Table Of ContentNonlinear Optics in Telecommunications
Springer-Verlag Berlin Heidelberg GmbH
Advanced Texts in Physics
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Thomas Schneider
Nonlinear Optics
•
In
Telecommunications
With 199 Figures, 14 Tables, and 70 Problems
Solutions for Instructors available online
at springeronline.com/3-540-20195-5
Springer
Professor Dr. Thomas Schneider
Deutsche Telekom AG
Fachhochschule Leipzig
Gustav-Freytag-Str. 43-45
04277 Leipzig, Germany
E-mail: [email protected]
ISSN 1439-2674
ISBN 978-3-642-°5772-4
Cataloging-in-Publication Data
Schneider, Thomas, 1965-
Nonlinear optics in telecommunications / Thomas Schneider.
p.cm. - (Advanced texts in physics, ISSN 1439-2674)
Includes bibliographical references and index.
ISBN 978-3-642-05772-4 ISBN 978-3-662-08996-5 (eBook)
DOI 10.1007/978-3-662-08996-5
1. Optical communications. 2. Nonlinear optics. I. Tide. II. Series.
TK5103.59.S362004
621.382'7-dc22
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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 phys
ical background of the different effects is described in detail. In most cases
the easiest way to explain the physics of nonlinear optics was chosen. Never
theless, 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 trans
lation: M. Sams (FR Telekom Leipzig), Dr. M. Ammann and Dr. A. Schwarz
bacher (Dublin Institute of Technology).
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
Contents
1. Introduction.............................................. 1
Part I. Fundamentals of Linear and Nonlinear Optics
2. Overview of Linear Optical Effects . . . . . . . . . . . . . . . . . . . . . . . . 9
2.1 The Wave Equation for Linear Media. ... . . . . . . . . . . . . . . . .. 10
2.2 Solution of the Linear Wave Equation . . . . . . . . . . . . . . . . . . . .. 13
2.3 The Harmonie Oseillator Model. . . . . . ... . . . . . . . . . . . . . . . .. 15
2.4 Attenuation ........................................... 19
2.5 Amplifieation.......................................... 22
2.6 The Refraetive Index ................................... 26
2.6.1 The Sellmeier Equation .......... . . . . . . . . . . . . . . . .. 26
2.6.2 Phase Velocity, Group Velocity, and Dispersion. . . . . .. 29
2.7 Birefringenee........................................... 36
Summary .................................................. 37
Exereises .................................................. 39
3. Optical Telecommunications . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 41
3.1 Fiber Types. . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . .. 42
3.1.1 Step-Index and Graded-Index Fibers. . . . . . . . . . . . . . .. 43
3.2 Single Mode Fibers . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . .. 44
3.2.1 Single Mode Fiber Types. . . . . . . .. . . . . . . . . . . . . . . . .. 46
3.3 Highly Nonlinear and Photonie Fibers. . . . . . . . . . . . . . . . . . . .. 49
3.4 Modulation............................................ 56
3.5 Optieal Transport Teehnologies. . . . . . . . . . . . . . . . . . . . . . . . . .. 59
Summary .................................................. 62
Exereises .................................................. 62
4. Nonlinear Effects . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 65
4.1 The Nonlinear Oseillator ................................ 66
4.2 Nonlinear Polarization .................................. 71
4.3 The Nonlinear Suseeptibility . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 73
VIII Contents
4.3.1 Estimation of the Order of Magnitude
of the Susceptibilities . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 78
4.4 The Nonlinear Wave Equation ........................... 81
4.5 Second Order Nonlinear Phenomena . . . . . . . . . . . . . . . . . . . . .. 82
4.6 Third Order Nonlinear Phenomena . . . . . . . . . . . . . . . . . . . . . .. 87
4.7 The Nonlinear Refractive Index. . . . . . . . . . . . . . . . . . . . . . . . .. 91
4.8 Effective Area and Nonlinear Coefficient. . . . . . . . . . . . . . . . . .. 96
4.9 Effective Length. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 98
4.10 Phase Matching . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 100
4.11 Capacity Limit of Optical Fibers .. . . . . . . . . . . . . . . . . . . . . . .. 107
Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 113
Exercises .................................................. 114
Part 11. Nonlinear Effects in Optical Waveguides
5. The Nonlinear Schrödinger Equation ..................... 119
5.1 Derivation of the Nonlinear Schrödinger Equation .......... 119
5.2 Dispersion and Nonlinear Length ......................... 125
5.3 The Linear Term ....................................... 127
5.4 Dispersion Management ................................. 134
5.5 The Nonlinear Term .................................... 138
5.6 Numerical Solution of the NSE ........................... 139
Summary .................................................. 140
Exercises .................................................. 141
6. Self- and Cross-Phase Modulation ........................ 143
6.1 Self-Phase Modulation (SPM) ............................ 144
6.1.1 SPM's Impact on Communication Systems .......... 147
6.1.2 Experimental Results ............................. 151
6.2 Cross-Phase Modulation (XPM) .......................... 154
6.2.1 Polarization Dependence of XPM ................... 157
6.2.2 XPM's Impact on Communication Systems .......... 159
Summary .................................................. 164
Exercises .................................................. 165
7. Four-Wave-Mixing (FWM) ............................... 167
7.1 Mixing between WDM Channels ......................... 168
7.2 Mathematical Description of FWM ....................... 171
7.3 Phase Matching ........................................ 174
7.4 FWM's Impact on Communication Systems ................ 180
7.5 FWM Suppression ...................................... 186
7.6 Experimental Results ................................... 189
7.7 Polarization Dependence of FWM ........................ 194
7.7.1 Numerical Simulation ............................. 195
Contents IX
7.7.2 Results .......................................... 196
Summary .................................................. 200
Exercises .................................................. 200
8. Intrachannel Nonlinear Effects ............................ 201
8.1 Mathematical Description ............................... 203
8.2 SPM and IXPM ........................................ 204
8.3 IFWM and Ghost Pulses ................................ 207
8.4 IFWM Suppression ..................................... 210
Sumrnary .................................................. 212
Exercises .................................................. 213
9. Solitons ................................................... 215
9.1 Mathematical Description ............................... 216
9.2 Higher Order Solitons ................................... 220
9.3 Limits of Solitons ....................................... 225
9.3.1 The Gordon-Haus Effect .......................... 226
9.3.2 The Acoustic Effect ............................... 228
9.4 Increasing the Bit Rate in Soliton Systems ................. 229
9.5 Mutual Interaction Between Solitons ...................... 232
9.6 Dispersion-Managed Solitons ............................. 234
Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 236
Exercises .................................................. 237
10. Raman Scattering ........................................ 239
10.1 The Scattering of Light ................................. 240
10.2 Origin of Raman Scattering .............................. 242
10.2.1 Raman Scattering in the Harmonie Oscillator Model .. 244
10.3 Raman Scattering in Optical Fibers ....................... 248
10.3.1 Spontaneous and Stimulated Scattering ............. 251
10.3.2 Threshold of Raman Scattering in Optical Waveguides 253
10.4 Impact of Raman Scattering on Communication Systems .... 258
Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 266
Exercises .................................................. 267
11. Brillouin Scattering ....................................... 269
11.1 Scattering of Optical Waves at Sound Waves ............... 270
11.2 Spontaneous and Stimulated Brillouin Seattering ........... 274
11.3 The Brillouin Gain ..................................... 277
11.3.1 Spectral Distribution ............................. 277
11.3.2 Frequency Shift .................................. 280
11.3.3 Gain Maximum .................................. 281
1l.4 Threshold of Brillouin Scattering ......................... 283
1l.5 SBS's impact on Communication Systems ................. 286
X Contents
11.6 Brillouin Scattering for Distributed Temperature
and Strain Sensors. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 292
Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 295
Exercises .................................................. 296
Part IIl. Applieations of Nonlinear Effeets in Teleeommunieations
12. Optieal Signal Proeessing ................................. 299
12.1 Spectrum Slicing and Nonlinear WDM Sources ............. 300
12.2 Wavelength Conversion .................................. 305
12.2.1 Wavelength Conversion with FWM ................. 306
12.2.2 Wavelength Conversion with XPM .................. 309
12.2.3 Wavelength Conversion with SOA .................. 311
12.3 Optical Switching ...................................... 315
12.3.1 Photorefractive Optical Switches ................... 317
12.3.2 Optical Switching with the XPM Effect ............. 323
12.3.3 FWM for Optical Switching ....................... 332
12.3.4 Ultrafast Optical Switching ........................ 333
12.4 Retiming, Reshaping, and All-Optical Clock Recovery ....... 337
12.5 Optical Filters with SBS ................................ 339
Summary ........................................ " ........ 341
Exercises .................................................. 342
13. Nonlinear Lasers and Amplifiers .......................... 343
13.1 Raman Amplifier ....................................... 344
13.2 Raman Laser .......................................... 350
13.3 Brillouin Amplifiers and Lasers ........................... 352
13.3.1 Radio-over-Fiber ................................. 355
13.4 Parametrie Amplifiers ................................... 358
Summary .................................................. 365
Exercises .................................................. 366
14. Nonlinear Optieal Phase Conjugation ..................... 367
14.1 Phase-Conjugating Mirrors .............................. 367
14.2 Distortion Compensation due to Phase Conjugation ......... 370
14.3 Theoretical Description of NPC .......................... 373
14.4 Phase Conjugation as Holographie Model .................. 376
14.5 Mid-span Spectral Inversion ............................. 378
Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 383
Exercises .................................................. 384
