normal GVD Regime 330
11.3.2 Shock in Multiple Four-Wave Mixing 333
11.3.3 The Focusing Singularity 335
11.3.4 Control of DSW and Hopf Dynamics 336
11.4 Competing Wave-Breaking Mechanisms 337
11.5 Resonant Radiation Emitted by Dispersive Shocks 338
11.5.1 Phase Matching Condition 339
11.5.2 Step-Like Pulses 340
11.5.3 Bright Pulses 341
11.5.4 Periodic Input 342
11.6 Shock Waves in Passive Cavities 343
11.7 Conclusion 345
Acknowledgments 345
References 345
12 Optical Wave Turbulence in Fibers 351
Antonio Picozzi, Josselin Garnier, Gang Xu, and Guy Millot
12.1 Introduction 351
12.2 Wave Turbulence Kinetic Equation 354
12.2.1 Supercontinuum Generation 354
12.2.2 Breakdown of Thermalization 360
12.2.3 Turbulence in Optical Cavities 365
12.3 Weak Langmuir Turbulence Formalism 371
12.3.1 NLS Model 372
12.3.2 Short-Range Interaction: Spectral Incoherent Solitons 372
12.3.3 Long-Range Interaction: Incoherent Dispersive Shock Waves 375
12.4 Vlasov Formalism 378
12.4.1 Incoherent Modulational Instability 380
12.4.2 Incoherent Solitons in Normal Dispersion 381
12.5 Conclusion 384
Acknowledgments 385
References 385
13 Nonlocal Disordered Media and Experiments in Disordered Fibers 395
Silvia Gentilini and Claudio Conti
13.1 Introduction 395
13.2 Nonlinear Behavior of Light in Transversely Disordered Fiber 396
13.3 Experiments on the Localization Length in Disordered Fibers 399
13.4 Shock Waves in Disordered Systems 403
13.5 Experiments on Shock Waves in Disordered Media 407
13.5.1 Experimental Setup 407
13.5.2 Samples 407
13.5.3 Measurements 409
13.6 Conclusion 412
Acknowledgments 413
References 413
14 Wide Variability of Generation Regimes in Mode-Locked Fiber Lasers 415
Sergey V. Smirnov, Sergey M. Kobtsev, and Sergei K. Turitsyn
14.1 Introduction 415
14.2 Variability of Generation Regimes 417
14.3 Phenomenological Model of Double-Scale Pulses 425
14.4 Conclusion 428
Acknowledgments 429
References 429
15 Ultralong Raman Fiber Lasers and Their Applications 435
Juan Diego Ania-Casta˜n´on and Paul Harper
15.1 Introduction 435
15.2 Raman Amplification 436
15.3 Ultralong Raman Fiber Lasers Basics 439
15.3.1 Theory of Ultralong Raman Lasers 439
15.3.2 Amplification Using URFLs 444
15.4 Applications of Ultralong Raman Fiber Lasers 452
15.4.1 Applications in Telecommunications 453
15.4.2 Applications in Sensing 455
15.4.3 Supercontinuum Generation 455
15.5 Conclusion 456
References 456
16 Shaping Brillouin Light in Specialty Optical Fibers 461
Jean-Charles Beugnot and Thibaut Sylvestre
16.1 Introduction 461
16.2 Historical Background 462
16.3 Theory 463
16.3.1 Elastodynamics Equation 463
16.4 Tapered Optical Fibers 465
16.4.1 Principles 465
16.4.2 Experiments 466
16.4.3 Numerical Simulations 467
16.4.4 Photonic Crystal Fibers 469
16.5 Conclusion 473
References 474
Index 477
