Springer-Verlag Berlin Heidelberg GmbH. Nonlinear Optics in Telecommunications

Transcription

1 Springer-Verlag Berlin Heidelberg GmbH Nonlinear Optics in Telecommunications

2 Advanced Texts in Physics This program of advanced texts covers a broad spectrum of topics which are of current and emerging interest in physics. Each book provides a comprehensive and yet accessible introduction to a field at the forefront of modern research. As such, these texts are intended for senior undergraduate and graduate students at the MS and PhD level; however, research scientists seeking an introduction to particular areas of physics will also benefit from the titles in this collection.

3 Thomas Schneider Nonlinear Optics In Telecommunications With 199 Figures, 14 Tables, and 70 Problems Solutions for Instructors available online at springeronline.com/ Springer

4 Professor Dr. Thomas Schneider Deutsche Telekom AG Fachhochschule Leipzig Gustav-Freytag-Str Leipzig, Germany ISSN ISBN Cataloging-in-Publication Data Schneider, Thomas, Nonlinear optics in telecommunications / Thomas Schneider. p.cm. - (Advanced texts in physics, ISSN ) Includes bibliographical references and index. ISBN ISBN (ebook) DOI / Optical communications. 2. Nonlinear optics. I. Tide. II. Series. TK S '7-dc22 This work is subject to copyright. All rights are reserved, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilm or in any other way, and storage in data banks. Duplication of this publication or parts tiiereof is permitted only under the provisions of the German Copyright Law of September 9, 1965, in its current version, and permission for use must always be obtained from Springer-Verlag Berlin Heidelberg GmbH. Violations are liable for prosecution under the German Copyright Law. springeronline.com Springer-Verlag Berlin Heidelberg 2004 Originally published by Springer-Verlag Berlin Heidelberg New York in 2004 Softcover reprint of the hardcover 1st edition 2004 AllWave and TrueWave are registered trademarks by Lucent Technologies, LEAF is a registered trademark by Corning, Inc. The use of general descriptive names, registered names, trademarks, etc. in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use. Typesetting: Camera-ready copy from the author using aspringer ];).TEX macro package Cover design: design & production GmbH, Heidelberg Printed on acid-free paper SPIN /3141/jl

5 Preface In today's backbone networks, data signals are almost exclusively transmitted by optical carriers in fibers. The continents and the whole world come closer together by a large number of optical fibers lying on the bottom of the oceans. Applications like the internet demand an increase of the available bandwidth in the network and reduction of costs for the transmission of data. Linear optics is, in principle, a special case of the much wider field of nonlinear optics. Nonlinearity can only be neglected if the optical intensities are small. With the increasing data rates, the optical amplification of the signals, and the incorporation of techniques like dense wavelength division multiplexing (DWDM) nonlinear optical effects become very important for system design since these effects can cause severe problems. On the other hand, the same effects offer the possibility for very fast all-optical signal processing. This book tries to give an introduction to the fascinating field of optical telecommunications. In order to write a useful text for students, technicians and researchers working in the field, the technical aspect as well as the physical background of the different effects is described in detail. In most cases the easiest way to explain the physics of nonlinear optics was chosen. Nevertheless, an attempt was always made to integrate the latest research results. Although the whole text was carefully written and corrected several times it could be possible that so me mistakes were overlooked. I apologize for this and I am very thankful for everybody who informs me about mistakes. First of all I want to thank my family, Kerstin and Clara for their support and understanding. Special thanks go to R. Fischer for the relief he gave me on important showplaces beside. I am deeply grateful to Prof. W. Glaser from the Rumboldt University in Berlin and to Prof. J. Reiffrom the Brandenburgische Technische Universität in Cottbus who gave me the opportunity to engage in the research of nonlinear optics. Special thanks to all the colleagues who discussed special subjects with me and who always had an open ear for any kind of problems: Dr. R. Schmid (BTU Cottbus), W. Ruhland and M. Messollen (FR Telekom Leipzig). I wish to acknowledge the colleagues who have read parts of the book manuscript and given their comments and suggestions to the English translation: M. Sams (FR Telekom Leipzig), Dr. M. Ammann and Dr. A. Schwarzbacher (Dublin Institute of Technology).

6 VI Preface Last hut not least I want to thank G. Biermann, from the lihrary of the FR Telekom Leipzig, who provided me with the required literature, as wen as the editors and production team from the Springer Verlag for their kind support. Leipzig, Octoher 2003 Thomas Schneider

7 Contents 1. Introduction... 1 Part I. Fundamentals of Linear and Nonlinear Optics 2. Overview of Linear Optical Effects The Wave Equation for Linear Media Solution of the Linear Wave Equation The Harmonie Oseillator Model Attenuation Amplifieation The Refraetive Index The Sellmeier Equation Phase Velocity, Group Velocity, and Dispersion Birefringenee Summary Exereises Optical Telecommunications Fiber Types Step-Index and Graded-Index Fibers Single Mode Fibers Single Mode Fiber Types Highly Nonlinear and Photonie Fibers Modulation Optieal Transport Teehnologies Summary Exereises Nonlinear Effects The Nonlinear Oseillator Nonlinear Polarization The Nonlinear Suseeptibility

8 VIII Contents Estimation of the Order of Magnitude of the Susceptibilities The Nonlinear Wave Equation Second Order Nonlinear Phenomena Third Order Nonlinear Phenomena The Nonlinear Refractive Index Effective Area and Nonlinear Coefficient Effective Length Phase Matching Capacity Limit of Optical Fibers Summary Exercises Part 11. Nonlinear Effects in Optical Waveguides 5. The Nonlinear Schrödinger Equation Derivation of the Nonlinear Schrödinger Equation Dispersion and Nonlinear Length The Linear Term Dispersion Management The Nonlinear Term Numerical Solution of the NSE Summary Exercises Self- and Cross-Phase Modulation Self-Phase Modulation (SPM) SPM's Impact on Communication Systems Experimental Results Cross-Phase Modulation (XPM) Polarization Dependence of XPM XPM's Impact on Communication Systems Summary Exercises Four-Wave-Mixing (FWM) Mixing between WDM Channels Mathematical Description of FWM Phase Matching FWM's Impact on Communication Systems FWM Suppression Experimental Results Polarization Dependence of FWM Numerical Simulation

9 Contents IX Results Summary Exercises Intrachannel Nonlinear Effects Mathematical Description SPM and IXPM IFWM and Ghost Pulses IFWM Suppression Sumrnary Exercises Solitons Mathematical Description Higher Order Solitons Limits of Solitons The Gordon-Haus Effect The Acoustic Effect Increasing the Bit Rate in Soliton Systems Mutual Interaction Between Solitons Dispersion-Managed Solitons Summary Exercises Raman Scattering The Scattering of Light Origin of Raman Scattering Raman Scattering in the Harmonie Oscillator Model Raman Scattering in Optical Fibers Spontaneous and Stimulated Scattering Threshold of Raman Scattering in Optical Waveguides Impact of Raman Scattering on Communication Systems Summary Exercises Brillouin Scattering Scattering of Optical Waves at Sound Waves Spontaneous and Stimulated Brillouin Seattering The Brillouin Gain Spectral Distribution Frequency Shift Gain Maximum l.4 Threshold of Brillouin Scattering l.5 SBS's impact on Communication Systems

10 X Contents 11.6 Brillouin Scattering for Distributed Temperature and Strain Sensors Summary Exercises Part IIl. Applieations of Nonlinear Effeets in Teleeommunieations 12. Optieal Signal Proeessing Spectrum Slicing and Nonlinear WDM Sources Wavelength Conversion Wavelength Conversion with FWM Wavelength Conversion with XPM Wavelength Conversion with SOA Optical Switching Photorefractive Optical Switches Optical Switching with the XPM Effect FWM for Optical Switching Ultrafast Optical Switching Retiming, Reshaping, and All-Optical Clock Recovery Optical Filters with SBS Summary... " Exercises Nonlinear Lasers and Amplifiers Raman Amplifier Raman Laser Brillouin Amplifiers and Lasers Radio-over-Fiber Parametrie Amplifiers Summary Exercises Nonlinear Optieal Phase Conjugation Phase-Conjugating Mirrors Distortion Compensation due to Phase Conjugation Theoretical Description of NPC Phase Conjugation as Holographie Model Mid-span Spectral Inversion Summary Exercises

11 Contents XI A. Appendices A.l div, grad, curl, rot A.2 The Gaussian Pulse A.3 Logarithmical Units References Index