11
Erbium-Doped Fiber Amplifiers:
Advanced Topics
PAUL F. WYSOCKI
Leco Corporation, St. Joseph, Missouri
11.1 INTRODUCTION
The erbium-doped fiber amplifier (EDFA) has become a key component in many optical
networks because it provides efficient, low-noise amplification of light in the optical fiber
low-loss telecommunications window near 1550 nm. As more systems using EDFAs have
been built and tested, new issues and effects have emerged as critical to the development
and expansion of this technology into the future. Single-channel amplification, as de-
scribed in Chapter 12, is being supplanted by multiple channel wavelength–division-
multiplexed (WDM) systems. EDFAs are being used in analog applications, not solely in
digital systems. In most new applications, a high-output power and a low-noise figure
(NF) are required. To achieve these goals, the emphasis has been placed on both fiber
optimization and clever EDFA designs. High-power pump sources have made this task
easier, while advances in fiber-grating technologies have facilitated more complex EDFA
designs.
This chapter assumes that the reader has a sound understanding of the basic physics
and characteristics of EDFAs discussed in Chapter 10. Because the issues faced in EDFA
design may evolve over time, the emphasis here is placed on developing intuition that
can be applied in future situations. Simplified treatments and models are used wherever
possible. The chapter is divided into four main sections. Section 11.2 deals with the EDFA
gain spectrum and how it affects the use of these amplifiers in various applications. Section
11.3 discusses fiber design optimization issues for selected applications. Section 11.4 dis-
cusses effects that are small in a single EDFA, but can become significant in systems
utilizing many EDFAs. Finally, Section 11.5 summarizes some of the novel EDFA designs
used to meet NF, power, and spectral requirements for various applications.
Copyright © 2001 by Taylor & Francis
11.2 GAIN SPECTRUM CONTROL
As erbium-doped fiber amplifiers are used in new applications, such as multiple-wave-
length WDM systems and analog CATV systems, the shape of the gain spectrum is in-
creasingly important [1]. This issue has led to three main areas of research. The first area
involves modification of the erbium host composition to produce fibers with improved
spectral characteristics. The second is the development of EDFA designs with integrated
components that overcome the inherent spectral shortcomings of the fiber. The third area
is the development of accurate spectral measurement techniques for the characterization
of basic spectral properties and multiple wavelength gain. All of these efforts have bene-
fited from the ability to model and predicts the behavior of different erbium-doped fibers
(EDFs) operated in various configurations. These three areas of research are discussed in
the following sections.
11.2.1 Modeling and the Homogeneous Gain Approximation
An energy level diagram of the lowest states of the erbium ion is illustrated in Figure 1. It
shows the center wavelength of the ground-state absorption (GSA) transitions, the standard
excited-state absorption (ESA) transitions from the
4
I
13/2
state, referred to as ESA1, and
the ESA transitions from the
4
I
11/2
state, referred to as ESA2. The decay rates (inverse
lifetimes) of these levels are shown in Figure 1 of Chapter 10. When modeling EDFAs,
it is important to note any ESA transition that is coincident with an absorption or emission
band of either the pump or the signal, because these transitions may produce important
loss mechanisms in practical devices. ESA1 transitions exist near 790 and 630 nm, making
pumping of EDFAs near the GSA bands at 800 and 650 nm very inefficient. However,
an ESA2 transition exists near 980 nm, where many EDFAs are pumped. In a silica-based
host, most models have treated erbium as nearly ideal when pumped near 980 nm. The
pump is absorbed to the
4
I
11/2
state and decays rapidly to the long-lived
4
I
13/2
state, which
produces gain near 1550 nm. Hence, under normal conditions, only the ground state and
4
I
13/2
state are appreciably occupied. When pumped near 1480 nm, this is guaranteed to be
true because pumping occurs directly into the
4
I
13/2
state. Furthermore, 1480 nm pumping is
free of both ESA1 and ESA2, and a high efficiency is expected. In fluoride glasses and
some other hosts, the
4
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11/2
state has a long lifetime and, therefore, can be appreciably
occupied. Furthermore, 980-nm power can be absorbed by the ESA2 process mentioned
earlier, thus wasting power. Even in silicates, the slight occupation of the
4
I
11/2
state can
cause efficiency reduction at high pump power levels near 980 nm. This issue is further
discussed in the following.
The basic rate equations governing the performance of EDFAs were derived in Sec-
tion 3 of Chapter 10. As EDFA use progresses into the future, more advanced and accurate
modeling will be required. A complete model for an EDFA might include the following:
1. Radial mode and dopant distributions
2. ESA from all levels, even those slightly occupied
3. Spectral or polarization hole-burning
4. Ion–ion interaction processes known as cooperative upconversion
5. Ion clustering or pairing and associated loss mechanisms
6. Background losses and contaminant losses present in the material
7. Time-dependent processes.
Copyright © 2001 by Taylor & Francis
Figure 1
Energy-level diagram of Er
3⫹
in a silicate host showing the three principal energy states
of population density N
1
, N
2
, and N
3
, as well as the center wavelengths for the ground-state absorption
(GSA) and excited-state absorption (ESA) transitions originating from these states.
An ideal model would include all of these effects because they are important under certain
conditions. Unfortunately, parameters for many of these processes are difficult to measure
and are not necessarily easy to incorporate in the model equations. For example, radial
distributions are difficult to measure because in many EDFs the erbium is present in only
trace amounts in small core areas. Measurements in the preform do not necessarily predict
where the dopant will be located after the thermal processing required to draw it into
fiber. Also, absolute concentration levels in the preform are often estimated only from
processing data. Additionally, ion clustering, upconversion, and hole-burning all require
knowledge about ion subsets and inhomogeneity that is not readily available. ESA loss
coefficients and cross sections are not fully known for all levels and are difficult to measure
except for ESA1 processes.
The model for EDFA performance presented in Chapter 10 is based on fundamental
physical quantities such as cross sections, lifetimes, and ion concentrations. Such physics-
based models are useful in understanding the properties of an EDF that affect its perfor-
mance as an EDFA. They can be used to predict ideal ion distributions, to study the
dependence of the EDFA performance on fiber numerical aperture (NA), or to compare
the theoretical performance of different host compositions. In fact, even if physical param-
eters are poorly known, such a model can be used to predict trends in EDFA performance
Copyright © 2001 by Taylor & Francis
with changes in fiber design. However, to accurately model and predict measured EDFA
gain spectra, power output, and NF as a function of operating conditions, it is more useful
to base a model on physically measurable quantities. The model used here is based on
work by Giles [2] that has been expanded to include the loss mechanisms of ion pairing
and ESA2 at 980 nm. Parameters for these processes, including an ion pair fraction and
an ESA2 loss coefficient, can be used to fit measured performance data. This model is
accurate for low-concentration silica-based EDFs under the following approximations [3]:
1. Radial distributions are well approximated by overlap integrals.
2. Hole-burning effects are small (mostly homogeneously broadened).
3. ESA1 does not occur at the pump (980 or 1480 nm) or signal wavelengths.
4. The glass phonon energy is low enough that the
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level decays radiatively
to the ground state.
5. The glass phonon energy is high enough that the
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pump state is nearly
unpopulated at steady state.
6. Homogeneous cooperative upconversion is weak at low concentrations.
7. The ion
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lifetime is long so that a steady-state approximation is appropriate.
Of particular importance is the assumption of homogeneous broadening. As shown in
Chapter 10, inhomogeneous broadening has been observed and measured in EDFs. How-
ever, because the magnitude of the inhomogeneity is small, it can be neglected to first
order. A correction can be added at the end of the process to account for residual inhomo-
geneous broadening, as discussed in Section 11.4.1.
When erbium is considered to be mostly homogeneously broadened in a silicate
host [4,5], many quantities can be computed without running a full computer model. In
particular, predicting the shape of the gain spectrum produced by an EDFA is relatively
simple if we assume homogeneity and occupation of only the
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I
13/2
and
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15/2
states. All
possible spectra are then predictable by fractional combinations of the gain spectrum mea-
sured when all ions are pumped to the
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13/2
state and the absorption spectrum measured
when all ions occupy the
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15/2
state. Neglecting background loss, the gain spectrum pro-
duced by a length of EDF with a given ion inversion (fraction in upper state) can be
written as:
G(λ,
Inv) ⫽ {[g*(λ) ⫹ α(λ)]
Inv ⫺ α(λ)}L (1)
where g*(λ) is the measured gain per unit length produced by the EDF when all ions are
in the
4
I
13/2
state, α(λ) is the measured loss per unit length produced by the EDF when all
ions are in the
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I
15/2
state, Inv is the fraction of ions inverted (in
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I
13/2
state) averaged along
the fiber length, and L is the EDF length. Note that Eq. (1) is expressed in decibels (dB)
if g*(λ) and α(λ) are expressed in decibels per meter (dB/m), and in nepers (np) if g*(λ)
and α(λ) are expressed in nepers per meter (np/m). The inversion coefficient is a dimen-
sionless number that can be written in terms of the level occupations (using the notation
shown on Fig. 1) as:
Inv ⫽
1
L
冮
L
z⫽0
冢
N
2
(z)
N
0
(z)
冣
dz (2)
where N
0
(z) ⫽ N
1
(z) ⫹ N
2
(z) is the total, radially averaged erbium-ion concentration, and
N
1
(z) and N
2
(z) are the fractional populations of the ground state and first excited state at
Copyright © 2001 by Taylor & Francis
position z, respectively. Assuming dopant longitudinal invariance, the coefficients g*(λ)
and α(λ) can be written in terms of the physical quantities described in Chapter 10 as:
g*(λ) ⫽ σ
H
e
(λ)N
0
Γ(λ) ⫽ σ
H
e
(λ)
冮
∞
0
ψ(r)N
0
(r)rdrdθ (3a)
α(λ) ⫽ σ
H
a
(λ)N
0
Γ(λ) ⫽ σ
H
a
(λ)
冮
∞
0
ψ(r)N
0
(r)rdrdθ (3b)
where σ
H
e
(λ) and σ
H
a
(λ) are the homogeneous emission and absorption cross sections,
respectively, ψ(r) is the normalized transverse mode envelop assuming circular symmetry,
N
0
(r) is the erbium-ion density assuming circular symmetry and longitudinal invariance,
and Γ(λ) is the spatial overlap between the dopant profile N
0
(r) and the mode profile ψ(r).
The computation of g*(λ) and α(λ) according to Eq. (3) is only as accurate as our
knowledge of the cross section, mode distribution, dopant distribution, and absolute dopant
concentration involved in the formula. The errors in these values are compounded when
used in Eq. (3) and produce an unacceptable error in the spectra computed with Eq. (1).
However, measured values for g*(λ) and α(λ) can be used in Eq. (1) without requiring
such detailed fiber characterization. The advantage of this approach is in its ease of use
and accuracy. Its main disadvantage is the loss of ability to fully explore EDF design.
Measured normalized spectra g*(λ) and α(λ) are shown in Figure 2a for a silica-based
EDF with a high aluminum concentration, and in Figure 2b for a fluoride-based EDF.
The measurement of these parameters in fluoride-based fibers has been described [6].
Equation (1) is useful for predicting the spectrum of a fluoride-based EDF when the fiber
is pumped near 1480 nm, but not near 980 nm, because pumping this host at this wave-
length produces occupation of the
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11/2
state. The absorption and gain spectra of Figure
2 have shapes similar to the cross section plots shown in Chapter 2, but differ in the fact
that they include the wavelength-dependent overlap of the ions with the mode profile [see
Eq. (3)]. The spectra of Figure 2 are for fibers that represent the state of the art for produc-
ing flat amplification. These spectra are used liberally in gain flatness calculations through-
out this chapter.
Equation (1) can be simplified by realizing that the gain and loss spectra are not
independent. All of the 56 possible transitions have the same emission and absorption
strengths, and each manifold is occupied according to Boltzmann statistics. Hence, the
probability of emission on a given transition is not equal to the probability of absorption
on the same transition, because these processes depend not only on the transition strength,
but also on the probability that the initial level of each process is occupied. It has been
shown by McCumber that the gain and absorption at a given wavelength for two Stark
split manifolds are related simply by [7,8]:
g*(λ)
α(λ)
⫽ exp
冤
hc
kT
冢
1
λ
⫺
1
λ
0
冣
冥
(4)
where h is Planck’s constant, c is the speed of light, k is Boltzmann’s constant, T is the
temperature in degrees Kelvin, and λ
0
is the crossover wavelength where the excited-state
gain equals the ground-state loss. Equation (4) is expected to hold for all transitions in
rare earth-doped fibers and its validity has been confirmed in EDFs [8]. Equations (1) and
(3) are used together in results presented in this chapter to reduce the number of measure-
ments required to assess spectral characteristics.
Copyright © 2001 by Taylor & Francis
