Essentials of Modern Optical Fiber Communication

343 Pages·2016·12.914 MB·English

by  Reinhold Noé (auth.)

Reinhold Noé
Essentials
of Modern
Optical Fiber
Communication
Second Edition
123
Essentials of Modern Optical Fiber Communication
é
Reinhold No
Essentials of Modern Optical
Fiber Communication
Second Edition
123
ReinholdNoé
Faculty of Computer Science, Electrical
EngineeringandMathematics, Institute
forElectricalEngineeringandInformation
Technology
Paderborn University
Paderborn
Germany
ISBN978-3-662-49621-3 ISBN978-3-662-49623-7 (eBook)
DOI 10.1007/978-3-662-49623-7
LibraryofCongressControlNumber:2016935217
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Preface
This book covers important aspects of modern optical communication. It is inten-
dedtoservebothstudentsandprofessionals.Consequently,asolidcoverageofthe
necessaryfundamentalsiscombinedwithanin-depthdiscussionofrecent relevant
research results.
The book has grown from lecture notes over the years, starting 1992. It
accompanies my present lectures on Optical Communication A (Fundamentals),
B(ModeCoupling),C(ModulationFormats)andD(SelectedTopics)atPaderborn
University in Germany.
I gratefully acknowledge contributions to this book from Dr. Timo Pfau,
Dr. David Sandel and Prof. Dr. Sebastian Hoffmann.
v
Contents
1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
2 Optical Waves in Fibers and Components. . . . . . . . . . . . . . . . . . . . 3
2.1 Electromagnetic Fundamentals. . . . . . . . . . . . . . . . . . . . . . . . . . 3
2.1.1 Maxwell’s Equations . . . . . . . . . . . . . . . . . . . . . . . . . . . 3
2.1.2 Boundary Conditions. . . . . . . . . . . . . . . . . . . . . . . . . . . 6
2.1.3 Wave Equation. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8
2.1.4 Homogeneous Plane Wave in Isotropic
Homogeneous Medium . . . . . . . . . . . . . . . . . . . . . . . . . 10
2.1.5 Power and Energy. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13
2.2 Dielectric Waveguides . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28
2.2.1 Dielectric Slab Waveguide . . . . . . . . . . . . . . . . . . . . . . . 29
2.2.2 Cylindrical Dielectric Waveguide . . . . . . . . . . . . . . . . . . 38
2.3 Polarization. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52
2.3.1 Representing States-of-Polarization . . . . . . . . . . . . . . . . . 52
2.3.2 Anisotropy, Index Ellipsoid . . . . . . . . . . . . . . . . . . . . . . 58
2.3.3 Jones Matrices, Müller Matrices . . . . . . . . . . . . . . . . . . . 65
2.3.4 Monochromatic Polarization Transmission . . . . . . . . . . . . 82
2.3.5 Polarization Mode Dispersion. . . . . . . . . . . . . . . . . . . . . 92
2.3.6 Polarization-Dependent Loss. . . . . . . . . . . . . . . . . . . . . . 100
2.4 Linear Electrooptic Effect. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 106
2.4.1 Phase Modulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 106
2.4.2 Soleil-Babinet Compensator . . . . . . . . . . . . . . . . . . . . . . 110
2.5 Mode Coupling. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 114
2.5.1 Mode Orthogonality. . . . . . . . . . . . . . . . . . . . . . . . . . . . 114
2.5.2 Mode Coupling Theory . . . . . . . . . . . . . . . . . . . . . . . . . 119
2.5.3 Codirectional Coupling in Anisotropic Waveguide. . . . . . . 122
2.5.4 Codirectional Coupling of Two Waveguides. . . . . . . . . . . 129
2.5.5 Periodic Codirectional Coupling . . . . . . . . . . . . . . . . . . . 135
2.5.6 Periodic Counterdirectional Coupling. . . . . . . . . . . . . . . . 140
vii
viii Contents
2.6 Differential Group Delay Profiles. . . . . . . . . . . . . . . . . . . . . . . . 142
2.6.1 DGD Profiles and Discrete Mode Coupling . . . . . . . . . . . 142
2.6.2 Polarization Mode Dispersion Compensation. . . . . . . . . . . 148
2.6.3 Chromatic Dispersion Compensation . . . . . . . . . . . . . . . . 154
2.6.4 Fourier Expansion of Mode Coupling . . . . . . . . . . . . . . . 160
2.6.5 DGD and PDL Profiles Determined
by Inverse Scattering. . . . . . . . . . . . . . . . . . . . . . . . . . . 165
2.7 Nonlinearities in Optical Fibers. . . . . . . . . . . . . . . . . . . . . . . . . 169
2.7.1 Self Phase Modulation. . . . . . . . . . . . . . . . . . . . . . . . . . 170
2.7.2 Cross Phase Modulation. . . . . . . . . . . . . . . . . . . . . . . . . 181
2.7.3 Four-Wave Mixing . . . . . . . . . . . . . . . . . . . . . . . . . . . . 184
3 Optical Fiber Communication Systems . . . . . . . . . . . . . . . . . . . . . . 189
3.1 Standard Systems with Direct Optical Detection . . . . . . . . . . . . . 189
3.1.1 Signal Generation, Transmission, and Detection . . . . . . . . 189
3.1.2 Regeneration of Binary Signals. . . . . . . . . . . . . . . . . . . . 206
3.1.3 Circuits and Clock Recovery. . . . . . . . . . . . . . . . . . . . . . 214
3.2 Advanced Systems with Direct Detection . . . . . . . . . . . . . . . . . . 222
3.2.1 Photon Distributions . . . . . . . . . . . . . . . . . . . . . . . . . . . 222
3.2.2 Noise Figure of Optical Amplifier. . . . . . . . . . . . . . . . . . 228
3.2.3 Intensity Distributions . . . . . . . . . . . . . . . . . . . . . . . . . . 232
3.2.4 Receivers for Amplitude Shift Keying . . . . . . . . . . . . . . . 236
3.2.5 Receivers for Differential Phase Shift Keying . . . . . . . . . . 241
3.2.6 Polarization Division Multiplex. . . . . . . . . . . . . . . . . . . . 256
3.3 Coherent Optical Transmission . . . . . . . . . . . . . . . . . . . . . . . . . 262
3.3.1 Receivers with Synchronous Demodulation. . . . . . . . . . . . 262
3.3.2 Carrier Recovery. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 273
3.3.3 Receivers with Asynchronous Demodulation. . . . . . . . . . . 283
3.3.4 Laser Linewidth Requirements . . . . . . . . . . . . . . . . . . . . 287
3.3.5 Digital Coherent QPSK Receiver. . . . . . . . . . . . . . . . . . . 294
3.3.6 Digital Coherent QAM Receiver. . . . . . . . . . . . . . . . . . . 306
3.3.7 Other Modulation Schemes. . . . . . . . . . . . . . . . . . . . . . . 324
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 327
Index . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 335
Chapter 1
Introduction
Attheendofthe1970s,telecomcarriersstartedtolayopticalfiberbetweentelecom
exchangeoffices,andcoaxialcableforelectricaldatacommunicationwasnolonger
deployed. The performance of optical fiber communication has since then grown
exponentially,verymuchlikeMoore’slawforthecomplexityofelectroniccircuits.
In the electronic domain, rising clock speeds, miniaturization offeature sizes, and
chip size increase along two, maybe soon along the third dimension, are con-
tributing to this truly impressive growth. The performance of optical communica-
tion is determined by clock speed as offered by a state-of-the-art electronic
technology, availability of several or if needed many fibers in one cable, multiple
optical channels carried on a single optical fiber by means of wavelength division
multiplex, and recently the transmission of several bits per symbol.
Theeconomicandsocietalimpactisdramatic:Opticalfibercommunicationisa
key enabler of the worldwide web, of e-mail and of all but local telephone con-
nections. The technically exploitable fiber bandwidth is roughly 10 THz, orders of
magnitude higher than in other media. Fiber attenuation is extremely small: After
100 km offiber there is still about 1 % of the input power left. Optical amplifiers,
with 4 THz bandwidth or more, overcome fiber loss so that transoceanic trans-
mission is possible without intermediate signal regeneration.
Around the year 2000, in the so-called dotcom era, growth rates of information
exchange of about one order of magnitude per year were forecast. This triggered
massiveinvestmentsandresultedinthefoundingofmanynewcompaniesinashort
time. A significant part of that investment was lost, while achieved technical pro-
gress remains available at large. The telecom industry has consolidated since then
because investments make sense only if customers pay them back. Of course,
customers don’t want to spend a significant part of their household budget for
communication, even though available bandwidth has grown by more than two
orders of magnitude thanks to DSL technology.
But today’s communication does indeed grow by a factor of 1.4 per year or so.
Private communication such as music downloading, video portals, personal web-
sites and of course also the ever more complex and video-laden media and
©Springer-VerlagBerlinHeidelberg2016 1
R.Noé,EssentialsofModernOpticalFiberCommunication,
DOI10.1007/978-3-662-49623-7_1
2 1 Introduction
enterprise websites are responsible for this, along with video telephony services,
drasticallyincreasingusageoftheinternetindevelopingcountries,andsoon.Asa
consequence there is healthy business. In contrast, revenues increase only on a
single-digit percent scale annually. The quantitative growth is entertained by the
technical and productivity progress.
With the rather conservative spending pattern of end users in mind, telecom
carriers want to preserve their enormous investments in fiber infrastructure, and to
use newly deployed fiber most economically. Multilevel modulation schemes,
includingtheuseoftwoorthogonalpolarizationmodes,areneededtoexploitfibers
optimally. At the same time, phase modulation increases noise tolerance. Recent
researchanddevelopmentplacesspecialemphasisontheseissues,andsodoesthis
book.
Understanding fibers requires a knowledge of dielectric waveguides and their
modes,includingpolarizations.Chapter2isthereforedevotedtowavepropagation
in ideal and nonideal optical waveguides, also exhibiting polarization mode dis-
persion and polarization-dependent loss, to mode coupling, electrooptic compo-
nents and nonlinear effects in silica fibers. Most optical components and
transmission effects are based on these features.
Chapter 3 discusses optical transmission systems of all kinds. The simplest are
standard intensity-modulated direct-detection systems. Their reach can be dramat-
ically extended by optical amplifiers, the theory of which is thoroughly described.
Performance is enhanced by binary and quadrature phase shift keying with inter-
ferometric detection. Symbol rate can be doubled by polarization division multi-
plex.Thesameispossiblealsowithcoherentopticalsystems.Butthesecanaswell
detect signal synchronously, which again increases performance. The principle is
that the received signal and the unmodulated signal of a local laser are superim-
posed.Thepowerfluctuationsresultingfromthisinterferencearedetected.Several
signal superpositions and detectors allow obtaining an electrical replica of the
optical field vector. Coherent optical transmission systems can therefore electron-
ically compensate all linear distortions suffered during transmission. Signal pro-
cessing and control algorithms for high-performance digital synchronous coherent
optical receivers conclude the book. Coherent transmission, which increases the
traditional fiber capacity 10- or 20-fold, has become a megatrend in optical com-
munication since 2007.
Fiber-to-the-home services can increase customer data rates by several more
orders of magnitude and make it likely that the pressure for increased capacity at
moderate cost in metropolitan area and long haul communication will continue.
Chapter 2
Optical Waves in Fibers and Components
2.1 Electromagnetic Fundamentals
2.1.1 Maxwell’s Equations
Electromagnetic radiations obeys Maxwell’s equations
@D
curlH¼ þJ Ampere0slaw; ð2:1Þ
@t
@B
curlE¼(cid:2) Maxwell-Faradayequation; ð2:2Þ
@t
divD¼q Gau(cid:1)0slaw; ð2:3Þ
divB¼0 Gau(cid:1)0slaw for magnetism; ð2:4Þ
We take the divergence of (2.1) and obtain with div curlA¼0 the
@q
divJ¼(cid:2) continuityequation; ð2:5Þ
@t
Itsaysthatthecurrentdrainedfromthesurfaceofadifferentialvolumeelement
equals the reduction of charge per time interval (preservation of charge). The
equations can be brought into integral form, using Gauß’s and Stokes’s integral
theorems,
I ZZ (cid:2) (cid:3)
H(cid:3)ds¼ @D þJ (cid:3)da¼@We þI ð2:6Þ
@t @t
©Springer-VerlagBerlinHeidelberg2016 3
R.Noé,EssentialsofModernOpticalFiberCommunication,
DOI10.1007/978-3-662-49623-7_2