1
Numerical Analysis Techniques for Wideband Amplifiers
Namkyoo Park, Won Jae Lee, Bumki Min, and Jaehyoung Park
Optical Communication Systems Laboratory
School of Electrical Engineering, Seoul National University, Seoul, Korea, 151-742
Tel : +82-2-880-1820 Fax : +82-2-885-5284 E-mail : nkpark@plaza.snu.ac.kr
ABSTRACT
Increasing demands on the high capacity wavelength division multiplexed (WDM) transmission system now
require newly developed transmission windows beyond the gain bandwidth supported by erbium-doped fiber
amplifiers (EDFA). With the intensive development efforts on new rare-earth dopants and fiber nonlinearity
(Raman process) for fast few years, wideband optical amplifiers now can support easily over 4-5 fold wider
gain bandwidth than it was formerly possible with the conventional EDFAs. Of various breeds for this
application, there exist three distinct approaches near 1500nm band, accessible in the commercial market.
These includes : Thulium-doped fluoride fiber amplifiers (TDFFA) for S+ band (1450-1480 nm) and S band
(1480-1530 nm), EDFAs for C band (1530-1560nm) and L band (1570-1610nm), Raman amplifiers with
100nm’s of gain bandwidth (with flexible location from S+ to L band), and hybrid amplifiers with serial /
parallel combination of above techniques. Even though there have been much increased experimental
reports for all of these amplifiers, the complexity of the amplification dynamics from the number of involving
energy levels and difficulty in measuring experimental parameters make it harder than ever to predict the
performance of wideband amplifiers in general. This lack of serious study on the analytic or numerical
analysis on wideband amplifiers could cause the future impairments for the prediction and estimation of the
amplifier performances for different applications, restricting the successful deployment of wideband amplifier
based transmission systems. In this paper, we present the numerical model and analysis techniques for
wideband amplifiers (C/L band EDFA, Raman amplifier, and TDFA), along with their application examples.
Keywords : Erbium-doped fiber amplifiers (EDFAs), Thulium-doped fiber amplifiers (EDFAs), Raman
amplifiers, Fiber amplifiers, wavelength division multiplexed (WDM) systems, optical fiber communication
1. C+L BAND EDFA MODELING
1.1 Introduction
Among many attempts suggested so far, the silica based EDFAs in parallel configuration (C-band: 1530 ~
1560nm, plus L-band: 1570 ~ 1610nm) [1, 2] have been considered to be the most immediate viable solution
for real system applications, from the maturity of the supporting technologies such as the host material and
pump sources. Still, when compared to the C-band EDFA (C-EDFA), there have not existed corresponding
accumulated research efforts on L-band EDFA (L-EDFA) except last few years. The most serious research
focus on L-EDFA recently has been addressed to the efficiency improvement, to relax the requirement for
much higher pump power when compared to C-EDFA. As one of the approaches to improve power
conversion efficiency in L-band EDFAs [3, 4], we have suggested a structure which recycles useless
backward amplified spontaneous emission (ASE) of L-EDFA as a secondary pumping source in the passive
section of EDFA [4]. In this section, we provide spatially resolved W-EDFA numerical analysis result in
detail, to clearly reveal the roles of the C-band injection source to the evolution dynamics of the primary
pump, L-EDFA backward ASE, C-band injection sources and L-EDFA signals. As an application example,
we investigate a novel W-EDFA structure, without the use of additional injection sources [5, 6].
Experimental results show considerable improvements on gain and noise figure (2.6dB and 0.6dB at –
3.5dBminput) in addition to the limiting behavior, with negligible channel crosstalk from C to L-EDFAs.
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1.2 Experiments / Numerical Analysis
1560/1570
WDM coupler
1560/1570
WDM coupler
1550/1600
WDM coupler
Isolator
APC
Circulator
980nm pump LD
53mW
980nm pump LD
57mW
980nm pump LD
90mW
EDF 20m
EDF 300m
Figure 1-1. Schematics for a coupled, C plus L-band silica based EDFA under study [ref].
Fig. 1-1 shows the coupled structure of C-band plus L-band silica based EDFA used in this study. As an
injection source, backward ASE from a C-EDFA was added to an L-EDFA through a circulator and a C/L
band WDM coupler. The EDF used in the experiment was a commercially available, Al-codoped one with a
peak absorption coefficient of 4.5dB/m at 1530nm. 980nm LDs were used at the power level of 90mW,
53mW, and 57mW, to forward-pump the C-band, forward/backward-pump the L-band EDFA. The
measured losses from circulator and C/L WDM coupler were below 0.6dB and 0.3dB. Two external cavity
lasers, tuned at 1540 and 1595nm, were used for the evaluation of the amplifier gain and noise figure, in
conjunction with the optical spectrum analyzer.
To compare the performances of the suggested structure with an uncoupled one, we first measured the
saturation output power at the signal wavelengths of 1540nm and 1595nm, with C-band backward ASE
injection to L-EDFA port being turned off (APC connector open in figure 1-1). The measured signal input /
output power for W-EDFA were –3.5dBm / 13.01dBm (@1540nm) and -3.5dBm / 10.47dBm (@1595nm)
respectively, exhibiting much lower power conversion efficiency for the L-band. Still, when the seed
injection port set in pass-state (APC connector closed), we observed dramatic improvement on the L-EDFA
output power over 2.6dB, with noticeable changes in background ASE spectral profile as well (Figure 1-2).
The estimated gain bandwidth of the amplifier from the ASE profile was larger than 80 nm.
Figure 1-2 (Left). Output spectra of the coupled ( — :solid line) and uncoupled structure (····· :dot) amplifier for –3.5dBm
saturating input signals at the wavelengths of 1540nm and 1595nm (RBW = 0.2nm).
Figure 1-3 (Right). Comparison of output powers as a function of 1595nm input power at various C-EDFA gain levels.
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To also investigate the possible performance variation of L-EDFA as a function of C-EDFA gain, we
measured the saturated output power at the wavelength of 1595 nm, while changing the C-EDFA pump power
(Figure 1-3). With the ASE injection port set in pass-state, the L-EDFA exhibited limiting amplifier
behavior, with considerable improvement in the gain (2.1~2.6 dB at –3.5 dBm, and 0.1~0.3dB at 6.5dBm
input) and noise figure (0.6dB), almost irrespectively of the C-EDFA gain values (6.57~17.72dB).
Considering the much smaller relative L-EDFA gain variation below 0.5dB for much larger gain change of C-
EDFA over 11.2dB (and correspondingly different levels of injected C-EDFA backward ASE power), we
attribute this behavior to the rapid amplification of the injected C-band ASE signal in the front section of the
L-EDFA to a saturation level which then being transferred to L-band photons in rear systems of the amplifier.
The above explanation can also be applied to explain the negligible, measured transient crosstalk effect to L-
EDFA from C-band input power changes. For 6dB variation of C-band input power (-4dBm to 2dBm), the
deviation of L-band output saturating power stayed below 0.2dB for wide range of L-EDFA input power
levels (-3.5dBm ~ 4.5dBm). Reminding previous results on transient controlled single C-EDFA [6], this C-
EDFA to L-EDFA crosstalk of 0.2dB would not pose a problem for most system applications.
To better understand and confirm the above dynamics / explanation on gain and noise figure improvements,
we conducted numerical simulations for the suggested structure. The amplifier was modeled as a
homogeneously broadened three level system including both spatial and spectral variations [7], with spectral
grid of 1 nm and spectral range of 120nm between 1500nm and 1620nm. Absorption and emission cross
sections, including other additional parameters were obtained from the fiber manufacturer’s data sheets. The
simulation results agreed well with the experiments within 1.5dB for most spectral range and operating points,
and reproduced the general tendency of all the relative performance improvements obtained from the
experiments. We attribute the discrepancies in the simulation (1.5dB max for absolute power) to the rather
inaccurate component loss profiles and data sets in the long wavelength regime.
The evolution spectra of the forward propagating waves in the L-EDFA sections of the coupled structure and
that of the uncoupled structure is shown in Fig 1-4(a) and Fig 1-4(b) respectively. In Fig 1-4(a), the small
peak in the shorter wavelength corresponds to the Rayleigh backscattered signal from the C-EDFA, which
was included in the simulations. With the injection of C-band backward ASE together with the 980nm
pump from the input, 1550nm band seeded forward ASE grows much faster in the input section, when
compared to the uncoupled structure. This stronger, amplified forward ASE then get absorbed over the
following stages of EDF and transfer its energy to longer wavelengths acting as the primary-pump to L-band
photon mediator, while at the same time suppressing the pump-power depleting, wasted backward ASE in the
L-EDFA.
Figure 1-4. Evolution of the forward propagating waves in the L-EDFA sections (a) in the coupled structure (RBW = 1
nm) and (b) in the uncoupled structure (RBW = 1 nm)
For comparison, the evolution spectrum of the uncoupled W-EDFA exhibits a peculiar dip in powers for
forward propagating ASE and signal at about 50m from the input end of L-EDFA. This can be explained by
the fact that there are no C-band seed photons in uncoupled structure which mediate the forward 980nm pump
to the L-band signals, resulting in the waste of pump power at much faster rate than coupled structure by the
strong backward ASE from L-EDFA. Additional distinguished feature can also be found from the evolution
-50
-40
-30
-20
-10
0
10
20
1500 1520 1540 1560 1580 1600 1620
300
250
200
150
100
50
Optical power(dBm)
Wavelength(nm)
EDF length(m)
-50
-40
-30
-20
-10
0
10
20
1500 1520 1540 1560 1580 1600 1620
300
250
200
150
100
50
Optical power(dBm)
Wavelength(nm)
EDF length(m)
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spectrum of the forward ASE in L-EDFA. In the L-EDFA input sections, ASE is generated mostly in C-
band. However, as soon as forward propagating waves diminishes, the newly generated ASE powers after a
dip in forward propagating waves are primarily consist of L-band photons. Comparing these two structures,
the differences in efficiencies can be attributed to the fact that the seeded photons in the coupled structure act
as a reservoir of pump powers for L-band signal amplification.
1.3 Discussion
To summarize, we have demonstrated a novel structure for ultra wideband amplifiers with enhanced
performances from C-band EDFA backward ASE injection to L-band EDFA, eliminating the need of
additional injection sources. Experimental results showed a considerable gain improvement over 2.6dB on
L-band EDFA, in addition to 0.6dB noise figure reduction, without noticeable amount of channel crosstalk
from the C-band EDFA to the L-band EDFA. Spatially resolved wideband EDFA simulation were
conducted for the first time to our knowledge confirming the experimental observations, and providing better
understanding on the dynamics of L-band EDFA.
2. RAMAN AMPLIFIER MODELING
2.1 Introduction
Raman fiber amplifiers (RFAs) are recently attracting many researcher’s attentions in DWDM system
application due to their distinctive flexibility in bandwidth designs and growing maturity of high power pump
module technologies [8]. However, known modeling techniques for RFAs based on solving ordinary
coupled differential equations require exhaustive computational efforts for acquiring well-matched prediction,
owing to larger bandwidth and longer fiber length which must be considered in RFAs. In this section, we
modify and rearrange the propagation equations of Raman fiber amplifiers so that average power analysis
technique can be applied to predictions of system performance with reasonably reduced simulation effort
without any degradation of accuracy. Applications of these equations to the numerical analysis of practical
RFA-based systems show computation time reduction over 2 orders of magnitude when compared with direct
integration approach with comparable accuracy.
2.2 Theory
The set of propagation equations governing forward and backward power evolutions in Raman fiber
amplifiers which include additional various effects such as Rayleigh backscattering and temperature
dependent spontaneous Raman emission can be modeled as [9, 10],
,),(),(
)(
),(
∑
>
+
±
−
=
νζ
ζζ
ζν
ν zPzP
eff
A
eff
K
r
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,),(),(
)(
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∑
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+
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−
=
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ν zPzP
eff
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eff
K
r
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zB
m
,
1
/)(
1
1),(),(
2
)(
),(
−
−
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=
kTh
e
zPzP
eff
A
r
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νζ
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ν
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5
For algebraic simplicity, the power-dependent parameters A, B, C and D were defined as above. The above
equations need numerical integration rather than analytical solutions because of the power-dependent A(z,
ν
),
B(z,ν), C(z,ν) and D(z,ν) parameters. However, this analysis problem can be solved with the assumption of
the average power analysis technique. First, the length of entire Raman fiber amplifier must be divided into
a series of concatenated elemental amplifier sections. Through similar derivation to EDFA analysis [11],
when replacing the A(z,ν), B(z,ν), C(z,ν) and D(z,ν) parameters with constant values A(ν), B(ν), C(ν) and
D(ν), the powers of signals and ASE are substituted by their length averaged powers in each elemental
amplifier sections for the calculations of the gain and spontaneous emission. Then iterations are performed
until self-consistent convergence condition is satisfied for that section. After these procedures, propagation of
powers along the full length of the fiber is continuously modified until the output powers satisfy overall given
convergence and boundary conditions through relaxation methods.
2.3 Numerical Analysis
As is well known for average power analysis, the simulation results strongly depend on the number of
elemental amplifier sections. Fig. 2-1. shows the example case result for the convergence test of the forward
and backward power calculated by average power analysis to the result obtained by numerical integration
method (using fourth-order Runge-Kutta method with variable step size), as a function of the number of
elemental amplifier sections. Though required number of sections is generally dependent on the operating
conditions of the Raman fiber amplifier, usually 20~30 sections are sufficient for most system performance
evaluations in terms of accuracy. The simulation time was proportional to the number of elemental amplifier
sections. By comparison, direct integration method took 228 times more than average power analysis with
20 elemental amplifier sections. Therefore, considerable reduction in computation time as much as 3 orders
of magnitude can be obtained for even longer length of Raman fiber amplifiers.
1 10 100
0.05939
0.05940
0.05941
0.05942
0.05943
0.05944
0.05945
Backward power (mW)
Number of elemental amplifier sections(#)
Forward power (mW)
0.00481
0.00482
0.00483
0.00484
0.00485
0.00486
0.00487
0.00488
Figure 2-1. Forward and backward output powers of RFA as a function of the number of elemental amplifier sections
In order to check the validity of the average power analysis for Raman amplifier, a muti-wavelength pumped
distributed Raman amplifier was simulated with the analogous parameter set as previous experimental report
[12]. Here, we assumed 25 km of transmission fiber, 12 backward pump sources (1405, 1412.5, 1420,
1427.5, 1435, 1442.5, 1450, 1457.5, 1465, 1480, 1495 and 1510 nm) and 100 input channels at various power
levels. Fig. 2-2. shows the gain and noise figure spectrum of the simulated results according to the various
power levels of input signal power. At the signal power levels of –8 dBm, gain deviation less than 1 dB over
98 nm is achieved with proper pump power assignments. However, the noise figure spectrum of simulated
RFA clearly shows that short wavelength channels near pump bands experience more severe noise
accumulation than long wavelength channels. Fig. 2-3. shows the pump evolutions along the length of RFA,
exhibiting the strong power transfers between pumps.
![Figure 1-1. Schematics for a coupled, C plus L-band silica based EDFA under study [ref].](/figures/figure-1-1-schematics-for-a-coupled-c-plus-l-band-silica-3c5747f8.webp)
](/figures/figure-3-2-left-pump-ground-state-absorption-gsa-sp1-pump-3jsnq8za.webp)
