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Fiber Optics

Fedor Mitschke Fiber Optics Physics and Technology 123

Prof. Dr. Fedor Mitschke Universit¨at Rostock Institut f¨ur Physik Universit¨atsplatz 3 18055 Rostock Germany fedor.mitschke@uni-rostock.de ISBN 978-3-642-03702-3 DOI 10.1007/978-3-642-03703-0 Springer Heidelberg Dordrecht London New York e-ISBN 978-3-642-03703-0 Library of Congress Control Number: 2009938485 c Springer-Verlag Berlin Heidelberg 2009 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 thereof 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. Violations are liable to prosecution under the German Copyright Law. 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. Cover design: eStudio Calamar S.L. Printed on acid-free paper Springer is part of Springer Science+Business Media (www.springer.com)

Absent a Telephone, a Bicyclist Had to Save the World On the height of the Cuban missile crisis in 1962, no direct telecommunication line existed between the White House and the Kremlin. All messages going back and forth had to be sent through intermediaries. The world teetered on the brink of nuclear Armageddon when in the evening of October 23 President John F. Kennedy sent his brother, Robert Kennedy, over to the Soviet Embassy for a last-ditch eﬀort to resolve the crisis peacefully. Robert presented a proposal how both sides could stand down without losing face. Right after the meeting, Ambassador Anatoly Dobrynin hastened to write a report to Nikita Khrushchev in Moscow. A bicycle courier was called in to take this letter to a Western Union telegraph station, and Dobrynin personally instructed him to go straight to the station because the message was important – which was hardly an exaggeration. That man on the bicycle, in my view, has saved the world. Most likely, without even knowing. A year later, a direct telegraph line was installed which was popularly called the “red telephone.” (There never was an actual red telephone sitting in the Oval Oﬃce.) A lesson had been learned: Communication can be vital when it comes to solving conﬂicts. Today the situation is vastly diﬀerent from what it was less than half a cen- tury ago. The world is knit together by a network of connections of economic, political, cultural, and other nature. That is only possible because virtually instantaneous long-distance communication at aﬀordable cost has become ubiq- uitous. In earlier centuries, important news – like the outcome of a battle, say – often was received only several weeks later. Today we are not the least bit as- tonished when we watch unfolding events in the remotest corner of the planet in real time, living color, and stereophonic sound. The biggest machine on earth is the international telephone network. It allows you to call this minute, on a lark, your neighbor, your friend in New Zealand, or the Department of Sanitation in Tokyo. And we got used to it! Behind the scenes, of course, there is a substantial investment in technology going into this, and more eﬀort is required to keep up with society’s ever-rising demands. Consider international calls: For some time satellites seemed to be the most eﬃcient and elegant means. Just a decade or two later, they were no more up to the growing task, and a new, earthbound technology took over: optical ﬁber transmission. V

VI Absent a Telephone, a Bicyclist Had to Save the World Meanwhile, the amount of data handled by ﬁbers exceeds anything that older technology could have handled ever. Today’s Internet traﬃc would not exist without ﬁber, and the cost of a long-distance phone call would still be as expensive as it was a quarter century ago. Optical ﬁbers, mostly made of glass but sometimes also other materials, are the subject of this book. The development toward their maturity we enjoy to- day was mostly driven by the challenges of telecommunications applications. Research has faced quite a number of questions concerning basic physics of guided-wave optics, and many researchers around the world toiled for answers. As a result, ﬁbers can do more than was anticipated: Besides the obvious appli- cation in telecommunications, they have also become useful in data acquisition. This is why engineers and technicians working in either ﬁeld need to know not only their electrical engineering, but increasingly also some optics. At the same time, it emerges that nonlinear physical processes in ﬁbers will lead to exciting new technology. This book has its origin in lectures for students of physics and engineering which I gave at the universities in Hannover, M¨unster, Rostock (all in Germany), and Lule˚a (Sweden). The book ﬁrst appeared in the German language. It was well received, but the German-speaking part of the world is not very big, and I heard opinions that an English version would ﬁnd a larger audience. The book presents the physical foundations in some detail, but in the in- terest of limited mathematical challenges, there is no fully vectorial treatment of the modes. On the other hand, I found it important to devote some space to nonlinear processes on grounds that over the years, they can only become more relevant than they already are. I proceed in outlining the limitation of the data-carrying capacity of ﬁbers as they will be reached in a couple of years, i.e., at a time when the student readers of this book will have entered their professional life as engineers or scientists, dealing with these questions. For the English edition, I have expanded certain sections slightly, to keep up to date with current developments. It is my hope that both natural scientists and engineers will ﬁnd the book helpful. Maybe physicist will think that some segments are quite “technical,” while engineers may feel that a treatment of nonlinear optics may be not so much for them. My answer to that is that either subject is required to form the full picture. In this context, it is sometimes unfortunate that the structure of our universities emphasizes the distinction between natural scientists and engineers more than is warranted. I envision that, in analogy to electronics engineers, we will see the emergence of photonics engineers. They would have good practical skills on the technical side and at the same time a deep understanding of the underlying physical mechanisms.

Contents I Introduction 1 A Quick Survey II Physical Foundations 2 Treatment with Ray Optics 2.1 Waveguiding by Total Internal Reﬂection . . . . . . . . . . . . . 2.2 Step Index Fiber . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.3 Modal Dispersion . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.4 Gradient Index Fibers . . . . . . . . . . . . . . . . . . . . . . . . 2.5 Mode Coupling . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.6 Shortcomings of the Ray-Optical Treatment . . . . . . . . . . . . 3 Treatment with Wave Optics 3.1 Maxwell’s Equations . . . . . . . . . . . . . . . . . . . . . . . . . 3.2 Wave Equation . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.3 Linear and Nonlinear Refractive Index . . . . . . . . . . . . . . . 3.3.1 Linear Case . . . . . . . . . . . . . . . . . . . . . . . . . . 3.3.2 Nonlinear Case . . . . . . . . . . . . . . . . . . . . . . . . 3.4 Separation of Coordinates . . . . . . . . . . . . . . . . . . . . . . 3.5 Modes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.6 Solutions for m = 0 . . . . . . . . . . . . . . . . . . . . . . . . . 3.7 Solutions for m = 1 . . . . . . . . . . . . . . . . . . . . . . . . . 3.8 Solutions for m > 1 . . . . . . . . . . . . . . . . . . . . . . . . . 3.9 Field Amplitude Distribution of the Modes . . . . . . . . . . . . 3.10 Numerical Example . . . . . . . . . . . . . . . . . . . . . . . . . . 3.11 Number of Modes . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.12 A Remark on Microwave Waveguides . . . . . . . . . . . . . . . . 3.13 Energy Transport . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 Chromatic Dispersion 4.1 Material Dispersion . . . . . . . . . . . . . . . . . . . . . . . . . . 4.1.1 Treatment with Derivatives to Wavelength . . . . . . . . . 4.1.2 Treatment with Derivatives to Frequency . . . . . . . . . 4.2 Waveguide and Proﬁle Dispersion . . . . . . . . . . . . . . . . . . 4.3 Normal, Anomalous, and Zero Dispersion . . . . . . . . . . . . . 4.4 Impact of Dispersion . . . . . . . . . . . . . . . . . . . . . . . . . 1 3 13 15 15 17 20 22 23 24 25 25 27 28 28 29 30 32 35 37 38 38 41 42 43 43 47 48 50 51 53 54 55 VII

VIII Contents 4.5 Optimized Dispersion: Alternative Refractive Index Proﬁles . . . 4.5.1 Gradient Index Fibers . . . . . . . . . . . . . . . . . . . . 4.5.2 W Fibers . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.5.3 T Fibers . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.5.4 Quadruple-Clad Fibers . . . . . . . . . . . . . . . . . . . . 4.5.5 Dispersion-Shifted or Dispersion-Flattened? . . . . . . . . 4.6 Polarization Mode Dispersion . . . . . . . . . . . . . . . . . . . . 4.6.1 Quantifying Polarization Mode Dispersion . . . . . . . . . 4.6.2 Avoiding Polarization Mode Dispersion . . . . . . . . . . 4.7 Microstructured Fibers . . . . . . . . . . . . . . . . . . . . . . . . 4.7.1 Holey Fibers . . . . . . . . . . . . . . . . . . . . . . . . . 4.7.2 Photonic Crystal Fibers . . . . . . . . . . . . . . . . . . . 4.7.3 New Possibilities . . . . . . . . . . . . . . . . . . . . . . . 5 Losses 5.1 Loss Mechanisms in Glass . . . . . . . . . . . . . . . . . . . . . . 5.2 Bend Loss . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.3 Other Losses 5.4 Ultimate Reach and Possible Alternative Constructions . . . . . 5.4.1 Heavy Molecules . . . . . . . . . . . . . . . . . . . . . . . 5.4.2 Hollow Core Fibers . . . . . . . . . . . . . . . . . . . . . . 5.4.3 Sapphire Fibers . . . . . . . . . . . . . . . . . . . . . . . . 5.4.4 Plastic Fibers . . . . . . . . . . . . . . . . . . . . . . . . . III Technical Conditions for Fiber Technology 6 Manufacturing and Mechanical Properties 6.1.1 Historical Issues 6.1.2 6.1.3 How Glass Breaks 6.1 Glass as a Material . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Structure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.2 Manufacturing of Fibers . . . . . . . . . . . . . . . . . . . . . . . 6.2.1 Making a Preform . . . . . . . . . . . . . . . . . . . . . . 6.2.2 Pulling Fibers from the Preform . . . . . . . . . . . . . . 6.3 Mechanical Properties of Fibers . . . . . . . . . . . . . . . . . . . 6.3.1 Pristine Glass . . . . . . . . . . . . . . . . . . . . . . . . . 6.3.2 Reduction of Structural Stability . . . . . . . . . . . . . . 58 58 59 61 61 62 64 64 65 67 69 73 74 75 75 77 79 80 81 82 83 83 85 87 87 87 88 91 93 93 96 98 98 99 7 How to Measure Important Fiber Characteristics 101 7.1 Loss . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 101 7.2 Dispersion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 102 7.3 Geometry of Fiber Structure . . . . . . . . . . . . . . . . . . . . 106 7.4 Geometry of Amplitude Distribution . . . . . . . . . . . . . . . . 108 7.4.1 Near-Field Methods . . . . . . . . . . . . . . . . . . . . . 108 7.4.2 Far-Field Methods . . . . . . . . . . . . . . . . . . . . . . 110 7.5 Cutoﬀ Wavelength . . . . . . . . . . . . . . . . . . . . . . . . . . 112 7.6 Optical Time Domain Reﬂectometry (OTDR) . . . . . . . . . . . 114

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