Mathematical Theory of Dispersion-Managed Optical Solitons discusses recent advances covering optical solitons, soliton perturbation, optical cross-talk, Gabitov-Turitsyn Equations, quasi-linear pulses, and higher order Gabitov-Turitsyn Equations. Focusing on a mathematical perspective, the book bridges the gap between concepts in engineering and mathematics, and gives an outlook to many new topics for furtherresearch.
1 Introduction
References
2 Nonlinear Schrodingers Equation
2.1 Derivation of NLSE
2.1.1 Limitations of conventional solitons
2.1.2 Dispersion-management
2.1.3 Mathematical formulation
2.2 Integrals of motion
2.3 Soliton perturbation theory
2.3.1 Perturbation terms
2.4 Variational principle
2.4.1 Perturbation terms
References
3 Polarization Preserving Fibers
3.1 Introduction
3.2 Integrals of motion
3.2.1 Gaussian pulses
3.2.2 Super-Gaussian pulses
3.2.3 Super-Sech pulses
3.3 Variational principle
3.3.1 Gaussian pulses
3.3.2 Super-Gaussian pulses
3.4 Perturbation terms
3.4.1 Gaussian pulses
3.4.2 Super-Gaussian pulses
3.5 Stochastic perturbation
References
4 Birefringent Fibers
4.1 Introduction
4.2 Integrals of motion
4.2.1 Gaussian pulses
4.2.2 Super-Gaussian pulses
4.3 Variational principle
4.3.1 Gaussian pulses
4.3.2 Super-Gaussian pulses
4.4 Perturbation terms
4.4.1 Gaussian pulses
4.4.2 Super-Gaussian pulses
References
5 Multiple Channels
5.1 Introduction
5.2 Integrals of motion
5.2.1 Gaussian pulses
5.2.2 Super-Gaussian pulses
5.3 Variational principle
5.3.1 Gaussian pulses
5.3.2 Super-Gaussian pulses
5.4 Perturbation terms
5.4.1 Gaussian pulses
5.4.2 Super-Gaussian pulses
References
6 Optical Crosstalk
6.1 In-band crosstalk
6.2 Gaussian optical pulse
6.2.1 Bit error rate
6.3 Sech optical pulse
6.4 Super-Sech optical pulse
References
7 Gabitov-Turitsyn Equation
7.1 Introduction
7.2 Polarization-preserving fibers
7.2.1 Special solutions
7.3 Birefringent fibers
7.4 DWDM system
7.5 Properties of the kernel
7.5.1 Lossless Case
7.5.2 Lossy Case
References
8 Quasi-linear Pulses
8.1 Introduction
8.2 Polarization-preserving fibers
8.2.1 Lossless system
8.2.2 Lossy system
8.3 Birefringent fibers
8.3.1 Lossless system
8.3.2 lossy system
8.4 Multiple channels
8.4.1 Lossless system
8.4.2 Lossy system
References
9 Higher Order Gabitov-Turitsyn Equations
9.1 Introduction
9.2 Polarization preserving fibers
9.3 Birefringent fibers
9.4 DWDM systems
References
Index
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