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E-raamat: Optical Multi-Bound Solitons

(Huawei Technologies, Munich, Germany)
  • Formaat: 567 pages
  • Sari: Optics and Photonics
  • Ilmumisaeg: 03-Sep-2018
  • Kirjastus: CRC Press Inc
  • Keel: eng
  • ISBN-13: 9781482237641
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Optical Multi-Bound SolitonsSuurem pilt
  • Formaat: 567 pages
  • Sari: Optics and Photonics
  • Ilmumisaeg: 03-Sep-2018
  • Kirjastus: CRC Press Inc
  • Keel: eng
  • ISBN-13: 9781482237641
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Optical Multi-Bound Solitons describes the generation and transmission of multi-bound solitons with the potential to form the basis of the temporal coding of optical data packets for next-generation nonlinear optical systems. The book deals with nonlinear systems in terms of their fundamental principles, associated phenomena, and signal processing applications in contemporary optical systems for communications and laser systems, with a touch of mathematical representation of nonlinear equations to offer insight into the nonlinear dynamics at different phases. The text not only delineates the strong background physics of such systems but also:

  • Discusses the phase evolution of the optical carriers under the soliton envelopes for the generation of multi-bound solitons
  • Explains the generation of multi-bound solitons through optical fibers
  • Examines new types of multi-bound solitons in passive and active optical resonators
  • Conducts bi-spectral analyses of multi-bound solitons to identify the phase and power amplitude distribution property of bound solitons
  • Presents experimental techniques for the effective generation of bound solitons

Optical Multi-Bound Solitons provides extensive coverage of multi-bound solitons from the dynamics of their formation to their transmission over guided optical media. Appendices are included to supplement a number of essential definitions, mathematical representations, and derivations, making this book an ideal theoretical reference text as well as a practical professional guidebook.

Arvustused

"The author gives a very clear and useful description of nonlinear systems in terms of their fundamental principles, associated phenomena and signal processing applications for communications and laser systems. The book is a valuable addition to the fields literature and complements other existing works. I would recommend this book especially to young researchersthey can learn about scientific results along with applications in optical communications. It also provides insight into developing original strategies when working with the difficult mathematical problems arising in chaos and solitons in complex systems." Optics & Photonics News, February 2016

Preface xvii
Author xix
Chapter 1 Introduction 1(18)
1.1 Ultrashort Pulse and Multi-Bound Solitons
1(2)
1.2 Mode-Locked Fiber Lasers as Soliton and Multi-Bound Soliton Generators
3(3)
1.3 Nonlinear Effects and Higher-Order Spectral Analyses
6(4)
1.3.1 Nonlinear Effects
6(2)
1.3.2 Nonlinear Processing and Higher-Order Spectral Analyses
8(2)
1.4 Motivation and Objectives of the Book
Chapters
10(2)
1.5 Organization of the
Chapters
12(2)
References
14(5)
Chapter 2 Generations of Solitons in Optical Fiber Ring Resonators 19(58)
2.1 Nonlinear Schrodinger Equations
19(7)
2.1.1 Nonlinear Response
19(3)
2.1.2 Nonlinear Schrodinger Equation
22(1)
2.1.3 Ginzburg—Landau Equation: A Modified NLSE
23(1)
2.1.4 Coupled Nonlinear Schrodinger Equations
24(2)
2.2 Optical Solitons
26(5)
2.2.1 Temporal Solitons
26(4)
2.2.2 Dissipative Solitons
30(1)
2.3 Generation of Solitons Using Nonlinear Optical Fiber Ring Resonators
31(15)
2.3.1 Master Equation for Mode-Locking
31(1)
2.3.2 Passive Mode-Locking
32(6)
2.3.3 Active Mode-Locking
38(8)
2.3.3.1 AM Mode-Locking
38(3)
2.3.3.2 FM Mode-Locking
41(3)
2.3.3.3 Rational Harmonic Mode-Locking
44(2)
2.4 Actively FM Mode-Locked Fiber Rings: An Experiment
46(12)
2.4.1 Experimental Setup
46(3)
2.4.2 Results and Discussion
49(9)
2.4.2.1 Soliton Generation
49(2)
2.4.2.2 Detuning Effect and Relaxation Oscillation
51(4)
2.4.2.3 Rational Harmonic Mode-Locking
55(3)
2.5 Simulation of Actively FM Mode-Locked Fiber Laser
58(12)
2.5.1 Numerical Simulation Model
58(2)
2.5.2 Simulation Results and Discussion
60(18)
2.5.2.1 Mode-Locked Pulse Formation
60(5)
2.5.2.2 Detuning Operation
65(5)
2.6 Concluding Remarks
70(2)
References
72(5)
Chapter 3 Multi-Bound Solitons: Fundamentals and Generations 77(34)
3.1 Introductory Remarks
77(1)
3.2 Bound Solitons by Passive Mode-Locking
78(3)
3.2.1 Multipulsing Operation
78(1)
3.2.2 Bound States in a Passively Mode-Locked Fiber Ring
79(2)
3.3 Bound Solitons by Active Mode-Locking
81(18)
3.3.1 Multi-Bound Solitons Conditions
81(3)
3.3.2 Experimental Generation
84(1)
3.3.2.1 Experimental Setup
84(1)
3.3.3 Results and Discussion
85(7)
3.3.4 Simulation Generation
92(7)
3.3.4.1 Formation of Multisoliton Bound States
92(4)
3.3.4.2 Evolution of the Bound Soliton States in an FM Fiber Loop
96(3)
3.4 Relative Phase Difference of Multi-Bound Solitons
99(3)
3.4.1 Interferometer Measurement and Experimental Setup
99(2)
3.4.2 Results and Discussion
101(1)
3.5 Multi-Bound and Saddle Solitons: Experimental Observations
102(5)
3.6 Concluding Remarks
107(1)
References
107(4)
Chapter 4 Multi-Bound Solitons under Carrier Phase Modulation 111(26)
4.1 Electro-Optic Phase Modulators
111(3)
4.1.1 Lumped-Type Modulator
111(2)
4.1.2 Traveling-Wave Modulator
113(1)
4.2 Characterization Measurements
114(7)
4.2.1 Half-Wave Voltage
114(3)
4.2.2 Dynamic Response
117(4)
4.3 Comb Spectrum in Actively Mode-Locked Fiber Ring Resonator Incorporating Phase Modulator
121(4)
4.3.1 Birefringence and Comb Spectrum in the Fiber Ring Using Phase Modulator
121(1)
4.3.2 Discrete Wavelength Tuning
122(3)
4.4 Influence of Phase Modulator on Multi-Bound Solitons
125(6)
4.4.1 Formation of Multi-Bound Solitons
125(3)
4.4.2 Limitation of Multi-Bound Soliton States
128(3)
4.5 Concluding Remarks
131(3)
References
134(3)
Chapter 5 Bound-Soliton Bispectra and Nonlinear Photonic Signal Processing 137(40)
5.1 Bispectrum of Multi-Bound Solitons
137(12)
5.1.1 Bispectrum
137(2)
5.1.2 Various States of Bound Solitons
139(3)
5.1.3 Transitions in Multi-Bound Soliton Formation
142(7)
5.2 Third-Order Nonlinearity Four-Wave Mixing for Photonic Signal Processing
149(5)
5.2.1 Four-Wave Mixing in Nonlinear Waveguides
150(2)
5.2.2 Phase Matching
152(1)
5.2.3 Simulink® Model for FWM in Optical Waveguides
152(2)
5.3 Applications of FWM in Photonic Signal Processing
154(16)
5.3.1 Signal Processing Based on Parametric Amplification
154(6)
5.3.2 Ultrahigh-Speed OTDM Demultiplexing (Optical Switching)
160(3)
5.3.3 FWM-Based Triple Correlation and Bispectrum
163(7)
5.4 Concluding Remarks
170(5)
References
175(2)
Chapter 6 Solitons and Multi-Bound Solitons in Passive Mode-Locked Fiber Lasers 177(74)
6.1 Introductory Remarks
177(1)
6.2 Soliton Generation by Passively Mode-Locked Fiber Lasers
178(6)
6.2.1 Pulse Propagation in Single-Mode Fibers
179(1)
6.2.2 Cavity Transmission of NLPR Mode-Locked Fiber Lasers
180(4)
6.3 Soliton Dynamics in Dual-Polarization Mode-Locked Fiber Lasers
184(20)
6.3.1 Experimental Configuration
184(1)
6.3.2 Soliton Deterministic Dynamics
185(19)
6.3.2.1 Period-Doubling Bifurcation and Chaos of Single-Pulse Solitons
186(4)
6.3.2.2 Period-Doubling and Quadrupling of Bound Solitons
190(4)
6.3.2.3 Period-Doubling of Multiple Solitons
194(3)
6.3.2.4 Period-Doubling of Dispersion-Managed Solitons at Point near Cavity Zero-Dispersion
197(2)
6.3.2.5 Period-Doubling of Gain-Guided Solitons with Large Net Normal Dispersion
199(3)
6.3.2.6 Period-Doubling of Vector Solitons in a Fiber Laser
202(2)
6.4 Soliton Deterministic Dynamics in Fiber Lasers: Simulation
204(23)
6.4.1 Round Trip Model of Soliton Fiber Lasers
204(1)
6.4.2 Deterministic Dynamics of Solitons in Different Fiber Lasers
205(24)
6.4.2.1 Period-Doubling Route to Chaos of Single Pulse Solitons
206(7)
6.4.2.2 Period-Doubling Route to Chaos of Bound Solitons
213(1)
6.4.2.3 Period-Doubling of Multiple Solitons
213(5)
6.4.2.4 Period-Doubling of Dispersion-Managed Solitons
218(3)
6.4.2.5 Period-Doubling of Gain-Guided Solitons
221(1)
6.4.2.6 Period-Doubling of Vector Solitons
222(5)
6.5 Cavity-Induced Soliton Modulation Instability Effect
227(2)
6.6 Multisoliton Formation and Soliton Energy Quantization in Passively Mode-Locked Fiber Lasers
229(17)
6.6.1 Introductory Remarks
229(2)
6.6.2 Experimental Observations of Multi-Bound Solitons
231(2)
6.6.3 Theoretical Modeling
233(2)
6.6.4 Simulation
235(5)
6.6.5 Multiple-Soliton Formation and Soliton Energy Quantization
240(5)
6.6.6 Remarks
245(1)
6.7 Concluding Remarks
246(1)
References
246(5)
Chapter 7 Multirate Multiplication Soliton Fiber Ring and Nonlinear Loop Lasers 251(60)
7.1 Introduction
252(2)
7.2 Active Mode-Locked Fiber Ring Laser by Rational Harmonic Detuning
254(12)
7.2.1 Rational Harmonic Mode-Locking
254(1)
7.2.2 Experiment Setup
255(1)
7.2.3 Phase Plane Analysis
256(4)
7.2.4 Demonstration
260(6)
7.2.5 Remarks
266(1)
7.3 Repetition-Rate Multiplication Ring Laser Using Temporal Diffraction Effects
266(14)
7.3.1 Phase Plane Analysis
268(1)
7.3.2 Uniform Lasing Mode Amplitude Distribution
269(4)
7.3.3 Gaussian Lasing Mode Amplitude Distribution
273(1)
7.3.4 Effects of Filter Bandwidth
274(1)
7.3.5 Nonlinear Effects
275(1)
7.3.6 Noise Effects
276(1)
7.3.7 Demonstration
276(3)
7.3.8 Remarks
279(1)
7.4 Bistability, Bifurcation, and Chaos in Nonlinear Loop Fiber Lasers
280(24)
7.4.1 Introduction
281(1)
7.4.2 Optical Bistability, Bifurcation, and Chaos
282(4)
7.4.3 Nonlinear Optical Loop Mirror
286(2)
7.4.4 Nonlinear Amplifying Loop Mirror
288(2)
7.4.5 NOLM—NALM Fiber Ring Lasers
290(3)
7.4.6 Experiment Setups and Analyses
293(21)
7.4.6.1 Bidirectional Erbium-Doped Fiber Ring Laser
293(4)
7.4.6.2 NOLM—NALM Fiber Ring Laser
297(5)
7.4.6.3 Amplitude-Modulated NOLM—NALM Fiber Ring Laser
302(2)
7.5 Concluding Remarks
304(2)
References
306(5)
Chapter 8 Optical Multisoliton Transmission 311(94)
8.1 Introduction
311(1)
8.2 Fundamentals of Nonlinear Propagation Theory
312(2)
8.3 Numerical Approach
314(5)
8.3.1 Beam Propagation Method
314(1)
8.3.2 Analytical Approach: ISM
315(4)
8.3.2.1 Soliton N= 1 by Inverse Scattering
316(1)
8.3.2.2 Soliton N= 2 by Inverse Scattering
317(2)
8.4 Fundamental and Higher-Order Solitons
319(2)
8.4.1 Soliton Evolution for N= 1, 2, 3, 4, and 5
319(2)
8.4.2 Soliton Breakdown
321(1)
8.5 Interaction of Fundamental Solitons
321(10)
8.5.1 Dual Solitons Interaction with Different Pulse Separation
321(2)
8.5.2 Dual Solitons Interaction with Different Relative Amplitude
323(2)
8.5.3 Dual Solitons Interaction under Different Relative Phase
325(1)
8.5.4 Triple-Soliton Interaction under Different Relative Phases
326(1)
8.5.5 Triple Solitons Interaction with Different Relative Phase and r= 1.5
326(5)
8.6 Soliton Pulse Transmission Systems and ISM
331(14)
8.6.1 ISM Revisited
334(2)
8.6.1.1 Step 1: Direct Scattering
334(1)
8.6.1.2 Step 2: Evolution of the Scattering Data
334(1)
8.6.1.3 Step 3: Inverse Spectral Transform
335(1)
8.6.2 ISM Solutions for Solitons
336(3)
8.6.2.1 Step 1: Direct Scattering Problem
336(1)
8.6.2.2 Step 2: Evolution of the Scattering Data
337(1)
8.6.2.3 Step 3: Inverse Scattering Problem
338(1)
8.6.3 N-Solitons Solution (Explicit Formula)
339(3)
8.6.4 Special Case A = N
342(1)
8.6.5 N-Soliton Solutions (Asymptotic Form as τ -+ + infinity)
342(2)
8.6.6 Bound States and Multiple Eigenvalues
344(1)
8.7 Interaction between Two Solitons in an Optical Fiber
345(5)
8.7.1 Soliton Pair with Initial Identical Phases
346(1)
8.7.2 Soliton Pair with Initial Equal Amplitudes
347(1)
8.7.3 Soliton Pair with Initial Unequal Amplitudes
348(1)
8.7.4 Design Strategy
349(1)
8.8 Generation and Transmission of Multi-Bound Solitons: Experiments
350(51)
8.8.1 Generation of Bound-Solitons Using Mode-Locked Fiber Ring Resonators
350(14)
8.8.1.1 Introductory Remarks
350(1)
8.8.1.2 Formation of Bound States in an FM Mode-Locked Fiber Laser
351(2)
8.8.1.3 Experimental Setup and Results
353(4)
8.8.1.4 Simulation of Dynamics of Bound States in an FM Mode-Locked Fiber Laser
357(7)
8.8.2 Active Harmonic Mode-Locked Fiber Laser for Soliton Generation
364(19)
8.8.2.1 Experiment Setup
364(1)
8.8.2.2 Tunable Wavelength Harmonic Mode-Locked Pulses
365(5)
8.8.2.3 Measurement of the Fundamental Frequency
370(1)
8.8.2.4 Effect of the Modulation Frequency
371(1)
8.8.2.5 Effect of the Modulation Depth/Index
372(1)
8.8.2.6 Effect of Fiber Ring Length
373(5)
8.8.2.7 Effect of Pump Power
378(5)
8.8.3 Transmission of Generated Multi-Bound Solitons
383(30)
8.8.3.1 Soliton Propagation in Optical Fibers
384(3)
8.8.3.2 Transmission of Multi-Bound Solitons: Experiments
387(5)
8.8.3.3 Dynamics of Multi-Bound Solitons in Transmission
392(6)
8.8.3.4 Remarks
398(3)
References
401(4)
Chapter 9 Concluding Remarks 405(6)
References
408(3)
Appendix A: Generic Mathematical Aspects of Nonlinear Dynamics 411(40)
A.1 Introductory Remarks
412(1)
A.2 Nonlinear Systems: Phase Spaces and Dynamical States
413(11)
A.2.1 Phase Space
413(2)
A.2.2 Critical Points
415(9)
A.2.2.1 Fixed Points in 1-D Phase Space
415(3)
A.2.2.2 Fixed Points in 2-D Phase Space
418(4)
A.2.2.3 Limit Cycles
422(2)
A.3 Bifurcation
424(10)
A.3.1 Pitchfork Bifurcation
425(1)
A.3.2 Saddle-Node Bifurcation
426(3)
A.3.3 Transcritical Bifurcation
429(1)
A.3.4 Hopf Bifurcation
429(5)
A.4 Chaos
434(16)
A.4.1 Definition
434(1)
A.4.2 Routes to Chaos
435(3)
A.4.2.1 Period-Doubling
435(1)
A.4.2.2 Quasi-Periodicity
436(1)
A.4.2.3 Intermittency
437(1)
A.4.3 Chaotic Nonlinear Circuit
438(41)
A.4.3.1 Simulation Results
439(4)
A.4.3.2 Experimental Results
443(7)
A.5 Concluding Remarks
450(1)
References
450(1)
Appendix B: Derivation of the Nonlinear Schrodinger Equation (NLSE) 451(6)
B.1 Wave Equation in Nonlinear Optics
451(1)
B.2 Generalized Nonlinear Schrodinger Equation
452(5)
Appendix C: Calculation Procedures of Triple Correlation and Bispectrum with Examples 457(8)
C.1 Triple Correlation and Bispectrum Estimation
457(1)
C.2 Properties of Bispectrum
458(1)
C.3 Bispectrum of Optical Pulse Propagation
458(6)
Reference
464(1)
Appendix D: Simulink Models 465(14)
D.1 MATLAB® and Simulink® Modeling Platforms
465(1)
D.2 Wavelength Converter in WDM System
465(1)
D.3 Nonlinear Phase Conjugation for Mid-Link Spectral Inversion
465(1)
D.4 Pulse Generator
465(1)
D.5 OTDM Demultiplexer
465(1)
D.6 Triple Correlation
466(12)
Reference
478(1)
Appendix E: Optical Waveguides 479(52)
E.1 Overview
479(1)
E.2 Optical Fiber: General Properties
479(12)
E.2.1 Geometrical Structures and Index Profile
479(3)
E.2.2 Fundamental Mode of Weakly Guiding Fibers
482(9)
E.2.2.1 Solutions of the Wave Equation for Step-Index Fiber
483(1)
E.2.2.2 Single and Few Mode Conditions
484(5)
E.2.2.3 Gaussian Approximation: Fundamental Mode Revisited
489(2)
E.3 Signal Propagation in Optical Fibers
491(11)
E.3.1 Attenuation
491(3)
E.3.1.1 Attenuation: Intrinsic or Material Absorption Losses
491(1)
E.3.1.2 Waveguide Losses
492(1)
E.3.1.3 Attenuation Coefficient
493(1)
E.3.2 Distortion
494(8)
E.3.2.1 Material Dispersion
495(4)
E.3.2.2 Waveguide Dispersion
499(3)
E.3.3 Polarization Mode Dispersion
502(1)
E.4 Transfer Function of Single Mode Fibers
502(12)
E.4.1 Linear Transfer Function
502(7)
E.4.2 Nonlinear Fiber Transfer Function
509(5)
E.5 Fiber Nonlinearity
514(9)
E.5.1 SPM, XPM Effects
515(1)
E.5.2 SPM and Modulation Instability
516(1)
E.5.3 SPM and Intra-Channel Nonlinear Effects
517(4)
E.5.4 Nonlinear Phase Noises in Cascaded Multi-Span Optical Link
521(2)
E.6 Numerical Solution: Split-Step Fourier Method
523(4)
E.6.1 Symmetrical Split-Step Fourier Method
523(4)
E.6.1.1 Modeling of Polarization Mode Dispersion
525(1)
E.6.1.2 Optimization of Symmetrical SSFM
526(1)
References
527(4)
Index 531
Le Nguyen Binh holds a B.Eng (Hons) and Ph.D from the University of Western Australia. He is currently a technical director at Huaweis European Research Centre in Munich, Germany, and has been awarded three Huawei Technologies Gold Medals for his work on advanced optical communication technologies. He was previously the chair of Commission D (Electronics and Photonics) of the National Committee for Radio Sciences of the Australian Academy of Sciences, and a professorial fellow at Nanyang Technological University, Christian-Albrechts-Universität zu Kiel, and various Australian universities. Widely published, Dr. Binh is the series editor of Photonics and Optics for CRC Press.
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