Influence of bidirectional pumping in high-power EDFA on single-channel,
multichannel and pulsed signal amplification
R. Deepa a,b , R. Vijaya a,∗
a Department of Physics, Indian Institute of Technology, Bombay, Powai, Mumbai 400-076, India
b VES College of Arts, Science and Commerce, Sindhi Society, Chembur, Mumbai 400-071, India
Abstract
A detailed analysis in terms of computational and experimental results of a high power erbium doped fibre amplifier using the bidirectional
pumping scheme is presented. The differences between the signal evolution are discussed for unidirectionally and bidirectionally pumped amplifier
for a single channel CW input. A comparison is made between the theoretically predicted gain and the experimental results for bidirectional
pumping. The numerical analysis is further extended to multiwavelength propagation in the forward and bidirectional pumping schemes. In the
case of a pulsed input, enhanced nonlinearity of the doped fibre and the differences in gain evolution between the different pumping schemes
result in drastic changes in the pulse quality during its propagation through the amplifier fibre. The modifications of a Gaussian pulse in the time
and spectral domains due to propagation through the doped fibre are analysed qualitatively to emphasise the advantages of bidirectional pumping
for high power amplification.
Keywords: Erbium doped fibre amplifiers; Bidirectional pumping; Pulse propagation; Multichannel systems
1. Introduction
The use of wavelength division multiplexed systems has increased the information carrying capacity of the existing optical
networks manifold. To cater to the demand for an increasing
number of channels, high signal powers, greater than 20 dB m,
are required at the output of each amplifier in the network link.
Cascaded/multistage amplifiers can provide such high signal
powers, but require extremely severe operating conditions [1].
Cladding pumped amplifiers have also been increasingly used
for generating high powers [2]. However, for commercially
deployed systems, standard core-pumped erbium doped fibre
amplifiers (EDFA) continue to be the most sought-after technology. EDFA operating with 980 nm pumping has proven advantages and constitutes one of the most efficient fibre-optic
amplifying systems [3]. Since the power available from a single commercial pump laser diode is limited, the deliverable
amplified signal power from a single pump amplifier is also
restricted. Use of more than one pump laser diode can solve
this problem. Among the several schemes available for pumping EDFAs, the best configuration to offer the highest output
power and relatively low noise figure is the bidirectional pumping scheme [4–10]. In this configuration, the signal to be amplified is launched from one end of the amplifier fibre and the
pump power is launched from both the ends of the fibre. The
larger powers in such amplifiers may result in significant nonlinear effects [11], that may not be tolerable for high rep-rate,
multichannel systems.
To the best of our knowledge, there has been no systematic
study of bidirectional pumping in EDFA, especially when the
pump and signal powers are large. In this paper, we present a
comprehensive study of a bidirectionally pumped EDFA, comprising of both suitable experimental and extensive computational results. Apart from the comparison of amplified signal
power evolution in unidirectional and bidirectional pumping
schemes for a single channel, we present a theoretical study of
the impact of bidirectional pumping in multichannel systems.
A commercial network handles signals in the pulsed format,
21
and hence the influence of bidirectional pumping in the case
of pulses is further analysed. The impairments due to gain dispersion and enhanced nonlinearity in the doped fibre are studied
and compared for the unidirectional and the bidirectional pumping schemes.
Section 2 presents the experimental results of the bidirectional pumping scheme. The dynamics of signal evolution in the
case of high power bidirectional pumping scheme in comparison with forward pumping are discussed and the advantages of
using a bidirectional system are also highlighted in this section.
Significant aspects of multichannel amplification in the case of
forward and bidirectional pumping schemes are compared in
Section 3. The effects of bidirectional pumping on pulsed signals are modelled in Section 4 using the generalised nonlinear
Schrodinger equation and the results for forward and bidirectional pumping are analysed. The conclusions of this work are
summarised in Section 5.
2. Effect of bidirectional pumping on single channel
systems
The typical experimental setup for the bidirectional pumping
scheme is as shown in Fig. 1. Two laser diodes emitting at 980
nm with maximum powers of 270 and 220 mW each are used
as pump sources. Signal is derived from a narrow line width
distributed feedback laser lasing at 1550 nm with a maximum
power of 10 mW. The signal and pump powers are combined using a wavelength division multiplexer (WDM1) and then propagated through the erbium doped fibre (EDF). WDM2 is used
to launch the backward pump, and the output signal is coupled
out of the EDF through the same WDM. The saturated operation of the amplifier results in minimal amplified spontaneous
emission (ASE). An isolator at 1550 nm (1 dB insertion loss)
is used to further minimise the build-up of the backward travelling ASE [12]. The output from the amplifier is fed to a band
pass filter (BPF; bandwidth 1 nm), with its peak transmission
centred at 1550 nm, and is subsequently measured using an
optical power meter. By using the BPF it is ensured that the
noise power outside the 1550 nm band is cut off and the power
measured is the signal power with the in-band ASE noise. All
splices are done using core-matched arc fusion technique. The
experiment was performed with EDF lengths varying from 12.4
to 25.8 m. For each length, it is ensured that the position of the
isolator is midway, which would provide the maximum noise
suppression [4,12]. Signal power of 22.6 dB m is obtained at a
Fig. 1. Schematic of the experimental setup of bidirectional pumping configuration.
length of 20 m for the maximum available forward and backward pumps.
In order to completely understand the effect of bidirectional
pumping in single channel systems, the EDFA is modelled as a
standard three level lasing system and the coupled differential
equations for the pump and the signal are solved numerically
using the fourth order Runge–Kutta technique using the boundary conditions appropriate to the type of pumping [13]. The
fibre considered has a core radius of 1.6 µm, numerical aperture
of 0.23 and is assumed to be uniformly doped with erbium ions
of density 5.5 × 1024 ions/m3 . Though the dopant concentration is assumed to be uniform in the radial direction, integration
over the radial axis is performed to include the effect of the
overlap between the pump and signal modes.
The emission and absorption cross-sections (σe and σa )
of the fibre were estimated independently at the pump and
the signal wavelengths (λp and λs ) by experimentally measuring the pump and signal absorption coefficients for different fibre lengths at low power levels (<0 dB m for pump
and < −30 dB m for signal). These experimental results were
subsequently used in the numerical program to obtain a fit
for the cross-sections. The values thus obtained are σa (λp ) =
0.9 × 10−25 m2 , σe (λs ) = 5.6 × 10−25 m2 and σa (λs ) = 5.8 ×
10−25 m2 . It is ensured that there are no discontinuities in the
evolution of gain coefficient with length while obtaining the fit.
These estimated cross-sections are then used in the program for
bidirectional pumping and the experimental data fits fairly well
with the theoretically predicted values for bidirectional pumping as shown in Fig. 2a. The losses at the input and output
WDM and at the band pass filter are experimentally evaluated
and those values are considered, while fitting the experimental
data. The effects of isolator are not included in the numerical
program used.
The fibre is inverted uniformly throughout its length in the
case of bidirectional pumping scheme, due to the presence of
pump throughout the fibre length. In a practical amplifier design, the fibre length has to be chosen carefully beyond the
optimum length since the residual pump power results in back
reflections into the pump laser diode and might damage the
diode. In certain cases, these residual powers are used to stabilise the performance of the pump diode [14,15], but such a
system has to be designed carefully. In the most general case,
in order to avoid such damages, it is always advisable to operate the system with isolators at 980 nm, or to use lengths
slightly longer than the optimum when the EDFA is operated
under the bidirectional pumping configuration. The rate of signal re-absorption beyond the optimum length is slower in this
scheme, as seen in Fig. 2a. Hence, the penalty on the power
conversion efficiency is minimal while operating beyond the
optimum length, thus facilitating the use of longer than optimum length in this scheme. It is also verified experimentally
that, the gain saturation performance of the forward and the
bidirectional pumping schemes is similar. The noise figure for
this scheme is expected to be between that of the forward and
the backward pumping schemes.
The difference between the gains in forward and bidirectional pumping would change, if the distribution of powers
22
Fig. 2. (a) Experimental values (shown as discrete data) and computed values (shown as lines) for bidirectional pumping at different pump power levels. F and
B indicates forward and backward pump powers, respectively. (b) Computed variation of output signal power with the ratio of backward pump power to the total
launched pump power at the corresponding optimum lengths. The variation of optimum length (L) with the pumping ratio is shown in the inset.
in the forward and backward directions are different. Fig. 2b
shows the variation of numerically computed output signal
power with the ratio of backward pump power to the total
pump power. (Zero would mean complete forward pumping
and 1 would mean backward pumping.) The optimum length
for each of the pump distribution considered is shown in the
inset. The optimum length and the gain are found to increase,
when the system moves towards backward pumping configuration [13,16]. However, the noise figure is also reported to be
higher in the backward pumping scheme [17,18].
Bidirectional pumping in high power EDFA, hence, would
be more advantageous in two aspects: (a) The power required
by the individual pump laser source need not be high. (b) Gain
and the noise figure can be adjusted judiciously between that of
the unidirectional pumping schemes, by adjusting the pumping
power ratio. For larger output powers, it is better to choose a
larger backward pump.
3. Effect of bidirectional pumping on multichannel
systems
Since wavelength division multiplexing is the most popular technique in optical communication systems, it is relevant
to understand the impact of bidirectional pumping in these
multichannel systems. When EDFA is used for multichannel
amplification, the gain in each channel is different due to the
wavelength dependence of the absorption and emission crosssections of the erbium doped fibre. When channels are dropped
in a multichannel system, the gain in each surviving channel
is found to change due to cross-saturation effects. The transient effects of dropping channels have been studied widely
and many methods have been suggested to remove these effects [19–21]. Analytical discussion on multichannel amplification in forward pumping can be found in [22].
In this section, we compare the changes in the gain and
cross-saturation when channels are dropped in a multichannel
system, in the case of forward and bidirectional pumping by
solving the coupled differential equations for the pump and signal wavelengths. The wavelengths chosen for the theoretical
analysis of multichannel system are from the ITU-T DWDM
Grid standards, consisting of 16 wavelengths from 1530.33 to
1542.14 nm with an interchannel frequency spacing of 100
GHz [23]. The emission and absorption cross-sections of EDF
for these wavelengths are assumed to vary from 6.76 × 10−25 to
4.52 × 10−25 m2 and from 7.82 × 10−25 to 5.68 × 10−25 m2 , respectively, and hence, the gain spectrum is not flat [13]. Most of
the gain equalisation techniques suppress those channels having
higher gain [22]. Hence, in a multichannel system, length optimisation has to be done for that channel which has the minimum
gain.
For the chosen values of emission and absorption crosssections, it is found that Channel 12 (CH12) has the least gain.
Hence, for an input signal power of 1 mW/channel, a fibre
length of 7 m is chosen such that the gain in CH12 reaches its
maximum possible value. It is found that the spectral variation
of the gain follows the same trend, irrespective of the pumping
scheme. The gain differences between the different pumping
schemes for different channels were found to be within 0.2 dB.
Since in a multichannel system, the absolute value of gain for
the different channels are almost equal in all the three pumping
schemes for the fibre considered, unidirectional pumping is not
superior over bidirectional pumping in this aspect. Bidirectional
pumping however would have the advantages of better noise
figure than backward pumping scheme, which is not analysed
in this paper.
Fig. 3a shows the computed variation of gain for different
channels at input signal powers of 0.5 and 1 mW per channel
in the case of bidirectional pumping. The total pump power is
400 mW. High power amplifiers operating in deep saturation
are reported to exhibit gain flattening characteristics [24]. This
is evident in this figure from the trend obtained for the higher
signal power. For the fibre and the powers considered, the gain
flattening response is also found to be independent of the pumping scheme. Fig. 3b shows the evolution of gain with position
of the fibre, in the case of forward and bidirectional pumping
schemes. Amongst the 16 channels considered, CH0 shows the
maximum gain and CH12, as discussed earlier, shows the minimum gain. It is clear from the figure that the evolution of gain
is similar in the case of bidirectional (solid lines) and forward
(dotted lines) pumping for shorter lengths. For longer lengths,
23
Fig. 3. (a) Gain in different channels for input signal powers (P ) of 0.5 and 1 mW per channel. (b) Variation of gain in CH0 and CH12 in the case of forward and
bidirectional pumping schemes for 16-channel propagation. Solid line represents bidirectional pumping and the dotted line represents forward pumping. Total pump
power = 400 mW, input signal power = 1 mW in each case; x-axis represents the position of launch of backward pump in the case of bidirectional pumping.
the gain falls off more rapidly in the case of forward pumping.
This is similar to the trend obtained for a single channel.
An analysis is also done to study the effects of crosssaturation. Cross-saturation occurs due to the dependence of
gain in any one channel on the total input power in all the
other channels [25,26]. The trends are the same for all the three
pumping configurations. The cross-saturation is found to be less
than 0.4 for even up to eight channels being dropped from the
16-channel system for an input signal power of 1 mW/channel.
The gain excursion in the reference channel (CH0) is also
found to be varying less than 0.5 dB until about 5 channels are
dropped from the system. Thus, bidirectional pumping offers
the same advantages as that of forward and backward pumped
high power EDFAs for multichannel operation.
4. Effect of bidirectional pumping on pulsed signals
The study of pulse propagation in EDFA is important for
network applications. Being bit rate independent, EDFA is expected to show the same gain characteristics for high rep-rate
pulses as that for CW signals. Pulse propagation in fibre amplifiers can be numerically studied by solving the generalised
nonlinear Schrodinger equation [27], given by
∂ 2A
∂A i + β2 + ig0 T22
∂z
2
∂T 2
i
1
= i γ + α2 |A|2 A + (g0 − α)A,
2
2
(1)
where A represents the pulse amplitude and a frame of reference moving with the pulse at a group velocity vg is considered.
T = t − β1eff z is the reduced time in this frame (β1eff = 1/vg ).
β2 is the group velocity dispersion (GVD) of the material of the
fibre, g0 is the gain coefficient of the fibre, T2 is the dipole relaxation time, the term due to ig0 T22 gives the contribution due
to gain dispersion, α2 is the two photon absorption coefficient,
α represents the fibre absorption coefficient, and γ is the nonlinear parameter, defined as
γ=
2πn2
.
λAeff
(2)
In Eq. (2), n2 is the nonlinear index coefficient of the fibre, λ is the wavelength of the signal, and Aeff is the effective
core area of the fibre at the signal wavelength. In the case
of high power EDFA, the gain coefficient is not a constant
along the fibre length because of pump depletion. The evolution of gain along the fibre length depends on the availability
of the pump power at each length. Hence, it needs to be calculated independently for the different pumping schemes. The
amplification factor, G for an amplifier of length L is given
by, G = exp((g0 − α)L). In order to incorporate the evolution of g0 correctly in Eq. (1), G for an incremental length
dz of the fibre is calculated using the Runge–Kutta algorithm
for the different pumping configurations. These values are used
to calculate (g0 − α), for each dz, and are in turn used while
solving Eq. (1) using the split step Fourier transform (SSFT)
method. The same step sizes are chosen for both the calculations. This value for the step size also ensures convergence.
The time window used for SSFT calculation is such that the
energy of the pulse is confined to the window. Since the evolution of gain is different, the input pulse would shape differently
in forward and bidirectional pumping schemes. The evolution
of signal power and (g0 − α) in the forward and bidirectional
pumping schemes are compared in Fig. 4. The backward pump
is assumed to be launched at 22 m in the case of bidirectional
pumping. Fig. 4a shows that the signal power increases differently between forward and bidirectional pumping schemes. The
signal encounters a larger gain in the initial length of the fibre in
forward pumping. In bidirectional pumping, it is seen that the
initial gain seen by the signal is comparatively smaller, and this
is maintained throughout the length of the fibre. Fig. 4b shows
the variation of (g0 − α), with length, which also indicates that
the initial gain coefficient seen by the signal is much larger in
forward pumping, and it then decreases to zero. On the contrary,
a finite value of gain is present at these lengths for bidirectional
pumping.
In order to examine the effects on pulsed signals due to a fibre similar to that used in Section 2, the nonlinear Schrodinger
equation is solved numerically for Gaussian pulses (corresponding to RZ format). Equation (1) is solved using the SSFT
algorithm [28], for Gaussian pulse of the form
24
Fig. 4. (a) Signal evolution in forward and bidirectional pumping. Fibre length considered is 22 m, with an input signal power of 10 mW. The total pump power in
either case is 400 mW. (b) Evolution of (g0 − α) with the length of the fibre, in the case of forward and bidirectional pumping. Input signal power = 10 mW, total
pump power = 400 mW.
A=
P0 e(−T
2 /2T 2 )
0
(3)
,
where T0 is the half width (at 1/e intensity point) and P0 is
the peak power. The values chosen are 20 ps and 28.22 mW
(corresponding to an average power of 10 mW at a bit rate of
10 Gbps), respectively. The two photon absorption is ignored
in the calculations. The value of T2 used for the doped fibre
is 100 fs. The wavelength of operation is 1550 nm and Aeff is
assumed to be 30 µm2 . The length of the fibre used is 22 m,
which is the optimum length for bidirectional pumping.
If β2 and n2 of the doped fibre were similar in magnitude to
those of ordinary fibres, the difference in the evolution of gain
between the different pumping configurations does not significantly affect the pulse propagation for the bit rates and powers
usually used in a commercial communication system. However
in a heavily doped fibre, the absorption induced effects in dispersion and nonlinearity need to be considered. The absorption
coefficient (α) of the fibre is given by
α(z, σ ) = N1 (z)σa (ω) − N2 (z)σe (ω),
(4)
where σa (ω) and σe (ω) represent the wavelength dependent
absorption and emission cross-sections of the fibre, while N1
and N2 are the population densities of the ground and excited
states [29]. Any change in α is accompanied by a change in the
refractive index. Nonlinear Kramer–Kronig relations [29–31]
can be used to relate the change in refractive index (
n) to the
change in the absorption coefficient (
α), caused due to some
perturbation, ξ , as
c
n(ω, ξ ) = P
π
∞
0
α(ω , ξ )
dω ,
ω2 − ω2
(5)
where P indicates the Cauchy’s principal value for the integral,
c is the speed of light in vacuum, and ξ is the source of perturbation in α, which could be due to a change in signal power,
pump power or in dopant concentration. Betts et al. [32] and
Montagna et al. [29] propose a polynomial expansion for n in
terms of the signal intensity, considering only the variation in
the signal power as the source of perturbation. n2 , evaluated as
the second-order term in the above expansion, for a fibre length
of 5 m at a pump power of 50 mW at 980 nm and with signal
at 1535 nm is 1.269 × 10−17 m2 W−1 , which is about three orders of magnitude larger than the nonlinear index coefficient of
a conventional fibre [29]. n2 is found to monotonously increase
with the dopant concentration, till a maximum value is reached
at a concentration of 1.05 × 1025 ions m−3 , beyond which it is
found to decrease [29]. It is also found to increase linearly with
the signal and pump intensities. Since the populations N1 and
N2 , and hence the absorption, strongly depend on the electromagnetic field intensities, n2 has a variation along the length
and across the cross-section of the fibre. Hence n2 may be expected to vary differently in different pumping schemes. This
concept of enhanced optical nonlinearities due to absorption
resonance is widely used in applications involving nonlinear
fibre couplers [33]. A refractive index change of the order of
10−6 at a signal wavelength of 1550 nm and a pump wavelength
of 980 nm is reported in one such work [11], which corresponds
to an n2 , four orders of magnitude larger than the conventional
value. Any change in refractive index would imply a change in
the GVD parameter. As a consequence, β2 is reported to vary
between ±3000 ps2 km−1 , with several oscillations about zero
between 1520 and 1555 nm [30,34].
In this paper, we attempt to numerically estimate the changes
in pulse propagation between the forward and bidirectional
pumping schemes, for a representative value of high nonlinear
refractive index. The large values of n2 in the doped fibre, coupled with the large powers in a high-power amplifier, make the
nonlinear length to be of the same order as that of the length
of doped fibre used for amplification. Hence, the differences
in signal evolution between the different pumping schemes, as
seen in Fig. 4a are expected to result in drastic differences in
pulse evolution. It is therefore very important to consider the
effects of the different pumping configurations on the pulse
evolution in high-power EDFA. To understand this, Eq. (1) is
solved numerically with a GVD parameter of −20 ps2 km−1
and n2 of 3.2 × 10−18 m2 W−1 . The value of n2 is chosen to
be two orders of magnitude greater than an ordinary fibre from
earlier work [29]. The longitudinal and transverse variation of
n2 is not considered since the motivation of this simulation is
to emphasise the need to treat unidirectional and bidirectional
pumping differently with regard to pulse propagation. Inclusion
25
Fig. 5. Optical pulse in the (a) time domain and (b) frequency domain. ‘Forw’ indicates forward pumping and ‘Bidi’ indicates bidirectional pumping. Input pulse
width is 20 ps and the fibre length considered is 22 m.
of longitudinal variation in n2 would further demarcate the two
pumping schemes.
Fig. 5a shows that the output pulse shape in time domain
is not considerably different between the forward and bidirectional pumping schemes. The output pulse spectrum however,
shows a significant difference (Fig. 5b). For the pulse width
considered here, the dispersive effects act only at very long
lengths compared to the length of the dopant fibre. Hence, the
significant contribution to the changes in the pulse spectrum is
due to self phase modulation (SPM) originating from the high
nonlinear index of the doped fibre. It is very clear from Fig. 5b
that, in the case of forward pumping, the pulse spectrum has
broadened significantly even within the length of the amplifier.
This is due to the large gain coefficient at the initial segment of
the fibre length in the case of forward pumping, which subsequently leads to a cumulative effect of SPM on the fast growing
pulse. The pulse spectrum in the case of bidirectional pumping
is not as broadened as in forward pumping. In this case, even
though there is a significant effect on the pulse due to SPM,
because of the lower gain slope, the nonlinear phase shift accumulated is not sufficient enough to broaden the spectrum much,
for the length of fibre and the powers considered. The impairment due to SPM can be minimised by reducing the peak power,
which in turn can be done by adjusting the average power and
the pulse width appropriately according to the bit rate of the
system. For example, at the same pulse width and bit rate, an
average power of 1 mW does not result in any significant spectral broadening in the forward as well as bidirectional pumping
case.
Retaining similar average input power levels, if the bit rate
is increased, the nonlinear effects reduce proportionately due
to the reduction in peak power. The pulse evolution is now
governed only by the dispersive effects. Even in this case, the
output pulse in the time and frequency domain would be considerably different between the different pumping schemes due
to the differences in the g0 contribution to the total dispersion
in the fibre. A similar situation arises at higher bit rates even
when a high value of the nonlinear coefficient is not considered
for the doped fibre. Normal dispersion at the operating wavelength would broaden the pulses in the time domain when the
bit rate is higher.
These results indicate that it is extremely essential to understand the propagation of signals through doped fibres with
reference to the pumping configuration. Due to the differences
in gain coefficient, the dispersive as well as the nonlinear effects are modified differently in the two pumping schemes
considered. Effects due to differences in dispersion parameters
due to resonant dispersion in dopants are not included in this
study. When one considers sub-picosecond pulses, the effect of
changes in β2 of the fibre also needs to be incorporated carefully. This study may be further extended to multichannel pulse
propagation as in [35], in order to analyse the impact due to
the differences in pumping schemes and the influence of other
nonlinear effects.
5. Conclusion
Bidirectional pumping is the best way of achieving high
power amplification with a moderate noise level, using a single
core EDF. The experimental results for bidirectional pumping
in a single channel system are compared with the numerical
modelling results and they are found to match reasonably well.
The maximum signal power obtained was 22.6 dB m. It is emphasised that, when the ratio of backward pump to the total
pump power increases, the optimum length and the gain increase. Thus, by choosing this ratio appropriately, one can design a system with a requisite gain and reduced noise figure.
Multichannel propagation with bidirectional pumping is also
analysed theoretically for CW signals and it is found that the
gain excursion and cross-saturation characteristics remain the
same as that of the unidirectional pumping schemes, and it retains all the advantages of a high power amplifier.
Pulse evolution within the fibre amplifier is found to be
distinctly different between the forward and the bidirectional
pumping schemes. Nonlinear optical effects are significant in
the EDF due to the high value of the nonlinear index coefficient reported by others for the doped fibre. The possible variations in the pulse evolution are calculated for a representative
value of high nonlinear index, and the results for the propagation of 20 ps, 10 Gbps Gaussian pulses show that the pulse
is significantly broadened in the frequency domain in the case
of forward pumping when compared to bidirectional pumping.
The impairment due to dispersive effects in higher bit rate sys-
26
tems is also different in both the pumping schemes. Hence for
a high-power EDFA, it is extremely important to consider the
gain evolution through the amplifier, rather than considering the
EDFA as a black box providing a bulk gain.
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