Erbium-doped fiber amplifiers: principles and applications

788 Pages·2002·49.36 MB·English

by  Desurvire E.

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ERBIUM-DOPED
FIBER AMPLIFIERS
Principles and Applications
EMMANUEL DESURVIRE
Department of Electrical Engineering
Columbia University
ffiWlLEY
~INTERSCIENCE
A JOHN WILEY & SONS, INC., PUBLICATION
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Erbium-doped fiber amplifiers: principles and applications I
Emmanuel Desurvire.
p. cm.
Includes bibliographical references and index.
ISBN 0-471-58977-2 (cloth: acid-free paper)
ISBN 0-471-26434-2 (paper)
I. Lasers. 2. Optical amplifiers. 3. Optical fibers. I. Title.
TAI667.D47 1994
621.382 '75-<1c20 93-22410
CIP
Printed in the United States of America
10 9 8 7 6 5 4 3 2 1
PREFACE
The field of optical fiber communications is now nearly 20 years old, and the maturity
of this technology is well reflected by the accelerated rate at which optical fiber links
currently are being deployed over the continents and across the oceans. The progress
can be measured by considering that existing transoceanic fiber links based on digital
communication techniques can transmit 40,000 to 80,000 simultaneous telephone
conversations, as compared to 48 in the first telephone cable deployed in 1956 between
the United Kingdom and the United States! Formidable technical obstacles had to be
overcome in order to reach this performance: essentially, these had to do with
manufacturing optical fibers with lowest possible loss and developing reliable laser
sources that could survive being turned on and off for several years. A sense of luck
may have guided the pioneers of this field because, in spite of such overwhelming
difficulties, the technology has never seemed to come to a dead end. In our present
information age, where data highways increase in length every day to form gigantic
networks on a planetary scale, lightwave technology has a bright future indeed.
Yet, in spite of the tremendous information-carrying capacity offered by lightwave
systems, the demand for transoceanic communications is still growing at a constant
rate of 25% a year. The demand may become even greater in terrestrial systems,
although harder to quantify, as it will follow not only the natural growth of intercity
communications, but also the predictable emergence of large-size computer networks
and fiber-to-the-home loops. Then, and this will not be the first time, one may wonder
whether the limits of lightwave technology are going to be felt soon. What are the
limits of its capacity? These are not to be found in the optical fiber itself. Between
1.3 and 1.55-Jlm, it offers a comfortable bandwidth of 45 THz still largely underused.
Then come the switching electronics used to generate electrical signals and modulate
optical sources: for the fastest transistors, the potential bandwidth is up to 100 GHz,
only a few times greater than the performance of currently available devices, and
greater than the modulation bandwidth of semiconductor optical sources. The real
limitation is the need to regenerate optical signals as they undergo attenuation and
loss when propagating along a fiber link or network.
v
vi PREFACE
The task of signal regeneration traditionally has been that of electronic repeaters
in which optical signals are converted into current by a photodiode; the current is
then regenerated and converted back into light by a laser diode. Repeaters must be
placed at intervals such that the optical signal power never drops below a level where
the probability of misreading digital symbols becomes unacceptably high. Current
transatlantic fiber links typically have a 70-km repeater spacing-about 100 repeaters
over their 7500-km length. The electronic speed of the repeaters is fixed once and for
all and cannot be upgraded. This limits the information rate of repeatered systems.
Another drawback of electronic regeneration is that wavelength multiplexing is
difficult and costly. This is because many parallel repeaters are needed to combine
several optical channels into the same fiber. By the end of the 19805, experts in the
field agreed that the maximum capacity of unrepeatered systems, expressed in terms
of a bit-rate -length product, had reached its peak. In the future, large systems spanning
continental and intercontinental distances would definitely have to rely upon the use
of electronic repeaters.
This view has now been radically changed, due to the recent and forceful emergence
of optical amplifiers, which have taken the form of laser-diode-pumped erbium-doped
fibers. Yet again, luck shines on lightwave technology. In 1985,just when conventional
unrepeatered systems had approached their peak performance, a research group at
the University of Southamptol) showed that optical fibers can exhibit laser gain at
a wavelength ncar 1.55 Jlm. The fibers were doped with the rare earth erbium and
were activated or pumped with low powers of visible light. In 1986, the author and
a small group at AT&T Bell Laboratories joined the investigation. In the years to
follow, the primary research work of the University of Southampton and Bell Labs
would have tremendous consequences in the conception of lightwave systems. Indeed,
if practical optical amplifiers were available, they would offer a much wider operating
bandwidth (4 THz) and could then replace electronic repeaters used so far in optical
communications.
No matter how noble the attempt, any breakthrough in the old field of lightwave
systems needs a bit of luck. The lucky nature of erbium ions is that they have some
properties of radiative decay with a long excited state lifetime in a glass host, such
as the fused silica used to make optical fibers. Their 1.55 Jlm lasing wavelength
happens to fall in the spectral region where optical fibers have the lowest loss-a
narrow window used for long-haul communications. But that's not all. Miniature
semiconductor laser diodes (as opposed to cumbersome, water-cooled laser sources)
can be used to pump the erbium-doped fibers, which makes them practical as optical
amplifier devices. And the gain characteristics of erbium-doped fibers offer all these
advantages: polarization insensitivity, temperature stability, quantum-limited noise
figure, and immunity to interchannel crosstalk. These advantages could hardly be
achieved, all at once, with other optical amplifier approaches.
By early 1989, the first laser-diode-pumped fiber amplifier devices had appeared
and system breakthroughs followed at an unprecedented rate. The first experimental
systems with lengths of about 1000 km and operations at multigigabit rates without
electronic repeaters were demonstrated. They represent a level of performance that
no expert could have predicted only a few years ago. At AT&T Bell Laboratories,
fiber loop experiments in which data were recirculated many times in order to emulate
the characteristics of very long-haul systems based on optical amplifier chains, showed
transmission potentials up to 20,000 km. Symbolically, this length is nearly the longest
PREFACE vII
distance possible on earth. Early in 1993, AT&T and the Japanese company KDD
reported a straight fiber link incorporating as many as 274 Er-doped fiber amplifiers;
the link was 9000 km long and carried optical data at to Gbit/s-a record capacity
of 9O.Thit/s.krn and 100 times the performance level of unrepeatered systems in 1985.
Such radical improvements have caused a wide consensus about the importance of
optical amplifiers in future optical communications, both in long-haul and network
system applications. By 1995, the first transoceanic cables based on optical amplifiers
will be deployed over both the Atlantic and Pacific. Each of these high capacity links
will have the potential to carry as many as 600,000 voice channels. And we are only
witnessing the beginnings of this technology.
The motivation for this book has been to provide the basic materials of a
comprehensive introduction to the principles and applications of erbium-doped fiber
amplifiers. The literature is abundant on this relatively new subject of many different
facets. Each facet reflects issues ranging from the most fundamental to the most
applied. For this reason, the student, the communications systems engineer, or the
research scientist approaching this field for the first time may feel confused about
where to start. This book is intended to answer the most basic and practical questions.
How is light amplified in the doped fiber? How much spontaneous emission noise
is generated at the output? How does amplification affect the photon statistics and
signal-to-noise ratio? What are the ultimate noise limits of fiber amplifiers? Why do
detectors with optical preamplifiers perform better than avalanche photodiodes? What
are the optimal locations of optical amplifiers in a system? What are the current
types and architectures of amplifier-based systems?
The book is organized in three parts that can be read independently. Part A is
theoretical. It deals with the fundamentals of light amplification and noise in
single-mode fibers, as well as the principles of photodetection of digital signals with
optical amplifiers. Part B outlines the characteristics of erbium-doped fibers, from
spectroscopic features to fiber amplifier gain and saturation properties. Part C
concerns both device and system applications of erbium-doped fibers.
The author is grateful to many coworkers at AT&T Bell laboratories, whose
expertise, rigor, and team spirit made the investigation of erbium-doped fiber
amplifiers a very challenging and rewarding experience.
EMMANUEL DESURVIRE
New York
April /993
CONTENTS
LIST OF ACRONYMS AND SYMBOLS xv
A FUNDAMENTALS OF OPTICAL AMPLIFICATION IN
ERBIUM-DOPED SINGLE-MODE FI BERS
1 MODELING LIGHT AMPLIFICATION IN ERBIUM-DOPED
SINGLE-MODE FIBERS 3
Introduction I 3
1.1 Atomic Rate Equations for Three-level Laser Systems I 5
1.2 Atomic Rate Equations in Stark Split Laser Systems I 8
1.3 Gain Coefficient and Fiber Amplifier Gain I 10
1.4 Amplified Spontaneous Emission I 16
1.5 General Rate Equations for Pump, Signal, and ASE I 17
1.6 Numerical Resolution I 26
1.7 Rate Equations With Step Er-doping I 28
1.8 Rate Equations With Confined Er-doping I 33
1.9 Analytical Model for Unsaturated Gain Regime I 36
1.10 Analytical Models for Low Gain Regime I 40
1.11 Density Matrix Description I 46
1.12 Modeling Inhomogeneous Broadening I 59
ix
X CONTENTS
2 FUNDAMENTALS OF NOISE IN OPTICAL FIBER
AMPLIFIERS 65
Introduction / 65
2.1 Minimum Amplifier Noise and Temperature / 68
2.2 Quantum Description of Noise / 72
2.3 Photon Statistics in Linear Gain Regime / 78
2.4 Optical Signal-to-noise Ratio and Noise Figure / 98
2.5 Lumped Amplifier Chains / 114
2.6 Distributed Amplifiers / 121
2.7 Photon Statistics of Optical Amplifier Chains / 136
2.8 Nonlinear Photon Statistics / 140
3 PHOTO DETECTION OF OPTICALLY AMPLIFIED SIGNALS 154
Introduction / 154
3.1 Quantum Photodetection Statistics / 156
3.2 Semiclassical Description of Photodetection / 163
3.3 Enhancement of Signal-to-noise Ratio By Optical
Preamplification / 167
3.4 Optical Preamplification Versus Avalanche Photodetection / 172
3.5 Bit-error Rate and Receiver Sensitivity in Digital Direct
Detection / 174
3.6 Bit-error Rate and Receiver Sensitivity in Digital Coherent
Detection / 186
3.7 Digital Photodetection With Optical Amplifier Chains / 191
3.8 Analog Signal Photodetection / 195
B CHARACTERISTICS OF ERBIUM-DOPED FIBER
AMPLIFIERS
4 CHARACTERISTICS OF ERBIUM-DOPED FIBERS 207
Introduction / 207
4.1 Characteristics of Laser Glass / 208
4.2 Fabrication of RE-doped Fibers / 212
4.3 Energy Levels of ErJ + : glass and Relaxation Processes / 215
4.4 Laser Line Broadening / 225
4.5 Determination of Transition Cross Sections / 244
4.6 Characterization of Er-doped Fiber Parameters / 270
4.7 Pump and Signal Excited State Absorption / 277
4.8 Energy Transfer and Cooperative Upconversion / 282
4.9 Refractive Index Changes and Resonant Dispersion / 295
4.10 Effect of Pump and Signal Polarization / 303
CONTENTS xl
5 GAIN, SATURATION AND NOISE CHARACTERISTICS OF
ERBIUM-DOPED FIBER AMPLIFIERS 306
Introduction / 306
5.1 Characteristics of Pump Laser Diodes and EDF A-related Optical
Components / 309
5.2 Gain Versus Pump Power / 319
5.3 Gain Versus Signal Power and Amplifier Saturation / 337
5.4 ASE Noise and Noise Figure / 354
5.5 Amplifier Self-saturation / 373
5.6 Optimization of Fiber Amplifier Parameters / 382
5.7 Amplifier Phase Noise / 399
5.8 Effects of Reflections and Rayleigh Backscattering / 404
5.9 Transient Gain Dynamics / 410
5.10 Picosecond and Femtosecond Pulse Amplification / 420
5.11 Soliton Pulse Amplification / 422
5.12 Other Types of Fiber Amplifiers / 440
C DEVICE AND SYSTEM APPLICATIONS OF ERBIUM-DOPED
FIBER AMPLIFIERS
6 DEVICE APPLICATIONS OF EDFAs 455
Introduction / 455
6.1 Distributed and Remotely Pumped Fiber Amplifiers / 456
6.2 Reflective and Bidirectional Fiber Amplifiers / 461
6.3 Automatic Gain and Power Control / 469
6.4 Spectral Gain Equalization and Flattening / 480
6.5 Optically Controlled Gates and Switches / 487
6.6 Recirculating Delay Lines / 499
6.7 Fiber Lasers / 511
7 SYSTEM APPLICATIONS OF EDFAs 524
Introduction / 524
7.1 EDFA Preamplifiers / 527
7.2 Digital Linear Systems / 534
7.3 Soliton Systems I 559
7.4 Analog Systems I 568
7.5 Local Area Networks I 574
xii CONTENTS
APPENDICES
A RATE EQUATIONS FOR STARK SPLIT THREE-LEVEL LASER
SYSTEMS 585
B COMPARISON OF LPo1 BESSEL SOLUTION AND GAUSSIAN
APPROXIMATION FOR THE FUNDAMENTAL FIBER MODE
ENVELOPE 587
C EXAMPLE OF PROGRAM ORGANIZATION AND SUBROUTINES FOR
NUMERICAL INTEGRATION OF GENERAL RATE EQUATIONS (1.68) 591
D EMISSION AND ABSORPTION COEFFICIENTS FOR THREE-LEVEL
LASER SYSTEMS WITH GAUSSIAN MODE ENVELOPE
APPROXIMATION 596
E ANALYTICAL SOLUTIONS FOR PUMP AND SIGNAL+ASE IN THE
UNSATURATED GAIN REGIME, FOR UNIDIRECTIONAL AND
BIDIRECTIONAL PUMPING 600
F DENSITY MATRIX DESCRIPTION OF STARK SPLIT THREE-LEVEL 607
LASER SYSTEMS
G RESOLUTION OF THE AMPLIFIER PGF DIFFERENTIAL EQUATION
IN THE LINEAR GAIN REGIME 614
H CALCULATION OF THE OUTPUT NOISE AND VARIANCE OF
LUMPED AMPLIFIER CHAINS 622
I DERIVATION OF A GENERAL FORMULA FOR THE OPTICAL NOISE
FIGURE OF AMPLIFIER CHAINS 624
J DERIVATION OF THE NONLINEAR PHOTON STATISTICS MASTER
EQUATION AND MOMENT EQUATIONS FOR TWO- OR
THREE-LEVEL LASER SYSTEMS 627
K SEMICLASSICAL DETERMINATION OF NOISE POWER SPECTRAL
DENSITY IN AMPLIFIED LIGHT PHOTODETECTION 631
L DERIVATION OF THE ABSORPTION AND EMISSION CROSS
SECTIONS THROUGH EINSTEIN's A AND B COEFFICIENTS 634
M CALCULATION OF HOMOGENEOUS ABSORPTION AND EMISSION
CROSS SECTIONS BY DECONVOLUTION OF EXPERIMENTAL
CROSS SECTIONS 638
N RATE EQUATIONS FOR THREE-LEVEL SYSTEMS WITH PUMP
EXCITED STATE ABSORPTION 640