Asymmetric Dual Core Waveguides: Dynamics of Self-Similar Waves

Description

This book highlights the dynamical behavior of self-similar waves in asymmetric dual-core waveguides. The proposed dual-core waveguide consists of two closely spaced adjoining fibers in which one fiber is active and the other is passive. Due to the linear coupling between them, the dynamics of the wave propagating through the passive core can be controlled by manipulating the dynamics of the wave propagating in the active core.  The optimal pulse compression or amplification of these waves as the length of the fiber tends to infinity is presented. The exact Mobius transform self-similar solutions that propagate through these waveguides self-similarly are subject to simple scaling rules. The book includes experiments conducted to corroborate the analytical predictions. Preface Contents 1 Nonlinear Compression of Self-Similar Waves in Asymmetric Dual-Core Waveguides 1.1 Introduction 1.2 Asymmteric Dual-Core Waveguides 1.3 Compression Problem 1.4 Conclusion References 2 Chirped Self-Similar Waves in Asymmetric Twin-Core Fibers with Nonlinear Gain 2.1 Introduction 2.2 Self-Similar Propagation in Asymmetric TCF 2.3 Exact Self-Similar Solutions 2.3.1 Trigonometric Solution 2.3.2 Pure Elliptic Solution 2.3.3 Dark Solitary Wave 2.4 Nonlinear Chirping 2.5 Nonlinear Compression 2.6 The Nonlinear Coherent Asymmetric Twin-Core Photonic Crystal Fiber Coupler 2.7 Conclusion References 3 Controlling Optical Similaritons in Graded-Index Nonlinear Waveguide with an External Source 3.1 Introduction 3.2 Our Model 3.3 Explicit Self-Similar Solutions 3.3.1 Self-Focusing Nonlinearity σ=1 3.3.2 Self-Focusing Nonlinearity σ=-1 3.4 Conclusion References 4 Dynamical Behavior of Optical Similaritons in a Tapered Graded-Index Nonlinear Fiber Amplifier with an External Source 4.1 Introduction 4.2 Asymmetric TCF and Similariton Propagation 4.3 Exact Self-Similar Solutions 4.3.1 Self-Focusing Nonlinearity, σ=1 4.3.2 Stability of the Exact Similaritons 4.3.3 Self-Defocusing Nonlinearity, σ=-1 4.4 Conclusion References 5 Controllable Approximate and Asymptotic Similaritons in Asymmetric Dual-Core Waveguide 5.1 Introduction 5.2 Similariton Propagation in TCF 5.3 Controllable Behavior of Similaritons 5.3.1 Dispersive Similaritons 5.3.2 Rectangular Similaritons 5.4 Stability of the Similaritons 5.5 Self-Similar Evolutions of Trigonometric and Hermite–Gaussian … 5.6 Our Model 5.7 Asymptotic Novel Similaritons 5.7.1 Trigonometric Similariton 5.7.2 Hermite–Gauss similariton 5.8 Conclusion References 6 Airy–Bessel Modulated Self-Similar Waves in Asymmetric Twin-Core Fiber Amplifiers 6.1 Introduction 6.2 Model Equation 6.3 Self-Similar Wave Packets in Asymmetric Twin-Core Fibers 6.3.1 Möbius Transform Wave Packet Similaritons for Self-Focusing Nonlinearity, σ=1 6.3.2 Möbius Transform Similaritons for Self-Defocusing Nonlinearity, σ=-1 6.4 Computer Simulations 6.5 Conclusion References 7 Controlling Spatiotemporal Waves in Asymmetric Dual-Core Waveguides 7.1 Introduction 7.2 Self-Similar Propagation Through Asymmetric DWG 7.3 Asymptotic Exact Self-Similar Solutions 7.4 Conclusion References 8 Conclusions and Future Perspectives Appendix Matlab Codes