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
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 . 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 .
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 . 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 .
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-shift-keying 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.
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 , and by signal distortions due to gain saturation for large input powers . 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.
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 , 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 Δgff = Δ(ln Gff) / L = Δg of the FtF net modal gain is identical to a change Δg of the net modal gain leading to a change Δneff 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 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
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 small-signal 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 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.
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 , which is defined with the inversion factor nsp and the single-pass chip gain G24]). 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 by1,25].
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 IQ-modulator. 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 I-channel 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.
The SOA is modeled following the approach in [26–30]. The model describes a quantum-dot (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.
The SOA model parameters are shown in Table 1 . The SOA model has been described in . 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.
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,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 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,32].
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 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.
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 constant-envelope 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 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.
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 . 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) . 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  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 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.
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 . The experimental setup (Fig. 9 ) comprises a software-defined multi-format transmitter  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.
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).
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 . 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  such leading to saturation effects and to a noticeable amplitude-phase coupling. The observable phase 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.
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.
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.
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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