what is edfa
TRANSCRIPT
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Introduction to the EDFA
A general introduction to the EDFA is presented in this chapter. It starts with an
overview of the implementation of this component in optical communications
networks, then a brief description of the amplifier operation and how to model the
spectral characteristics. Important amplifier parameters such as the optical noise
figure, amplifier bandwidth, and methods to achieve equalisation of the EDFA gain
spectrum are introduced.
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2 Introduction to the EDFA 10
new dopants and glasses to provide amplification at different wavelength bands (see
section 2.4) or by using Raman amplifiers.
EDFAs have been used successfully in WDM transmission systems as all-
optical lumped amplifiers at which the gain is boosted at a point of the transmission
line. On the other hand, the fibre amplifiers based on Raman effect also have
attracted huge research attention nowadays due to its tunability of amplification
band by simply changing pump wavelength, since ever-increasing demand of optical
data transmission capacity expansion in telecommunications has generated
enormous interest in optical communication bands (S-, L-band) [7, 8] outside of a
conventional EDFA gain bandwidth (C-band). The principle of the Raman amplifieris based on the stimulated emission process associated with Raman scattering in
fibre for the amplification of signals. The inelastic non-linear effects can be regarded
as scattering of a pump beam off phonon (molecular vibrational state) and the
transfer of energy into a lower energy beam. The Stokes shift corresponds to the
Eigen-energy of an optical phonon, which is approximately 13.2 THz for optical
fibres. In Raman amplifiers, signal wavelength is longer than pump wavelength by
the equivalent amount of the frequency shift. By using multiple pumps across the
target gain window, over 100nm band Raman amplifiers can be achieved [9]. The
major drawbacks of this technology are the requirement of high pump power or long
length of fibre and the related Rayleigh scattering issue. However, availability of
cheap and high power pump lasers, and highly non-linear fibres enables fibre Raman
amplifiers to be a promising technology for the increase of transmission capacity of
current and future WDM networks.
2.2 Theory
2.2.1 Energy levels
The EDFA absorption and emission cross sections are the signature of the energy
levels of the Er3+
ion in the glass host. When the erbium ion is introduced into a host
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2 Introduction to the EDFA 11
medium the energy levels are modified by local electric fields through Stark-
splitting. These levels are in thermal equilibrium due to rapid nonradiative
transitions between these levels. The amplifier is assumed to have homogeneous
broadening but if the local electric field is different at various sites along or across
the fibre due to impurities, clustering effects, or other glass structural disorders, then
inhomogeneous broadening occurs resulting in different electronic transitions at
respective sites. The incorporation of a network modifier such as Aluminium (Al) to
enhance the solubility of the Er3+
ions in the glass structure changes each energy
levels Stark-splitting and increases the inhomogeneity of the medium. The energy
transitions typically associated with Er
3+
in a silicate glass are the
4
I11/2,
4
I13/2, and4I15/2states, and are illustrated in Figure 2.2.
Figure 2.2 a) Energy level diagram for Er3+
ions showing the dominant transitions. b)
Stark-splitting of the energy levels due to the crystal or glass electric field.
W12, W21are the rates for the stimulated transitions while A32and A21are the rates
for the spontaneous emission. A32is assumed to be essentially nonradiative and A21
essentially radiative [10]. The subscripts 1, 2 and 3 correspond respectively to the
energy levels4I15/2,
4I13/2, and
4I11/2.
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2 Introduction to the EDFA 12
Generally the EDFA is pumped with 980nm radiation, exciting electrons from
the ground state4I15/2 to level
4I11/2 or at 1480nm by exciting electrons from the
ground state to a high-energy Stark-split sublevel of the4
I13/2manifold. Rigorously
this implies, when pumping the EDFA using a wavelength of 980nm, that the
amplifier corresponds to a three-level system while when using a 1480nm pump the
amplifier is a quasi three-level system (as pumping is to a higher-energy Stark-split
state within the I13/2manifold). However, both pumping schemes can be described
effectively in terms of the populations of two levels. This approximation is justified
in the 980nm pumping case due to the nonradiative decay rate A32being much larger
than the stimulated emission rate from 3 to 1, and therefore the population of level 3(4I11/2) can be neglected. In the case of 1480nm pumping the two-level system is
justified due to the rapid thermalisation decay that transfers the higher-energy
electrons of the4I13/2manifold to lower-energy Stark sublevels. The rate equations
for the populations of a two-level system are written as:
2212211122
nAnWnWdt
dN= (2.1a)
21 nnnt += (2.1b)
where ntis the Er3+
ion density and n1and n2the fractional density of the lower and
upper excited levels respectively. These equations hold even for the more complex
system where the manifolds are split into Stark sublevels. In this situation the
transition rates correspond to the sum over all the possible j-k (j,k=1,2) transitions
multiplied by the population weight of the transition, given by the Boltzman
distribution [10]. In practice however the exact energy levels corresponding to the
individual Stark levels are dependent upon the ion distribution and host material.
Thus the population and decay rates for the energy levels of interest, typically have
to be determined experimentally through absorption and emission cross section
measurements.
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2.2.2 Numerical modelling of spectral properties
The wavelength dependent properties of EDFAs can be modelled following the
method proposed by [11] in which the spatial characteristics of the amplifier are
integrated. This model involved dividing the EDFA spectrum into discrete optical
channels of frequency bandwidth, k, centred at the optical wavelength k.
Assuming homogeneous broadening and a uniform distribution of the Er3+
ions
across the fibre core, the amplifier can be characterised by introducing four
measurable fibre parameters: The absorption spectrum, k, the gain spectrum g*k, the
fibre saturation power, PkSat
, and the fibre background loss, lk, that are given by:
tkekk ng =*
(2.2a)
tkakk n= (2.2b)
**)(
kk
k
kk
teffkSat
kg
h
g
nAhP
+=
+=
(2.2c)
Where; ak and ek are respectively the wavelength dependent absorption and
emission cross sections, ntis the total concentration of the erbium ions, =Aeffnt/is
the ratio of the linear density of erbium ions to the fluorescence lifetime, Aeff=b2
eff
is the effective area of the doped region, is the metastable level 2 lifetime, and k
is the overlap integral between the dopant and optical mode distributions that in the
case of uniform doping of the erbium ions (beff=b) is given by:
=
2
0 0
),(
b
kk rdrdrI (2.3)
Where b is the radius of the Er3+
-doped region. If this assumption is unrealistic then
modification of the integral is required to include the Er3+
ion distribution. The
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2 Introduction to the EDFA 14
above overlap integral depends in general on the wavelength channel, k, for which it
is calculated. Under steady-state operation, assuming a uniform distribution for the
excited lower state and upper state populations (n1and n2respectively), the excited
upper state population density for the EDFA is given by [11]:
+
+=
kSat
k
k
kSat
k
k
kk
k
t
P
zP
P
zP
g
n
n
)(1
)(*
2
(2.4a)
21 nnnt += (2.4b)
The equations that describe the propagation of the beams of wavelength kand the
pump through the fibre are [10]:
( ) ( )
+++= )()( 2*2* zPlmh
n
ngzP
n
ngu
dz
dPkkkkk
t
kk
t
kkkk
(2.5a)
( ) ( )
++= )()(2* zPlzP
n
ngu
dz
dPpumppumppumppump
t
pumppumpk
pump (2.5b)
Pk(z) is the signal power at frequency k at a certain position along the amplifier
length; uk represents the direction of the travelling beam uk=1 for a forward
propagating beam and uk=-1 for backward propagation; the term mhkk is the
contribution of the spontaneous emission from the local excited state population n2,
with m=2 corresponding to the number of polarisation modes supported by the fibre,
and h the Plank constant; lk is a wavelength dependent background loss. Thus the
two-level amplifier system can be fully characterised using equations (2.5a) and
(2.5b) that describe the propagation of the signal, ASE and pump along the erbium-
doped fibre and equation (2.4.a) describing the population inversion and saturation
characteristics along the amplifier. When using a pump wavelength of 980nm, the
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2 Introduction to the EDFA 15
gain coefficient is null 0g*
980 = and equation (2.5b) describing the pump evolution
along the EDF can be simplified.
Details of the model used herein for numerical simulations of the EDFA
performance are described in Chapter 7. Briefly though it was implemented by
dividing the full EDFA bandwidth (from 1420nm to 1620nm) into equal segments.
The wavelength dependence of () and g*() were obtained by digitising
absorption and gain parameters measured for an actual EDF as illustrated in Figure
2.3. Using the measured value for the fibre background loss lbgand the ratio of ion
density to the fluorescence lifetime , the rate and propagation equations were
solved until the specified convergence parameters were reached.
0
1
2
3
4
5
6
7
1420 1470 1520 1570 1620
Wavelength (nm)
Abs
orption/Gain(dB/m)
g*()
()
Figure 2.3 Measured absorption and gain parameters for the fibre used in the numerical
simulations.
2.3 Noise figure
The analysis of noise in optical systems is sufficiently complex that it can be
characterised either with simple engineering formulae or by a thorough quantum
theoretical approach. It is not the aim of this section to provide a deep introduction
to noise in optical systems, but rather to give the basic definitions, which quantify
the optical noise generation in the EDFA. These definitions will be used in chapter 6
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2 Introduction to the EDFA 16
to discuss the effect on the EDFA performance, in terms of a noise figure, when the
concept of gain equalising filters is introduced. The optical noise figure is a
parameter used for quantifying the noise penalty added to a signal due to the
insertion of an optical amplifier. That is, before light enters an amplifier the signal to
noise ratio is SNR(0), after amplification it is SNR(z). Thus, optical noise figure can
be defined as:
)(
)0(
zSNR
SNRNF
Opt = (2.6)
If the noise figure of the amplifier were 1, then the initial signal to noise ratio would
be maintained throughout amplification. However it has been shown that the
quantum limit for an optical amplifier [10] is 3dB, therefore the signal to noise ratio
after amplification is half (50%) of the original value. For real optical amplifiers the
noise figure can be as high as 6dB whereby the signal quality is sufficiently
deteriorated that the detectors ability to discriminate signal from noise is
compromised.
The signal to noise ratio can be described as the ratio between the average
signal intensity and the standard deviation of intensity fluctuations from that
average. The definition follows in terms of the average number of photons
and the variance 2=-
2:
)(
)(2
2
z
znSNR
= (2.7)
where z is the position along the amplifier or fibre link. It has also been shown, [10]
that the noise figure of an optical amplifier can be described as:
)(
1
)(
1)(2
zGzG
zGnNF
kk
kspOpt
+
= (2.8)
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where Gk(z) is the amplifier gain at a given position, z, at a wavelength kand where
nspis the spontaneous emission factor that takes the form:
12
2
NN
Nn
ek
aksp
= (2.9)
Here, N1 and N2 are the populations of the ground and excited energy levels
respectively. For a total population inversion N1=0, nsp=1 and therefore the noise
figure is close to 2, which is the quantum limit for the amplifier noise. The
spontaneous emission factor is related to the total power of the amplified
spontaneous emission PASEwithin the bandwidth, k, by the following expression
[10]:
( ) kk
ASEsp
hG
Pn
=
12 (2.10)
2.4 Larger bandwidth
The usable 35nm bandwidth of the EDFA operating in the Conventional band (C-
Band) enabled fibre communications using WDM and DWDM. However growing
demand for increased bandwidth and subsequent research have given rise to fibre
amplification at shorter and longer wavelength bands. The L-band EDFA, where the
EDFA gain is shifted to the longer wavelengths (1560nm-1580nm) [12], in
conjunction with the recently demonstrated Thulium-doped fibre amplifier operating
at the S-band (short wavelengths) around 1490nm [13], provide the basis for future
transmission capacity of 10Tbits/s channels multiplexed across the three amplifier
bands [2]. Figure 2.4 illustrates the three amplification bandwidths covered by the
three types of amplifiers.
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1.46 1.48 1.5 1.52 1.54 1.56 1.58 1.6 1.62
Wavelength (m)
L-Band
S-Band
C-Band
Figure 2.4 Wavelength bandwidth covered by the amplifiers.
2.5 Gain equalisation
Equalisation of an amplifiers gain spectrum is essential for balancing the channel
powers in order to achieve error free detection of the signals transmitted through the
optical fibre link. Several methods for achieving EDFA equalisation, either intrinsic
or extrinsic, have been proposed in the literature. Intrinsic methods constitute
changing the spectroscopic properties of the erbium-doped glass absorption and
emission cross sections by co-doping with other ions, different glass matrices or
special fibre designs. Fluoride-based glasses [14, 15] are known to improve the
flatness of the EDFA gain spectrum. Extrinsic methods are based on filtering
devices that are designed with a wavelength dependent loss spectrum. Several filters
have been demonstrated in the literature [16-26]. These can be divided in active
devices that are re-configurable, which may accommodate changes in the amplifier
gain spectrum due to saturation effects, and passive devices that cannot be tuned.
Active devices reported include; acousto-optic tunable filters [16-19], strain-tuned
fibre Bragg gratings [27], micro mechanical filters [24], and a planar integrated
optical filter [25]. Some passive devices include long period gratings [21, 23], Bragg
gratings [22], and filters using Samarium doped fibres [20]. All these devices have
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characteristic equalisation properties and insertion losses that can be as low as the
splicing loss between the EDF fibre and the filter fibre or as high 8-9dB as reported
in [24, 25].
In chapter 6 an acousto-optic tunable filter based on the profile of a multi-
tapered optical fibre and its spectral transmission properties [18, 19], is discussed.
The amplified spontaneous emission spectrum of an EDFA was equalised for
different saturation levels in order to demonstrate the potential of the device. The
tunable parameters of the device were, the acoustic wave frequency and the filter
loss shape, which was dependent upon the tapered fibre profile. Although this filter
lacks the flexibility of reshaping the spectral profile, it is very easy to tunedepending only on 2 to 4 parameters as opposed to the 12 tuning parameters of other
designs [17].
Figure 2.5 Basic EDFA gain flattening configurations. Top: Filter placed outside the
amplifier. Bottom: Filter placed within the amplifier.
Determination of the ideal filter shape in order to equalise the EDFA is not a
trivial task. The loss spectrum of filters placed outside the EDFA (configuration 1 in
Figure 2.5) can be obtained by inverting the amplifier output gain across the desired
bandwidth. Although the loss due to the insertion of the filter, dependent upon the
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type of filter and the fabrication procedure, can be up to 8-9dB [24, 25], and
therefore another amplification stage is usually required after the filter. If however,
the filter is placed at a certain position inside the EDFA (configuration 2 in Figure
2.5), the penalty in amplifier loss can be reduced but the exact filter shape and
placement is not known. Liaw [20] used the loss spectrum of a samarium-doped
fibre and found the best position at which it should be placed in a given amplifier by
splicing it at different positions along the amplifier. Acoustooptic tunable filters [26]
have also been used in this configuration and optimised by tuning the filter shape
until the desired performance is reached. This is an iterative process and quite time
consuming, as the filters may not be placed in the optimum position along theamplifier. A solution to these problems is proposed in chapter 7, where the
theoretical design of ideal filters that in addition to gain flattening also compensate
for insertion losses, and their position within an amplifier for equalising the EDFA
gain spectrum is discussed. Performance of the above filter configurations is
compared.
2.6 Summary
A brief introduction to the EDFA, one of the most important components in WDM
communications, was given in this Chapter. Starting with fundamental principles of
amplifier operation, a well-known model based on a two-level amplifier system
including the spectral characteristics of the EDFA, was presented. Important issues
relating to the amplifier performance, namely the optical noise figure and amplified
bandwidth were introduced. Finally, the chapter concluded with a review of existing
technologies utilised for equalising the EDFA gain spectrum. The concepts
introduced in this chapter are fundamental to section II where the equalisation of the
EDFA gain spectrum is addressed in more detail.