Shaping Light in Nonlinear Optical Fibers

Sonia Boscolo, Christophe Finot, Sonia Boscolo, Christophe Finot

• Publisher: Wiley
• Year: 2017
• Print ISBN:
  9781119088127
• Edition: 1
• eBook ISBN:
  9781119088158
• Topic: Technology & Engineering
• Subtopic: Electrical Engineering & Telecommunications
• Index: Technology & Engineering

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.

CHAPTER 1
Modulation Instability, Four-Wave Mixing and their Applications

Tobias Hansson,¹ Alessandro Tonello,² Stefano Trillo,³ and StefanWabnitz⁴

¹ INRS-EMT, 1650 Boulevard Lionel-Boulet, Varennes, Québec, Canada
² Institut de Recherche XLIM, UMR 7252 CNRS, Université de Limoges, Limoges, France
³ Department of Engineering, University of Ferrara, Ferrara, Italy
⁴ Information Engineering Department, University of Brescia, Brescia, Italy

1.1 Introduction

Modulation instability (MI) of a continuous wave (CW) background solution of the nonlinear Schrödinger (NLS) equation is a well-known phenomenon that occurs in a variety of fields, such as nonlinear optics, hydrodynamics, plasma physics and Bose-Einstein condensation [1, 2]. In the nonlinear optics context, MI is the main mechanism for the generation of optical solitons, supercontinuum (SC) [3, 4], and rogue waves [5]. MI may be induced either by quantum noise or by a weak seed signal [6]: in the latter case, the initial stage of exponential signal amplification is followed first by the generation of higher-order sideband pairs by cascade four-photon mixing processes. Next, nonlinear gain saturation occurs, owing to pump depletion. After the maximum level of pump depletion is reached, which depends on the initial sideband detuning, the pump power and the fiber dispersion, energy flows back from the sidebands into the pump, until the initial condition is recovered, and so on. This phenomen provides a classical example of the so-called Fermi-Pasta-Ulam (FPU) recurrence [7, 8]. This process can be described in terms of exact solutions of the NLS equation [9–12], and has been experimentally observed in different physical settings, such as deep water waves [13, 14], in nonlinear optical fibers [15–20], in nematic liquid crystals [21], magnetic film strip-based active feedback rings [22], and bimodal electrical transmission lines [23]. Important qualitative physical insight into the FPU recurrence dynamics (e.g., the existence of a homoclinic structure and the associated dependence of the FPU recurrence period upon the input relative phase between pump and initial sidebands) may be obtained by means of a truncation to a finite number of Fourier modes, which may lead to simple, low-dimensional models [24–26].

In Section 1.1, we present an overview of the analysis of the nonlinear dynamics of MI by means of a simple three-mode truncation. Next we discuss how the coupling between two polarization modes in a birefringent optical fiber may extend the domain of MI to the normal dispersion regime. Also in the vector case, an important qualitative insight into the dynamics of the nonlinear development of MI may be obtained by using a three-mode truncation. We also briefly discuss the case where the MI is induced by two pumps and occurs on top of multiple four-wave mixing. We further present the effect of higher-order MI, which occurs whenever not only the initial modulation seed but also some of its harmonics are modulationally unstable. In this case, at some distance along the fiber one can observe the development of a full modulation of the CW pump with a frequency which is double the initial modulation. A similar situation also occurs in a random birefringence telecom fiber that may be described by means of the Manakov system. In this case, the doubling of the initial modulation frequency occurs whenever the CW pump and the signal are orthogonally polarized. We conclude the first section by examining the competition between spontaneous or noise-induced MI and induced MI, which leads to a break-up of the FPU recurrence after a small number of periods.

MI is a time domain description of a degenerate four-wave mixing (FWM) process in the frequency space. Interestingly, in optical fibers there are a variety of FWM processes: in Section 1.2, we present a peculiar non-degenerate MI process which is also known as Bragg scattering FWM. In this process, two intense pumps lead to a periodic power exchange between a seed signal and an idler, without any exponential amplification of the sid...

Table of contents

• Cover
• Title Page
• Copyright
• List of Contributors
• Preface
• Chapter 1 Modulation Instability, Four-Wave Mixing and their Applications
• Chapter 2 Phase-Sensitive Amplification and Regeneration
• Chapter 3 Novel Nonlinear Optical Phenomena in Gas-Filled Hollow-Core Photonic Crystal Fibers
• Chapter 4 Modulation Instability in Periodically Modulated Fibers
• Chapter 5 Pulse Generation and Shaping Using Fiber Nonlinearities
• Chapter 6 Nonlinear-Dispersive Similaritons of Passive Fibers: Applications in Ultrafast Optics
• Chapter 7 Applications of Nonlinear Optical Fibers and Solitons in Biophotonics and Microscopy
• Chapter 8 Self-Organization of Polarization State in Optical Fibers
• Chapter 9 All-Optical Pulse Shaping in the Sub-Picosecond Regime Based on Fiber Grating Devices
• Chapter 10 Rogue Breather Structures in Nonlinear Systems with an Emphasis on Optical Fibers as Testbeds
• Chapter 11 Wave-Breaking and Dispersive Shock Wave Phenomena in Optical Fibers
• Chapter 12 Optical Wave Turbulence in Fibers
• Chapter 13 Nonlocal Disordered Media and Experiments in Disordered Fibers
• Chapter 14 Wide Variability of Generation Regimes in Mode-Locked Fiber Lasers
• Chapter 15 Ultralong Raman Fiber Lasers and Their Applications
• Chapter 16 Shaping Brillouin Light in Specialty Optical Fibers
• Index
• EULA