Linear semiconductor optical amplifiers for
amplification of advanced modulation formats
R. Bonk,1,* G. Huber,1 T. Vallaitis,1 S. Koenig,1 R. Schmogrow,1 D. Hillerkuss,1 R.
Brenot,2 F. Lelarge,2 G.-H. Duan,2 S. Sygletos,1,3 C. Koos,1,4 W. Freude,1,4 and
J. Leuthold1,4
1
Institute of Photonics and Quantum Electronics (IPQ), Karlsruhe Institute of Technology (KIT), Engesserstr. 5,
76131 Karlsruhe, Germany
2
III-V Lab, a joint lab of Alcatel-Lucent Bell Labs France, Thales Research and Technology and CEA Leti, Campus
Polytechnique, 1, Avenue A. Fresnel, 91767 Palaiseau cedex, France
3
Photonic Systems Group, Tyndall National Institute, University College Cork, Lee Maltings, Dyke Parade, Cork,
Ireland
4
Institute of Microstructure Technology (IMT), Karlsruhe Institute of Technology (KIT), Hermann-von-HelmholtzPlatz 1, 76344 Eggenstein-Leopoldshafen, Germany
*rene.bonk@kit.edu
Abstract: The capability of semiconductor optical amplifiers (SOA) to
amplify advanced optical modulation format signals is investigated. The
input power dynamic range is studied and especially the impact of the SOA
alpha factor is addressed. Our results show that the advantage of a lower
alpha-factor SOA decreases for higher-order modulation formats.
Experiments at 20 GBd BPSK, QPSK and 16QAM with two SOAs with
different alpha factors are performed. Simulations for various modulation
formats support the experimental findings.
©2012 Optical Society of America
OCIS codes: (250.5980) Semiconductor optical amplifiers; (250.5590) Quantum-well, -wire
and -dot devices; (060.1660) Coherent communications.
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23 April 2012 / Vol. 20, No. 9 / OPTICS EXPRESS 9658
1. Introduction
Semiconductor optical amplifiers (SOA) will need to cope with advanced modulation format
signals in next-generation optical networks. In particular, the complexity of emitters and
receivers may require integrated boosters or pre-amplifiers to compensate the losses of the
multi-stage modulation and demodulation steps. The question though is how well SOAs can
amplify advanced modulation format data signals and which parameters matter in the
selection of an SOA. Further, it is of interest how the parameters need to be optimized in the
SOA design for an optimum operation with such modulation formats.
An ideal SOA for advanced modulation formats needs to amplify symbols with both small
and large amplitudes alike. This presumably requires an SOA with a large input power
dynamic range (IPDR). The IPDR defines the power range in which error-free amplification
can be achieved [1]. A large IPDR is obtained when the SOA has a large saturation input
power Psatin such that it can cope with largest amplitudes as well as when the SOA has a low
noise figure such that it can deal with weak amplitudes. Successful attempts towards
increasing the linear operation range for on-off-keying (OOK) data signals were by
introducing gain clamped SOA or holding beam techniques [2–6]. Other approaches exploited
special filter arrangements [7,8] in order to mitigate the bit pattern effects of an SOA when
operated in its nonlinear regime. However, a recent detailed study for OOK modulation
formats revealed that conventional SOAs may as well offer a large IPDR exceeding 40 dB (at
a bit error ratio of 10−5) when properly designed [1].
But, an ideal SOA for advanced modulation formats not only needs to properly amplify
signals with various amplitude and power levels but also should preserve the phase relations
between the symbols [9]. Prior work on SOA has focused on phase-shift keying (PSK)
modulation formats such as differential phase-shift keying signals (DPSK) [10–14] and
differential quadrature phase-shift keying signals (DQPSK) [15,16]. These modulation
formats basically have a constant modulus and therefore naturally may be anticipated to be
more tolerant towards SOA nonlinearities.
However, so-called M-ary quadrature amplitude modulation (QAM) formats comprise
both amplitude-shift keying (ASK) and PSK aspects. Thus an ideal SOA should amplify such
QAM signals with high amplitude and phase fidelity. In SOAs gain changes and phase
changes are related by the so-called Henry’s alpha factor αH. Thus, one might assume that a
low alpha factor SOA is advantageous. As quantum-dot (QD) SOAs tend to have lower alpha
factors one might expect that they should outperform bulk SOA as amplifiers for advanced
modulation formats. Yet, a recent publication showed that things get more intricate when
QAM signals are used [17].
In this paper, we show that SOAs for advanced modulation formats primarily need to be
optimized for a large IPDR (i. e. linear operation with low noise figure). Additionally, an
SOA with a low alpha factor offers advantages when modulation formats are not too complex.
The findings are substantiated by both simulations and experiments performed on SOAs with
different alpha factors for various advanced modulation formats. In particular it is shown that
the IPDR advantage of a QD SOA with a low alpha factor reduces when changing the
modulation format from binary phase-shift-keying BPSK (2QAM) to quadrature phase-shiftkeying QPSK (4QAM) and it vanishes completely for 16QAM. This significant change is due
to the smaller probability of large power transitions if the number M of constellation points
increases. The smaller probability of large power transitions in turn leads to reduced phase
errors caused by amplitude-phase coupling via the alpha factor.
The paper is organized as follows: Section 2 covers the effects which limit the signal
quality when amplifying signals having advanced modulation formats. Section 3 presents the
simulation results for differentially phase encoded, non-differentially phase encoded and
QAM signals, respectively. In Section 4 we compare for bulk and QD SOA the measurements
of 20 GBd BPSK, QPSK and 16QAM signals. Section 5 states the conclusions of this work.
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2. Limits in signal quality when amplifying M-ary QAM signals
The quality of signals after an SOA is limited by SOA noise for low input powers [18], and by
signal distortions due to gain saturation for large input powers [19]. Saturation of the gain not
only induces amplitude errors but also phase errors due to the coupling of the alpha factor.
Saturation also may induce inter-channel crosstalk if several wavelength division
multiplexing (WDM) channels are simultaneously amplified by the same SOA. The ratio of
the lower and upper power limits, inside which the reception is approximately error-free, is
expressed by the IPDR. In this paper, the term “error-free” is used for two distinct cases. The
first case requires a signal quality which corresponds to a bit error ratio (BER) of 10−9. In the
second case, the use of an advanced forward error correction (FEC) is assumed, which allows
error-free operation for a raw BER of 10−3.
Fig. 1. Constellation diagrams showing the limitations of the signal quality for amplification of
a 4QAM (QPSK) data signal. (a) The input power into the SOA is very low resulting in a low
OSNR at the output of the amplifier. The constellation diagram of the 4QAM signal shows a
symmetrical broadening of the constellation points. This broadening due to ASE noise causes a
low signal quality. (b) Error-free amplification of the data signal is observed for a nonsaturating input power. (c) For high input powers a nonlinear phase change induced by a
refractive index change within the SOA causes a rotation of the constellation points. This
rotation causes a reduction of the signal quality.
2.1 Low input power limit
For low input signal powers the limitations are due to amplified spontaneous emission (ASE)
noise which in this case is virtually independent of the signal input power. Thus, if the input
power decreases while the ASE power remains constant, the optical-signal-to-noise ratio
(OSNR) will become poor. An example of such an OSNR limitation is presented in Fig. 1(a)
for an optical QPSK (4QAM) signal. The constellation diagram shows a symmetrical
broadening of the constellation points. The optimum situation where the input signal power is
neither too low nor too high is shown in Fig. 1(b).
2.2 Large input power limit
For large input powers the SOA gain is reduced due to gain saturation. Transitions between
symbols are affected by the complex SOA response. Therefore, depending on the modulation
format both the amplitude and phase fidelity of the amplification process are impaired to a
different degree. Among the many implementations of M-PSK and M-ary QAM formats the
best performing transmitters often use zero-crossing field strength transitions [20], and
therefore generate power transitions (solid line), see Fig. 2(a), 2(b). These power transitions
change the carrier concentration N and therefore the SOA fiber-to-fiber (FtF) gain Gff =
exp(gff L), where the FtF net modal gain gff is assumed to be independent of the SOA length L
and comprises the SOA net modal chip gain g (G = exp(g L)) as well as any coupling losses
αCoupling to an external fiber, Gff = αCoupling G αCoupling, with 1 > αCoupling ≥ 0. A change gff =
(ln Gff) / L = g of the FtF net modal gain is identical to a change g of the net modal gain
leading to a change neff of the effective refractive index neff by amplitude-phase coupling,
which in turn is described by the so-called Henry’s alpha factor αH. With the vacuum wave
number k0 = 2π / λs, signal wavelength λs, the complex output field is in proportion to (Gff)0.5
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Received 22 Feb 2012; revised 9 Apr 2012; accepted 9 Apr 2012; published 12 Apr 2012
23 April 2012 / Vol. 20, No. 9 / OPTICS EXPRESS 9660
exp(– j k0 neff L) where the output phase (not regarding any input phase modulation) is defined
by φ = –k0 neff L. Output phase change ∆φ and effective refractive index change are related by
∆φ = –k0 ∆neff L. For the alpha factor we then find
∂neff / ∂N
n
2 ϕ
≈ −2k0 eff =
=
∂g ff / ∂N
g ff
g ff L
2 ϕ
=
( ln Gff )
2 ϕ
.
( ln G )
(1)
SOA Phase
1
−2 k0
Gain
Power
αH =
Fig. 2. Response of a saturated SOA in reaction to a BPSK (2QAM) signal with two possible
transitions from symbol to symbol. Phase errors induced by power transitions from one BPSK
constellation point to the other. (a) BPSK constellation diagram with in-phase (I) and
quadrature component (Q) of the electric field. Solid line: zero-crossing transition; dashed line:
constant-envelope transition. (b) Time dependencies for the two types of power transitions.
SOA response that affects the (c) gain and (d) refractive index which leads to an SOA-induced
phase deviation ∆φ. SOAs with lower alpha factors induce less amplitude-to-phase conversion
and therefore amplify the electric input field with a better phase fidelity. BPSK constellation
diagram after amplification with a saturated SOA for (e) zero-crossing transition (for two alpha
factors) and (f) constant-envelope transition.
Thus, by amplitude-phase coupling in the SOA, gain changes induce unwanted phase
deviations. An illustration of this effect is schematically depicted in Fig. 2 assuming a BPSK
format and a saturated SOA. If the signal power reduces at time t0, Fig. 2(b), the gain starts
recovering from its operating point described by a saturated chip gain GOp (given by the
average input power) towards the unsaturated small-signal chip gain G0. After traversing the
constellation zero the signal power increases and reduces the gain towards its saturated value
GOp, Fig. 2(c). Coupled by the alpha factor, a gain change induces a refractive index change
and therefore an SOA-induced phase shift ∆φ. SOAs with a lower alpha factor (αH,1 < αH,2)
have less amplitude-to-phase conversion and therefore give rise to less phase changes, see
Fig. 2(d), and also Fig. 1(c). As a consequence, SOAs with lower alpha factors are expected to
show better signal qualities for phase encoded data with a high probability of large power
transitions. The constellation diagrams with induced phase errors are presented in Fig. 2(e) for
the two alpha factors. If the transition between the two constellation points maintains a
constant envelope (Fig. 2(a), 2(b), dashed line) so that gain and phase changes do not happen
(Fig. 2(c), 2(d)), no phase errors occur, Fig. 2(f). If the device could be operated in the smallsignal gain region even for high SOA input power levels, the constellation points would lie on
the dotted circle. However, due to the described operation under gain saturation, the
amplitudes at the SOA output are reduced, see Fig. 2(e), 2(f).
Typically, the phase recovery in SOAs is slower than the gain recovery [21–23], so a
phase change induced at the power transition time has not necessarily died out at the time of
signal decision (usually in the center of symbol time slot), so that the data phase is perturbed
and errors occur. Additionally, the strength of the phase change induced by the SOA and
detected at the decision point depends on the required time to change between constellation
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Received 22 Feb 2012; revised 9 Apr 2012; accepted 9 Apr 2012; published 12 Apr 2012
23 April 2012 / Vol. 20, No. 9 / OPTICS EXPRESS 9661
points, and thus on the symbol rate and the transmitter bandwidth. If the time to change
between constellation points (approximately 10 ps…30 ps for 30 GBd…10 GBd) is not
significantly faster than the SOA phase recovery time (about 100 ps), severe phase changes
will degrade the signal quality. Thus, only at very high symbol rates, no significant phase
change from the SOA is expected indicating the benefit of a limited SOA recovery time. In
addition to phase errors amplitude errors are expected to occur in M-ary QAM signals.
Because M-ary QAM signals comprise multiple symbols with different amplitude levels
extreme transitions from one corner to the other are less likely. Thus, phase errors due to
amplitude-phase coupling are less likely as well. In average the amplitude distances between
symbols reduce due to gain saturation.
(a)
BPSK
QPSK
16QAM
BPSK
QPSK
16QAM
0.5
0.5
1.0 0.0
1.0 0.0
Normalized Amplitude Change
0.5
(b)
75
50
25
0
0.0
1.0
Fig. 3. Constellation diagrams and transition probabilities for different modulation formats. (a)
Constellation diagrams with amplitude and phase transitions for BPSK, QPSK and 16QAM
data signals. (b) Transition probability as a function of the amplitude change normalized to the
largest possible amplitude transition. The probability of large transitions decreases for higher
order modulation formats.
Some examples of amplitude transitions in constellation diagrams for practical PSK and
M-ary QAM implementations are shown in Fig. 3(a) for BPSK, QPSK and 16QAM. The
transition probabilities for all occurring normalized amplitude changes are depicted in Fig.
3(b). The transition probability of the largest amplitude change reduces from 50% for BPSK
to 25% at QPSK down to below 5% for 16QAM. Thus, the probability to observe a large
amplitude change decreases the higher the order of the modulation format.
2.3 Parameters relevant for linear SOAs
In this section, we discuss the parameters which determine the usable input power range of an
SOA, namely noise which sets the lower level P1, and amplifier saturation which is
responsible for the upper level P2. The ratio P2 / P1 defines the IPDR for linear operation, a
quantity which will be discussed in Section 3.2 in more detail.
The low input power limit is basically determined by the ASE noise. The amount of ASE
noise added by the SOA is described by the noise figure NF [18], which is defined with the
inversion factor nsp and the single-pass chip gain G
NF =
1
G −1
+ 2nsp
.
G
G
(2)
The low input power limit when amplifying data signals with an SOA can be decreased with a
lower noise figure. NF is minimized using a population inversion factor nsp approaching 1.
This can be achieved by adapting the current density J, i. e. choosing it as high as possible,
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with low internal waveguide losses αint, by choosing the proper dimensionality of the
electronic system in the active region, i.e. quantum well rather than bulk, and an optimized
device structure (e. g. good results have been shown in [24]). A low FtF noise figure NFff
additionally requires a low fiber-to-chip coupling loss at the input.
The high input power limit basically is determined by gain saturation induced phase and
amplitude changes on the data signal. Thus, a large saturation input power Psatin is required to
avoid gain saturation. The saturation input power Psatin can be approximated by
hf 2 ln(2) A 1 1
Psatin = s
,
G0 − 2 Γ a τ c
(3)
with the Planck constant h, the optical signal carrier frequency fs, the small-signal chip gain
G0, the area of the active region A, the optical confinement factor Γ, the differential gain a and
the effective carrier lifetime τc. The high input power limit when amplifying data signals with
an SOA can be increased by choosing the gain moderately high, by having a large modal
cross section A / Γ, with a doping of the active region to decrease the effective carrier lifetime,
with a high bias current density J, and with a low differential gain a. Additionally, if gain
saturation cannot be avoided, an SOA with a low alpha-factor and moderately fast gain and
phase dynamics are desirable. More details on linear SOA can be found in [1,25].
3. Modeling the impact of the alpha factor on the signal quality
In this section, the impact of the SOA’s alpha factor on the amplification of advanced optical
modulation format signals is investigated with simulations. Two SOAs with identical
performance in terms of unsaturated gain, saturation input power, noise figure, and SOA
dynamics are used. The SOAs only differ in their alpha factor. Simulations with alpha factors
of 2 and 4 are performed for differentially phase encoded and non-differentially phase
encoded data signals, respectively.
3.1 Models for transmitter, SOA and receiver
The simulation environment as shown in Fig. 4 consists of a 28 GBd transmitter (Tx), two
virtual switches for either investigating the back-to-back (BtB) signal quality, or for
simulating the influence of the SOA on the signal quality. The SOA model takes into account
phase changes and ASE noise. The 28 GBd receiver (Rx) is either a direct receiver, a
homodyne coherent or a differential (self-coherent) receiver, respectively. In the following
each section of the simulation setup is discussed in more detail.
The transmitter (Tx) in Fig. 4 consists of a continuous wave (cw) laser and an optical IQmodulator. To achieve a realistic signal quality, the electrical signal-to-noise-ratio (SNR) of
the modulator input signal in the electrical domain is adjusted to 20 dB. A pulse carver is
added in front of the IQ-modulator that either shapes the cw laser light to 33% or 50% RZ
pulses, or just lets the cw light pass through for NRZ operation. The electrical data signals
supplied to the optical modulator are low-pass filtered with a 3 dB bandwidth of 25 GHz.
Jitter of 500 fs and rise and fall times of 8 ps are modeled to mimic realistic optical BtB data
signals. This transmitter is used to generate signals with higher-order optical modulation
formats such as (D)QPSK and 16QAM. For OOK and (D)BPSK data signals only the Ichannel of the IQ-modulator is used. The output signal of the modulator is amplified and
subsequently filtered by an optical band pass filter. The in-fiber input power Pin to the SOA
can be adjusted with an attenuator.
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Fig. 4. Simulation environment for investigating the impact of the SOA alpha factor on signals
with advanced optical modulation formats. The transmitter (Tx) generates OOK, (D)BPSK,
(D)QPSK, or 16QAM data signals. Virtual switches define a reference path for back-to-back
(BtB) simulations. The rate-equation based SOA model inside the dashed box provides a chip
gain G and takes into account fiber-to-chip losses αCoupling of −3.5 dB per facet, gainindependent amplified spontaneous emission (ASE) noise, and phase changes. Depending of
the transmitted data format, the receiver (Rx) is chosen.
The SOA is modeled following the approach in [26–30]. The model describes a quantumdot (QD) SOA which is longitudinally subdivided into 20 segments. In each segment the
evolution of the photon and carrier density along the propagation direction is governed by
rate-equations for the photon number and the optical phase. The ASE noise is simulated as
white Gaussian noise added to the output of the SOA.
Table 1. Parameter values of the SOA model [26] used in the simulations.
Parameter
Current density
Area density of QD
Number of QD layers (separated by spacers and wetting layers (WL))
Amplifier length
Thickness of active region
Width of active region
Carrier lifetime (WL refilling time)
Characteristic relaxation time (QD refilling time)
Relative line broadening (inhomogeneous/homogeneous)
Resonant cross section (measure of photon-QD carrier interaction, describing the
probability of stimulated radiative transitions)
Internal waveguide losses
Alpha-factor (Henry factor)
Area density of WL states (WL states serve as a carrier reservoir for QD states)
Average binding energy (energy of QD electrons and holes relative to the WL
bandedge)
Parameter and Value
J = 7.5 kA/cm2
N = 8.5 × 1014 m−2
l=6
L = 1 mm
twg = 0.125 µm
w = 1.75 m
τc = 100 ps
τrel = 1.25 ps
γinhom / γhom = 0.33
σres = 1.3 × 10−19 m2
αint = 400 m−1
αH = 2 and αH = 4
nwl = 1.08 × 1016 m−2
Ēbind = 150 meV
The SOA model parameters are shown in Table 1. The SOA model has been described in
[28]. The parameters are chosen to provide a FtF gain Gff of 13.5 dB, a 3 dB in-fiber
saturation input power Psat,fin of –2 dBm and a FtF noise figure NFff of 8.5 dB. The estimated
per-facet coupling loss αCoupling is –3.5 dB. To investigate the influence of the alpha factor on
the amplification of signals with advanced modulation formats, we simulate two SOAs with
alpha factors 2 and 4, respectively. The FtF gain Gff and the FtF noise figure NFff versus the
in-fiber input power Pin of the two SOAs are shown in Fig. 5(a) and 5(b). The input signal is
set to a wavelength of λ1 = 1554 nm. The modulus |∆φ| of the phase changes of the SOAs are
plotted in Fig. 5(c). Large input powers cause carrier depletion. Thus the gain is suppressed,
and the phase change due the amplifier saturation increases with increasing input power. The
device with the larger alpha factor shows stronger phase changes under gain suppression.
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23 April 2012 / Vol. 20, No. 9 / OPTICS EXPRESS 9664
in
Psat
Phase Change |∆φ| [rad]
FtF Noise Figure [dB]
FtF Gain [dB]
in
Psat
in
Psat
Fig. 5. Comparison of SOA characteristics for devices which only differ in the alpha factor. An
SOA with an alpha factor of 2 (black) and an SOA with an alpha factor of 4 (blue) are used for
the simulation. (a) FtF gain Gff as a function of the SOA input power is shown. The unsaturated
FtF gain Gf0 is 13.5 dB at a wavelength of 1554 nm, and the 3 dB saturation input power is −2
dBm. (b) FtF noise figure as a function of SOA input power. (c) Phase change ∆φ ≤ 0 as a
function of SOA input power. The SOA with larger alpha factor causes larger magnitudes |∆φ|
if the SOA becomes saturated.
The receiver model depends on the modulation format. Basically, it comprises a noisy
optical amplifier and a noise-free photoreceiver. Three receiver types are available: For direct
detection, for coherent detection and for differential (self-coherent) detection. OOK-formatted
(intensity encoded) signals are directly detected with a photodiode. The differentially phase
encoded DPSK and DQPSK formats are received with delay interferometer (DI) based
demodulators followed by balanced detectors. Signals with non-differentially phase encoded
formats such as BPSK, QPSK and 16QAM are received using a homodyne coherent receiver
comprising a noise-free local oscillator (LO), and balanced detectors for the in-phase and the
quadrature-phase components, respectively.
3.2 Signal quality evaluation by error vector magnitude, Q2 factor and IPDR
To estimate the signal quality of simulated (and measured) data signals after amplification
with the SOAs, we employ the error vector magnitude (EVM) for non-differentially phase
encoded data signals, and the Q2 factor method for differentially phase encoded data signals.
With these data, we estimate the IPDR of the SOAs.
Advanced modulation formats such as M-ary QAM encode the data in amplitude and
phase of the optical electric field. The resulting complex amplitude of this field is described
by points in a complex IQ constellation plane defined by the real part (in-phase, I) and
imaginary part of the electric field (quadrature-phase, Q). Figure 6(a) depicts a transmitted
reference constellation point Et,i ( ) and the actually received and measured signal vector Er,i
( × ), which deviates by an error vector Eerr,i from the reference. We use non data-aided
reception and define the EVM for non-differentially phase encoded data signals as the ratio of
the root-mean-square (RMS) of the error vector magnitude for a number of I received random
symbols, and the largest magnitude of the field strength Et,m belonging to the outermost
constellation point,
EVM m =
σ err
Et, m
, σ err
2
=
2
1 I
Eerr,i , Eerr,i = Er,i − Et,i .
∑
I i =1
(4)
The errors in magnitude and phase for the received constellation points are also evaluated
separately. The EVM measures the quality of an advanced modulation format signal much the
same way as it is customary with the Q2 factor [31,32].
With the measured EVM as in Fig. 6(b), the IPDR is defined as the range of input powers
Pin into an SOA at which error-free amplification of a data signal can be ensured. The input
power limits for error-free amplification are set by the EVM limit EVMlim corresponding to a
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BER of 10−9 or 10−3. The ratio of the corresponding powers P2 and P1 in Fig. 6(b) define the
IPDR measured in dB,
IPDR = 10 log ( P2 P1 ) .
(5)
Our EVM limits are 23.4% for BPSK, 16.4% for QPSK (indicating a BER = 10−9), and 10.6%
for 16QAM (indicating a BER = 10−3) [32].
Et ,m
P2
P1
Eerr ,i
Er , i
Et ,i
P1
P2
Fig. 6. Error-vector magnitude (EVM), power penalty (PP) and input power dynamic range
(IPDR) for non-differential (QAM) and differential (DPSK, DQPSK) modulation formats. For
QAM, subfigures (a) and (b) illustrate the EVM definition and the determination of the IPDR
for given EVMlim. For DPSK and DQPSK, subfigures (c) and (d) clarify what is meant with the
power penalty for a given Q2 of 15.6 dB, and how the IPDR is determined from a PP of 2 dB.
Differential modulation formats such as DPSK or DQPSK encode information as phase
difference between two neighboring bits. On reception, these phase differences are converted
into an intensity change by using a delay interferometer demodulator. The signal quality of
the obtained eye diagram is estimated by the Q2 factor irrespective of the fact that
demodulated phase noise is not necessarily Gaussian, and that therefore the inferred BER is
inaccurate. The I and Q data of the DQPSK signals are evaluated separately and lead to
virtually identical Q2 factors. In Fig. 6(c) the Q2 factor as a function of receiver input power is
presented schematically for the back-to-back case (BtB, without SOA) and for the case with
SOA. The power penalty (PP) is the factor by which the power at the receiver input must be
increased to compensate for signal degradations compared to the BtB case. In Fig. 6(d) the
IPDR for DPSK and DQPSK is again defined according to Eq. (5), but this time by the
logarithm of the ratio of SOA input powers P2 / P1 for which the PP is less than 2 dB at a Q2
of 15.6 dB.
3.3 Modulation formats that are advantageous together with low alpha-factor SOAs
In this section, we show by simulation that the use of a low alpha-factor SOA can have an
advantage. The alpha factor mostly matters for simple phase encoded signals. Figure 7 shows
for both SOA with alpha factors of 2 and 4 the respective EVM and the power penalties as a
function of the SOA input powers for (a) BPSK, (b) QPSK, (c) 16QAM, (d) OOK, (e) DPSK
and (f) DQPSK. In the case of the DQPSK modulation we considered two variants: The
standard NRZ modulation technique which directly switches between different constellation
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points so that power transients occur, and a modulation format which maintains a constant
signal envelope (red curve in Fig. 7(f) for αH = 2 and αH = 4), so that power transients are
absent. The limiting EVM and the limiting power penalty are indicated by gray horizontal
lines. The intersections of the EVM or PP curves with these horizontals define the limiting
points for the IPDR.
Fig. 7. Simulations illustrate an IPDR advantage for SOA with αH = 2 over SOA with αH = 4, if
signals with advanced modulation format and large power transitions between the constellation
points are amplified. (a)-(c) EVM as a function of SOA input power for BPSK, QPSK and
16QAM signals (d)-(f) Power penalty as a function of SOA input power for OOK, DPSK and
DQPSK signals. The red curve in subfigure (f) assumes a constant-envelope modulation and
holds for both, αH = 2 and αH = 4. The IPDR is indicated by red arrows, and the corresponding
EVMlim and PP of 2 dB are shown by the gray horizontal lines.
The simulated IPDR for modulation techniques having power transitions between the
constellation points reduces from BPSK (2QAM) to QPSK (4QAM) to 16QAM, and from
DPSK to DQPSK. The IPDR difference for the SOAs with different alpha factors is largest
for the BPSK and the DPSK modulation format, which have the highest probability of large
power transition. The power penalty as a function of SOA input power for OOK signal shows,
as expected, no difference for the two SOA samples, Fig. 7(d). The results for constantenvelope DQPSK modulation exhibit a very low power penalty at high input powers, Fig.
7(f). This clearly demonstrates the strong influence of power transitions.
Table 2 summarizes the IPDR simulation results for both SOA types. The IPDR values are
obtained assuming a certain bit error ratio limit (gray horizontal lines in Fig. 7), and for a
specific evaluation method, i. e. PP or EVM. Further, the difference IPDR2 − IPDR4 of the
IPDRα for the devices with αH = 2 and with αH = 4 is specified.
These results show that:
• For amplifying phase encoded signals, low alpha-factor SOAs are preferable, see IPDR2
− IPDR4 in Table 2, e. g. rows “NRZ BPSK” and “QPSK”.
• The influence of the alpha factor on high-order M-ary QAM signals reduces
significantly, compare IPDR2 − IPDR4 values in Table 2 rows “NRZ BPSK”,
“QPSK” with “NRZ 16QAM”.
• As a general tendency the IPDR reduces for increasing complexity of the optical
modulation format: For a given average transmitter power the distance between
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constellation points reduces with their number, and the required OSNR increases.
This moves intersection point P1 in Fig. 6 to higher powers. On the other hand, if the
average power is increased to improve the OSNR, there is a larger risk of amplifier
saturation, so that high-power constellation points move closer together. This would
shift the intersection point P2 in Fig. 6 to lower powers.
• Long “1”-sequences of NRZ signals lead to a stronger carrier depletion than “1”sequences of RZ signals, if the carrier recovery time (100 ps) is in the order of the
pulse repetition rate (36 ps). This is the reason why in our case 50% RZ DQPSK
modulation leads to an IPDR which is about 14 dB larger than that for NRZ DQPSK,
Table 2.
Table 2. Devices with lower alpha factor show larger IPDR for modulation formats with
high probability of large power transitions. IPDR for various modulation formats for a
symbol rate of 28 GBd for two SOA devices only differing in the alpha factor are shown.
The evaluation method, i. e., PP or EVM and the corresponding BER limit are defined.
The results of the IPDR difference are also presented. The advantage of a low alphafactor device manifests in a large IPDR difference.
Format
−log10 BER
(PP, EVM)
IPDR Difference
IPDRα [dB]
αH = 2
αH = 4
IPDR2 − IPDR4 [dB]
33% RZ OOK
9 (PP)
19
19
0
NRZ DPSK
9 (PP)
~ 40
29
~11
NRZ DQPSK
9 (PP)
18
14
4
50% RZ DQPSK
9 (PP)
32
27
5
Const. Envelope DQPSK
9 (PP)
> 30
> 30
IPDR2,4 indistinguishable
NRZ BPSK (2QAM)
9 (EVM)
39
32
7
NRZ QPSK (4QAM)
9 (EVM)
31
26
5
NRZ 16QAM
3 (EVM)
14
13
1
4. Measurement results for 20 GBd BPSK, QPSK, and 16QAM signals
To verify the prediction from the simulations two SOA devices are tested with 20 GBd BPSK,
QPSK and 16QAM signals. Both SOA are very similar in terms of gain, noise figure,
saturation input power as well as dynamics. However, the devices differ in their alpha factors
since actually different structures are used, i. e. a bulk and a QD SOA. Here, we focus on the
measurement of SOAs amplifying non-differentially phase encoded data signals. In our
previous experimental work, results for the differently phase encoded data signals were
already presented [16]. All experiments have been performed with 20 GBd rather than 28
GBd due to limitations in our equipment.
4.1. QD and bulk SOA characteristics
For the study we selected devices with similar characteristics. We performed the experiments
with a 1.55 µm QD SOA (1 mm length with 6 layers of InAs/InP quantum dots) and a 1.55
µm low optical confinement (20%) bulk SOA (0.7 mm length) [33]. Both were operated at the
same current density. Figure 8(a) shows that FtF gain, FtF noise figure and in-fiber saturation
input powers are indeed comparable. The gain peak of both devices is around 1530 nm, and
the –3 dB bandwidth is 60 nm each. The phase change was measured with a frequency
resolved electro-absorption gating (FREAG) technique based on linear spectrograms [34] by
evaluating the cross-phase modulation seen on a weak (−15 dBm) cw probe signal in response
to a 42.7 Gbit/s ‘1010…’ sequence. The ‘1’-impulses are 8 ps wide and repeat at a period of
47 ps (duty cycle 17%). For this case, an average input power of + 7 dBm corresponds to a
peak input power + 15 dBm. Figure 8(b) shows the phase response of the QD and bulk SOA.
The bulk SOA shows 1.7 times higher phase changes than the QD SOA. Therefore, the ratio
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2
Q [dB]
FtF Gain [dB]
Power [nor.]
FtF Noise Figure [dB]
in
Psat
Phase Change [rad]
of the alpha factors is αH,bulk / αH,QD = 1.7. In Fig. 8(c) the signal quality (Q2) of a 42.7 Gbit/s
RZ OOK data signal with varying SOA input power is shown after amplification with the QD
and bulk SOA. The IPDR for the target Q2 factor of 15.6 dB is around 22 dB for both
amplifiers. From these findings we conclude that the devices are comparable with respect to
their gain recovery times, and that the overall performance only differs in their phase changes.
This fact enables a comparison for advanced modulation format signals in terms of the alpha
factor only.
Fig. 8. Comparison of QD and bulk SOA characteristics. (a) FtF gain, FtF noise figure and infiber saturation input powers for a 1.55 µm QD SOA (black) and bulk SOA (blue). For equal
current densities all characteristics are comparable. (b) Phase response (left vertical axis) in
relation to an 8 ps wide impulse (right vertical axis). The bulk SOA shows 1.7 times the peakto-peak phase change of the QD SOA. (c) Q2 factor for amplification of a 43 Gbit/s RZ OOK
data signal for different device input powers. Since the dynamic range (IPDR indicated by red
arrow, gray horizontal line is Q2 = 15.6 dB) of both SOA is almost identical, the device
performance differs only in the alpha factor.
4.2 Multi-format transmitter and coherent receiver
The IPDR for amplification of NRZ BPSK, NRZ QPSK and NRZ 16QAM data signals has
been studied by evaluating the EVM [32]. The experimental setup (Fig. 9) comprises a
software-defined multi-format transmitter [35] encoding the data onto the optical carrier at
1550 nm, the SOA and a coherent receiver (Agilent N4391A Optical Modulation Analyzer
(OMA)). The symbol rate is 20 GBd resulting in 20 Gbit/s BPSK, 40 Gbit/s QPSK and 80
Gbit/s 16QAM signals. The power of the signal is adjusted before launching it into the SOA.
After amplification, we analyze EVM as well as magnitude and phase errors. The OMA
receives, post-processes, and analyzes the constellations.
Fig. 9. Experimental setup, comprising a software-defined multi-format transmitter encoding
20 GBd BPSK, QPSK and 16 QAM signals onto an optical carrier. The signal power level is
adjusted before launching it to the QD or bulk SOA. The optical modulation analyzer receives,
post-processes, and analyzes the data.
4.3 Large IPDR with low alpha-factor SOAs for low-order QAM formats
In Fig. 10(a)-10(c) the EVM for the different modulation formats is depicted as a function of
the SOA input power. Figure 10(a) shows for BPSK modulation an IPDR exceeding 36 dB
with around 8 dB enhancement for the QD SOA compared to the bulk SOA. Figure 10(b)
shows for QPSK modulation an IPDR of 29 dB with an improvement of 4 dB for the QD
SOA. The IPDR for 16QAM is 13 dB, and shows no difference between both amplifier types,
Fig. 10(c).
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EVM [%]
EVM [%]
EVM [%]
Bulk
SOA
QD
SOA
Fig. 10. EVM for different modulation formats and two types of SOA versus input power. (a)
Low alpha-factor QD SOA shows an IPDR enhancement of 8 dB compared to bulk SOA for
BPSK modulation. In both cases the IPDR exceeds 36 dB. (b) IPDR enhancement at QPSK is
reduced, but still 4 dB. An IPDR of 29 dB is found. (c) No difference is found at 16QAM. The
IPDR for both devices is 13 dB. The BtB EVMs are indicated by the red dashed lines. The
IPDRs are shown by the red arrows, and the gray horizontal lines represent the EVMlim. (d)-(f)
Constellation diagrams for various SOA input powers which are associated with the respective
subfigure (a)-(c) immediately above. Bulk SOA (upper row) and QD SOA (lower row) are
compared.
In addition, in Fig. 10(d)-10(f) constellation diagrams for bulk SOA and QD SOA are
presented below the respective EVM subfigures for the three modulation formats, and for
three different input power levels. For low input powers the constellations points are
broadened by ASE noise. For optimum input powers the constellation points have almost BtB
quality. For large input powers the signal quality again reduces. Obviously, the limitation for
BPSK and QPSK stems from phase errors, whereas the limitation for the 16QAM signal
stems from both, amplitude and phase errors. The phase errors with the PSK formats are
larger for the bulk SOA than for the QD SOA.
It has already been shown that EVM is an appropriate metric to estimate the BER and
describe the signal quality of an optical channel limited by additive white Gaussian noise [32].
Here, the EVM is also used to estimate the BER if the signal quality is limited by nonlinear
distortions. In our experiments, the BER is measured for all formats around the upper input
power limit of the IPDR indicated by EVMlim. At theses input powers, BER values of about
8·10−10 for BPSK, 3·10−9 for QPSK and 1.4·10−3 for 16QAM are measured. Thus, the EVM is
used to obtain a reliable tendency of the IPDR.
To study the IPDR limitations for low and high input power levels, the magnitude and
phase errors (Fig. 11) relative to the BtB magnitude and phase values are evaluated. For low
input powers it is seen from Fig. 11(a)-11(c) that magnitude and phase errors decrease with
increasing input power. No difference can be seen between bulk and QD SOA. The behavior
of the SOA samples differs, however, for large input powers. For BPSK and QPSK encoded
signals the amplitude is virtually error-free, whereas the phase error significantly increases
with increasing input power. For the 16QAM signal, both, magnitude and phase errors
contribute to the EVM. In Section 2 the physical reasons leading to the measured results in
Fig. 11 were discussed in detail.
We compare experimental results with the outcome of a numerical model, which was
developed for a QD SOA. However, due to the admissible injection currents, we operate the
QD SOA in a region were the wetting layer can be depleted to some extent [28] such leading
to saturation effects and to a noticeable amplitude-phase coupling. The observable phase
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23 April 2012 / Vol. 20, No. 9 / OPTICS EXPRESS 9670
recovery times are long enough so that numerically and experimentally there is no difference
between QD and bulk SOA. What actually differs for physical devices, is the alpha factor, and
this is reflected in the experimental and the numerical outcome.
Bulk
0 QD
240 230 220 210 0 10
SOA Input Power [dBm]
10
Bulk
QD
5
0
240 230 220 210 0 10
SOA Input Power [dBm]
15
(c)
QPSK
10
5
Bulk
0 QD
240 230 220 210 0 10
SOA Input Power [dBm]
10
5
Bulk
QD
0
240 230 220 210 0 10
SOA Input Power [dBm]
∆ Magnitude Error [%]
5
15
15
∆ Phase Error [deg]
10
∆ Magnitude Error [%]
15
(b)
BPSK
∆ Phase Error [deg]
∆ Magnitude Error [%]
15
∆ Phase Error [deg]
(a)
15
16QAM
10
Bulk
5
QD
0
240 230 220 210 0 10
SOA Input Power [dBm]
10
Bulk
5
QD
0
240 230 220 210 0 10
SOA Input Power [dBm]
Fig. 11. Magnitude error and phase error increase as compared to BtB measurements. The
degradation for low input powers is due to OSNR limitations. The upper limit is due to phase
errors for (a) BPSK and (b) QPSK. Magnitude errors are insignificant. (c) At 16QAM the
phase error is accompanied by gain saturation inducing magnitude errors. The alpha-factor
impact decreases due to a lower probability for large power transitions.
In Table 3 the experimentally obtained results of the IPDR difference for both SOAs
(IPDRQDSOA − IPDRbulkSOA) are compared to the simulation result for various modulation
formats. The IPDR differences show good agreement between simulation and measurement
within a range of 1 dB. While from the FREAG measurements Fig. 8 only the ratio of alpha
factors for bulk and QD SOA could be extracted, the comparison of simulations with
experiments now allows to conclude also the absolute values 4 and 2, respectively.
We checked that the symbol rate difference between simulation and measurement is of
minor importance. Only for symbol rates larger than 35 GBd we found an increase of the
upper IPDR limit P2. The upper IPDR limit increases between 35 GBd (P2 = 10 dBm) and 45
GBd (P2 ~20 dBm) and it was tested with DPSK modulation and an alpha factor of 4.
Table 3. Comparison of measurement and simulation results for the difference of the
IPDR for ithe lower alpha-factor SOA and the higher alpha-factor SOA for various
modulation formats. The evaluation method, i. e. PP or EVM and the corresponding BER
limit are defined according to Section 3. Measurements and simulations show the same
tendency in spite of the fact that the symbol rate had to be reduced for the measurement
from 28 GBd (as assumed for the simulations) to 20 GBd due to limitations in the
available equipment. The pound character (#) indicates measured results for 28 GBd
NRZ DQPSK taken from our previous work [16].
Format
−log10 BER
IPDR Difference
(PP, EVM)
IPDRQDSOA − IPDRbulkSOA
[dB]
Measurement
NRZ DQPSK
9 (PP)
5#[16]
4
NRZ BPSK
9 (EVM)
8
7
NRZ QPSK
9 (EVM)
4
5
NRZ 16QAM
3 (EVM)
0
1
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IPDR2 –IPDR4
[dB]
Simulation
Received 22 Feb 2012; revised 9 Apr 2012; accepted 9 Apr 2012; published 12 Apr 2012
23 April 2012 / Vol. 20, No. 9 / OPTICS EXPRESS 9671
5. Conclusion
Semiconductor optical amplifiers have been studied as amplifiers for advanced modulation
formats. In particular we have studied the influence of the alpha factor on the amplification
process. It is found that low alpha-factor SOAs are advantageous for purely phase encoded
signals (BPSK, (D)QPSK). It is further found that an SOA with large alpha factor can be
successfully used to amplify M-ary signals with a large number of amplitude levels. This is
due to a lower probability for large power transitions in complex modulation formats which in
turn reduces the influence of gain changes and the associated phase errors.
Acknowledgments
This work was supported by the Center of Functional Nanostructures (CFN) of the German
Research Foundation (DFG), by the Karlsruhe School of Optics & Photonics (KSOP), by the
European project EURO-FOS, by the Karlsruhe Nano-Micro Facility (KNMF), the BMBF
project CONDOR, and the Agilent University Relations Program.
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23 April 2012 / Vol. 20, No. 9 / OPTICS EXPRESS 9672