Optical Communication Systems

Limits and Possibilities

Andrew Ellis, Mariia Sorokina, Andrew Ellis, Mariia Sorokina

• Publisher: Jenny Stanford Publishing
• Year: 2019
• Print ISBN: 9789814800280
• eBook ISBN: 9780429648267
• Topic: Computer Science
• Subtopic: Computer Networking
• Index: Computer Science

Telecommunications have underpinned social interaction and economic activity since the 19th century and have been increasingly reliant on optical fibers since their initial commercial deployment by BT in 1983. Today, mobile phone networks, data centers, and broadband services that facilitate our entertainment, commerce, and increasingly health provision are built on hidden optical fiber networks. However, recently it emerged that the fiber network is beginning to fill up, leading to the talk of a capacity crunch where the capacity still grows but struggles to keep up with the increasing demand. This book, featuring contributions by the suppliers of widely deployed simulation software and academic authors, illustrates the origins of the limited performance of an optical fiber from the engineering, physics, and information theoretic viewpoints. Solutions are then discussed by pioneers in each of the respective fields, with near-term solutions discussed by industrially based authors, and more speculative high-potential solutions discussed by leading academic groups.

Chapter 1

Modelling High-Capacity Nonlinear Transmission Systems

Hadrien Louchet, Nikolay Karelin, and André Richter

VPIphotonics, Berlin, 10587, Germany

[email protected]

1.1 Introduction

In 1966 Charles Kao and George Hockham [1] predicted that silica-based fibre could be a very effective medium for communication offering huge bandwidth and potentially very low loss compared to co-axial cables and copper wires despite of the very high attenuation of the first optical fibres (1000 dB/km). As early as 1970 a team at Corning [2] managed to produce about 100 m of fibre with characteristics close to the one predicted by Kao and Hockham¹. Since then fibre fabrication and design have been improved thriving to design fibres with characteristics as close as possible to the ones of an ideal transmission channel with identity transfer function. All deviations from this ideal channel such as loss, chromatic dispersion (CD), polarization mode dispersion (PMD) and nonlinearities are usually called transmission impairments. Notable exceptions to this approach are Soliton systems (see Chapter 7) that explicitly make use of the dispersive and nonlinear nature of the optical fibre. Erbium-doped fibre amplifiers (EDFAs) [3–4] and dispersion compensating fibres [5] (DCF) have been introduced in the 1980s and 1990s, respectively, to compensate for the fibre attenuation and CD unlocking the optical fibre potential for long haul high-capacity transmission.

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¹ The well-documented history of optical fibre can be found at http://opticalfibre-history.co.uk as well as in Hecht, Jeff. City of Light: The Story of Fiber Optics. Oxford University Press on Demand, 2004.

Nowadays the digital coherent optical technology, as introduced by Nortel Networks, allows to compensate all linear effects (CD, PMD, polarization rotation) at the receiver. Consequently, the remaining deviations from the identity channel are due to amplified spontaneous emission, ASE, modelled as additive white Gaussian noise, filtering effects and cross-talk resulting from optical add-drop multiplexers and complex interactions between linear and nonlinear propagation effects. While filtering and cross-talk effects can be modelled easily, accurate modelling of nonlinear interactions and their impact on the system performance remains an important challenge. This is especially true for high-capacity systems operating in the nonlinear regime and approaching or exceeding the nonlinear Shannon limit (see Chapter 5). Key aspects for accurate modelling of nonlinear effects in such systems are reviewed in this chapter.

1.2 Nonlinear Fibre Propagation: From Single to Multimode

1.2.1 Wave Equation

The propagation of an optical field, which is particular case of an electromagnetic wave, in an optical fibre is governed by Maxwell’s equations. In a dielectric medium like fused silica, nonlinear effects are weak and can be treated as perturbation. In this framework, the wave equation takes the following form:

${\nabla }^2\tilde{E}+{\overline{n}}^2\frac{{\omega }^2}{c^2}\tilde{E}=0,$

(1.1)

where Ẽ is the Fourier transform of the electrical field vector E expressed in the time domain, c is the light velocity in vacuum and $\overline{n}$ the (complex) refractive index of the waveguide. $\overline{n}$ is related to the medium relative permittivity ε_r and electric susceptibility χ_e as follows: $\overline{n}=\sqrt{{\epsilon }_{\text{r}}}=\sqrt{1+{\chi }_{\text{e}}}$. In an isotropic medium, i.e. when $\overline{n}$ is independent of the position...

Table of contents

• Cover
• Half Title
• Title Page
• Copyright Page
• Table of Contents
• Preface
• 1. Modelling High-Capacity Nonlinear Transmission Systems
• 2. Basic Optical Fiber Nonlinear Limits
• 3. Fiber Nonlinearity Compensation: Performance Limits and Commercial Outlook
• 4. Phase-Conjugated Twin Waves and Phase-Conjugated Coding
• 5. Information-Theoretic Concepts for Fiber Optic Communications
• 6. Advanced Coding for Fiber-Optics Communications Systems
• 7. Nonlinear Fourier Transform-Based Optical Transmission: Methods for Capacity Estimation
• 8. Spatial Multiplexing: Technology
• 9. Spatial Multiplexing: Modelling
• Index