Ethernet has evolved from a 10 Mbits/s technology tothe 100 Gbits/s standard that is currently being de-fined by the IEEE P802.3ba Task Force [1]. This re-cent update is in response to the constant need forincreased bandwidth applications, such as high per-formance computing, video on demand, and massivedata centers [2,3]. The update will be used mainly inmetropolitan area networks (MANs), where Ether-net characteristics such as ease of use, data support,and cost effectiveness are important considerations.For MAN applications, a single-mode fiber (SMF)link designed to reach up to 40km will be realizedas four wavelengths centered at 1302nm, each run-ning at a bit rate of 25.78 Gbits/s [4]. Externallymodulated lasers (EMLs) in a nonreturn-to-zero for-mat are used as transmitters, and a semiconductoroptical amplifier (SOA) that amplifies all channelssimultaneously is used to meet power budget re-quirements. The optical receiver then comprises
the preamplifier, the demultiplexer, and four opticalfront ends (OFEs) with corresponding electrical re-ceivers. Figure 1 presents the link setup.
Although the optical link has been designed for amaximum reach of 40km, it must be noted that theIEEE 802.3 standard does not specify a minimumlink length or span loss for a system. Moreover, itis common practice by operators to deploy the sametype of transceiver for interconnects of variouslengths. For example, at this time operators are de-ploying 40km transceivers for 10 Gbit Ethernet onlinks that are only a few kilometers or even a fewme-ters long. Therefore, correct operation of the systemis required at any fiber length up to 40km. Based onthis assumption, a numerical analysis to prove thetechnical feasibility and investigate the impact ofthe semiconductor optical preamplifier in the perfor-mance of the proposed (and similar) wavelengthdivision multiplexing (WDM) optical link has beenreported [5]. In particular, it was shown that, for fiberlengths shorter than approximately 15km, where theSOA input power is high, the preamplifier nonlinearresponse severely degrades the system performance.Moreover, under such high input power conditions,
OFE overloading becomes a limiting factor. Recently,a control scheme to alleviate this difficulty was pro-posed [6]. The solution consists in adjusting the cur-rent injected into the SOA according to the currentproduced by the photodiodes (i.e., the input opticalpower). Each photodiode is monitored independentlyto adjust the SOA gain such that all four OFEsreceive optimum power to closely achieve the desiredsystem performance level. According to the 802.3bastandard being defined, the maximum power differ-ence between any two channels cannot exceed 4 dB.It is expected that the control scheme will increasethe dynamic range of the overall receiver. Most prob-ably, it will be implemented in a microprocessor, in-tegrated together with the SOA, optical filters, andOFEs. The setup shown in Fig. 1 includes the gain-control system, which would, in principle, allow theintegrated receiver to operate at its optimum pointregardless of the fiber length used (within the0–40km interval). Therefore, we propose a numeri-cal analysis of the aforementioned proposal (to ourknowledge, never applied to this kind of system) toinvestigate the convenience and actual designmargins of the automatic gain-control (AGC) pream-plified optical receiver as part of the 100 Gbits/sEthernet (GbE) extended reach link architecture.The relevance of our analysis is clear from the impactthat the 100GbE standard is expected to have duringthe next decade as one of the most widely deployedhigh-speed transmission commercial products.In particular, we show that, by varying the current
injected into the SOA, the amplifier gain and satura-tion power can accordingly be modified. This proce-dure can be used to shift the dynamic range of anoptical receiver, comprising a SOA coupled with anOFE, to compensate variations in the fiber length (orlosses) of an optical link. Further, it will be shownthat, by using such a gain-controlled optical receiver,a maximum bit error rate (BER) of 1 × 10−12 can beachieved along each fiber length between 0 and40km for minimum and maximum transmitter out-put powers. Results for links operated with fixed-gain receivers are also presented for comparison.Automatic electronic gain control schemes have
been used in the past to compensate for low-frequency gain fluctuations in erbium-doped fiberamplifiers (EDFAs) [7] and, more recently, in hybrid
Raman–EDFAs [8] and SOAs [9]. The fluctuationsnormally come as a result of traffic bursts and opticalchannel add–drop, which can be reduced by auto-matically adjusting the EDFA pump power or SOAinjection current. Similar schemes have beensuccessfully demonstrated to enhance the input dy-namic range of cross-phase modulation-based wave-length converters [10,11]. AGC schemes, however,have not been directly applied (to our knowledge) toenhance the dynamic range of SOA preamplified re-ceivers in variable-link length transmission systems.This is due, perhaps, to the fact that AGC of the OFEtransimpedance electronic amplifier has tradition-ally been preferred [12,13].
In Section 2 we present the simulation details withcharacterization curves of the SOA and OFE. In Sec-tion 3 we analyze the performance of the preampli-fied receiver, and in Section 4 we show simulationsof the 100GbE link, demonstrating the advantage ofusing the AGC scheme. Our conclusions are given inSection 5.
2. Simulation Setup
The numerical analysis presented in this paper wascarried out with a sophisticated optical transmissionsystem simulator implemented in the graphic pro-gramming language known as LabVIEW [14,15].The main program consists of elaborate data struc-tures and hundreds of interconnected modules.Among them, it is worth mentioning four cwlasers centered at 1295.56, 1300.05, 1304.58, and1309:14nm, four electroabsorption modulators(EAMs) driven by four decorrelated, specially de-signed, pseudorandom bit test patterns, 512 bitslong, a MUX, a dispersive and nonlinear SMF, fourelectrical receivers with digital phase detectorsand eye monitors that are capable of finding the op-timum decision threshold based on the BER perfor-mance, a BER analyzer, and several display andmonitoring units. The implementation details of theaforementioned devices are omitted for brevity, withthe exception of the SOA, DEMUX, and four identicalindependent OFEs that comprise the preamplifiedreceiver. Simulation parameters are presented inTable 1.
The OFE is an optical receiver that consists of aphotodiode and a transimpedance amplifier (TIA).It has an optoelectronic 3dB bandwidth of 20GHzwith a fifth-order Bessel characteristic and a respon-sivity of 0:7A=W. The TIA has a conversion gain of800Ω with an input current noise density of18pA=
ffiffiffiffiffiffiffi
Hzp
. In contrast with more common simula-tion engines, our OFE model takes into account re-ceiver overload that is due to excessive inputoptical power. The simulated OFE characteristics(without the presence of the SOA and fiber) areshown in Fig. 2. The receiver sensitivity and overloadat a BER of 1 × 10−12 for the 25:78Gbits=s signal arecalculated as −10:3 and þ3dBm, respectively. Fol-lowing the 802.3ba objectives, the BER of 1 × 10−12
was taken as the error-free operating threshold. The
Fig. 1. Setup for the 4 × 25Gbits=s optical link. Tx (Rx) repre-sents electrical transmitter (receiver). The dotted lines indicateelectrical connections. The elements that comprise the optical re-ceiver are bounded by the dashed line.
horizontal line in Fig. 2 shows the optical power perchannel range received by the photodiode when thepresence of the SOA is omitted on the 100GbE sys-tem. Clearly, the preamplifier is a must to meet thepower budget of the system. Figure 2 also shows thateven with the use of a linear amplifier the photodiodeinput dynamic range is too narrow to fulfill the linkpower requirements.The optical DEMUX, similar to the MUX, has a
third-order Gaussian passband with 175GHzFWHM, 25dB cross talk, and an insertion loss of4:0dB that includes losses due to filtering, splicing,aging, accuracy, and interoperability. The MUX in-sertion loss was set to 2:5dB.The SOA implementation is based on an efficient
unidirectional time-domain model conceived to study
nonlinear pulse propagation and interaction within asemiconductor waveguide [16]. The model solution isbased on analytic integration of the photon densitypropagation equation along the longitudinal coordi-nate and numerical integration of the coupled rateequations that characterize the semiconductor mate-rial. The model equations not only capture interbandeffects but also the influence of carrier heating (CH)on the amplitude and phase of the electromagneticpropagating waveform. The model is suitable to de-scribe the dynamics of optical pulses having thewidth and power treated in this study. The genera-tion and amplification of the amplified spontaneousemission (ASE) is also included in the model. Most ofthe SOA parameters are shown in Table 1. Thesmall-signal gain (SSG) and output saturationpower, Pout
sat , are not shown because both parametersare assumed to be dependent on the injection cur-rent, which in turn varies according to the AGCscheme.
The amplifier model used in the current simula-tions has been designed for system-level simulations(as opposed to device-level simulations) in whicheach component or device is described with a simplebut efficient model to keep the computational timesof the entire system within reasonable limits.Although efficient, this SOA model does not containa functional relation between SSG and Pout
sat ,which are entered as independent parameters. Tocircumvent this limitation and therefore be able toinclude in our analysis the variation of Pout
sat that cor-relates to the variation of the SSG, we used a recentlyreported [17], more sophisticated, bulk SOA model.This SOA model allows describing the variation ofthese two parameters as a function of the injectedcurrent, thus numerically establishing their corre-spondence. By means of a lookup table we were thenable to match each value of the SSG with its corre-sponding Pout
sat value for a given current. The (SSG,Poutsat ) pairs were in turn used to feed the system level
SOA model. This procedure allowed us to run moreaccurate simulations without compromising the effi-ciency of the entire transmission system simulator.The (SSG, Pout
sat ) pairs used in the simulations are gra-phically displayed as a function of injection currentin Fig. 3. To produce this graph and to ensure a func-tional relation close to the experimental one, we firstemployed the SOA device-level simulator to fit sev-eral steady-state experimental curves reported in[18] for a 1mm long InGaAsP SOA. For this we usedmany of the extracted parameters already presentedin [18]. We then used the fitting parameters and thedevice-level simulator to write the correspondinglookup table.
The accuracy of the system-level SOA model usedin this work can be perceived by the simulated staticcharacterization curves presented in Fig. 4. It showsthe variation of the gain as a function of outputpower for three (SSG, Pout
sat ) pairs read out from Fig. 3.They are (23dB, 11:33dBm), (18dB, 5:0dBm), and(9dB, 0:22dBm). For low powers, the gain effectively
Fig. 2. (Color online) BER performance of the OFE as a functionof average input optical power. The sensitivity and overload pointsare highlighted. The horizontal line indicates the range of powersreceived by the photodiode in the 100GbE link when the SOA isnot present.
Table 1. Parameter Values Used in the Simulations
EML Parameters Value Units
Output OSNR 40 dBExtinction ratio 6 dBOutput power 0, +5 dBm3dB electro–optic bandwidth 25 GHzASE spectrum width 5 THzFiber parameters at 1310 nmDispersion coefficient D −0:20 ps/nm/kmDispersion slope S 0.090 ps=nm2=kmSlope of dispersion slope −6:8 × 10−5 ps=nm3=kmAttenuation coefficient 0.45 dB/kmEffective mode area 80 μm2
corresponds to the SSG parameter value. The 3dBoutput saturation power also coincides with the cor-responding parameter.The SOA model used for the simulations does not
take into account the variation of the noise figure(NF) as a function of the injected current. This ap-proximation is valid from middle-to-high values ofthe injected current. For example, in [19] a variationof less than 1dB in the NF of a 1mm long SOA isreported when the amplifier fiber-to-fiber gain variesfrom approximately 16 to 2dB because of an injectioncurrent reduction from 150 to 50mA; see Fig. 3(a) in[19]. Here we vary the gain from 23 to 9dB using in-jection currents above 60mA. The constant NF ap-proximation is thus valid. Moreover, variations ofthe NF are expected for low rather than high injec-tion currents, corresponding to modest gain values[19]. It will be shown that in the analyzed 100GbElink, low gain values are used for short link lengths(i.e., high optical power into the SOA). It has beenshown [5] that under these conditions the SOA ismainly affected by nonlinear effects, whereas the op-tical signal-to-noise (OSNR) degradation does not
play any appreciable role. Furthermore, for large in-cident signal powers, the NF is due mainly to signalASE beating, which produces an almost constantNF [20].
Finally, with regard to the spectral characteristicsof the SOA, it must be noted that the gain spectrumshould preferably be positioned such that the chan-nel plan lies on the long wavelength side of the SOAgain peak. There, the slope of the gain versus wave-length curve is negative, whereas the slope of the sa-turation power versus wavelength curve is positive.This results in more convenient values of Pout
sat. How-ever, this also produces an asymmetry of the gain andsaturation power observed by the WDM channels,with the shortest wavelength channel suffering fromthe highest gain and the lowest Pout
sat . In other words,the shortest wavelength channel is affected by ahigher amplifier saturation level as compared withthe longest wavelength channel. To this effect, it isimportant to point out that, because of the SOAmod-eling limitations, the amplifier gain (and NF) disper-sion is not taken into account in our simulations.Moreover, the noise power distribution of the ASE atthe EML output is considered practically uniformwithin the channel spectrum span (i.e., the sameOSNR for each channel). As a result of this shortcom-ing, the worst transmission characteristics, whichnormally would be observed at the shortest wave-length channel, are now expected to exist in thetwo central channels [21]. Therefore, our BER analy-sis was carried out on the demultiplexed channel cen-tered at 1300:05nm.
3. Preamplified Optical Receiver
Figure 5 shows the performance of the optical receiv-er that comprises the photodiode, DEMUX, and SOAfor three different values of SSG (and Pout
sat ). Graphs oflog(BER) versus average power injected into the SOAare depicted. All four channels contribute to the totalinput power. Figure 5 also shows that the sensitivityand overloading point at the BER of 1 × 10−12 shiftstoward lower values of the total optical power as thegain increases. This can be confirmed from Fig. 6,which shows the sensitivity and overload points asa function of SSG for the analyzed preamplified re-ceiver. Values of the SSG ranging from 9 to 23dBare presented. The receiver sensitivity curve showsa variation of slightly more than 10dB for a changeof 14dB in the SSG. The curve follows a quasilinearbehavior (in decibels), having a penalty of approxi-mately 0:7dB for a reduction of 1dB in the SSG.The variation of the overload curve is higher andamounts to approximately 18dB for the same SSGinterval, which is due to the steeper curve exhibitedby this phenomenon for high gain values. Indeed,when low gain values are utilized, the overload pointbarely varies, whereas for high gain values an in-crease of this parameter is accompanied by a consid-erable decrease of the required input power. Thisbehavior can be explained by considering gain sa-turation in the SOA and by bearing in mind that
Fig. 3. (Color online) Simulated SSG and output saturationpower as a function of injected current for a typical SOA. Data pro-duced with themodel reported in [17] fitted to experimental curvespresented in [18].
Fig. 4. Gain compression of the SOA as a function of outputpower for three values of the SSG: 23, 18, and 9 dB. The dashedlines show the 3dB gain compression that corresponds to 11.33,5.0, and 0.22 dBm, respectively.
the photodiode overload power is practically con-stant. When a high SSG is utilized the amplifier re-quires low input power to reach the photodiodeoverload point. The SOA can be assumed to operatewithin the linear regime and hence a variation in thegain requires a similar variation in the input power.In contrast, when a low SSG is used, a powerful inputsignal is required to reach the photodiode overloadpoint. Moreover, under these conditions, the SOA sa-turation power is lower (see Fig. 4). The SOA re-sponse is therefore nonlinear, and, consequently, avariation in the SSG requires a less severe variationof the input power to reach the same overload powerin the photodiode.Figure 6 is also useful to point out that the use of
SSG values above 23dB does not provide a markedimprovement in receiver performance because thedynamic range (difference between both curves inFig. 6) becomes shorter as the gain increases. Thatis, while the overload curve becomes steeper, the sen-sitivity curve tends to a constant value. Flattening ofthe sensitivity curve toward high SOA SSG valuescan be explained if one considers that, for high inputpowers into the SOA, a small reduction in the powerinjected into the SOA (i.e., a small increase of the sys-tem fiber length) can be compensated by correspond-
ingly increasing the SSG, so that the minimumpower required for proper operation of the OFE (sen-sitivity) can be recovered. For low input powers intothe amplifier, however, OSNR degradation inducedby the SOA becomes the main limiting factor affect-ing the OFE [5]. Compensation of this deleterious ef-fect cannot be achieved by increasing the SSG. Inother words, for low input powers, the overall sensi-tivity of the preamplified receiver remains practi-cally constant, regardless of SOA SSG variations.
Figure 5 also shows a horizontal line that repre-sents the total optical power range that is receivedat the SOA for the link and EML powers analyzed.It is shifted 10dB with respect to that depicted inFig. 2 because of the presence of three extra channels(6dB) and DEMUX losses. The information in Fig. 5makes it clear that there is no single SOA SSG valuethat provides a dynamic range wide enough to fit theinterval of received optical powers (i.e., the horizon-tal line). Figure 5 also shows, however, that by vary-ing the SOA SSG it is possible to cover a much widerrange of input powers. In other words, the simula-tions show that through the use of a gain-varying ele-ment it is possible to effectively enlarge the actualdynamic range of the preamplified optical receiver.In this way, error-free performance (BER of< 1 × 10−12) can always be attained regardless ofthe fiber length used (within 0 and 40km). Suchan improved dynamic range is also marked in Fig. 5for a SSG varying between 9 and 23dB. Actually, itcan be observed that a SSG variation from 23 to18dB suffices to attain error-free performance of thesystem. A natural result then is the proposal of anautomatic gain-controlled preamplified optical re-ceiver that not only increases the input power dy-namic range of the receiver but is also able to providea more uniform system performance along the re-quired fiber reach (0–40km). Finally, Fig. 5 pointsout that, given the relatively wide dynamic rangeof the receiver for a single SSG value, which variesfrom 10.4 to 22:8dB depending on the SSG (see alsoFig. 6), the AGC scheme is not necessarily required tobe accurate, thus leaving room for relatively ampledesign margins.
4. Gain-Controlled Preamplified Optical Receiver
To demonstrate the value proposition of the gain-controlled preamplified optical receiver, we now com-pare the BER performance as a function of fiberlength of the unamplified receiver (OFE only), theamplified receiver for an SOA SSG of 18dB, and theautomatic gain-controlled preamplified optical re-ceiver. EML output powers of 0 and þ5dBm werechosen because they practically correspond to theminimum and maximum values that are consideredfor the 100GbE standard [4]. The curves for the threesituations outlined above are presented in Figs. 7and 8 for 0 and þ5dBm, respectively. As expected,the unamplified case exhibits poor performance forfiber lengths above 3.9 and 15km, respectively. Theamplified situation with a SSG of 18 dB is
Fig. 5. (Color online) BER performance of the optical receiver(i.e., SOA, DEMUX, and OFE) as a function of average input op-tical power for three SOA gain values. The horizontal line indi-cates the power range received by the SOA in the 100GbE link.
Fig. 6. (Color online) Sensitivity and overload power of the opti-cal receiver at a BER of 1 × 10−12 as a function of SOA SSG.
acceptable for the analyzed fiber lengths when themaximum EML power is utilized (Fig. 8). Still, forshort fiber lengths the excessive gain overloads thephotodiode, but the BER performance is kept to with-in error-free margins. The situation differs when theminimum EML power is analyzed (Fig. 7). In thiscase the gain is not enough when long fiber lengthsare used, leading to poor BER performance (above1 × 10−12) for fiber lengths longer than 34km. In con-trast, the automatic gain-controlled optical receiverexhibits error-free performance along any fiberlength and for maximum and minimum EMLpowers. Moreover, uniform performance can beachieved through careful control of the SOA SSG(i.e., injected current). In this case, for the corre-sponding fiber length, we have calculated the opti-mum SSG necessary to achieve a constant BERperformance of 1 × 10−15, well below the maximum
requirements of 1 × 10−12. The resulting curves, as-suming an accurate control scheme, are shown inFigs. 7 and 8 (curves with triangles). The decreasein BER performance observed in Fig. 7 for fiberlengths longer than 35km is due to insufficient gainbecause we set 23dB as the maximum SOA gain forour analysis. Nonetheless, our simulations show thata gain of 23dB suffices to achieve a constant BER of1 × 10−12. The use of the AGC preamplified principlethus shows excellent performance regardless of fiberlength. Naturally, a less accurate control scheme willlead to similar curves with some variations aroundthe target BER value.
Figures 7 and 8 also present an extra curve (filledcircles) that shows the performance of the automaticgain-controlled optical receiver when, instead of aconstant BER value, the minimum BER for each fi-ber length is sought. According to our simulations,for short fiber lengths, BER values that are toolow to be of practical interest (and therefore not dis-played), can in principle be achieved. A relatively lowSSGmust be used in this case. For fiber lengths long-er than approximately 20 or 25km, a SSG valueabove 20dB is necessary to reach the minimumBER. Other optimization algorithms can also be im-plemented using the presented 100GbE simulator.Corresponding SSG versus fiber length tables canthen be produced for a desired target BER. Such ta-bles can then be fed into the microprocessor that isused to control the power injected into the SOA toattain the desired or optimum system behavior.
The SSG versus fiber length graphs necessary toachieve the constant BER of 1 × 10−15 (triangles) andthe minimum BER (filled circles) curves shown inFigs. 7 and 8 are presented in Figs. 9 and 10, respec-tively, for the two EML output powers analyzed (0and þ5dBm). To be consistent with the rest of ourcalculations, the gain was varied from 9 to 23dB.With respect to the constant BER curves, it can beobserved from Figs. 9 and 10 (triangles) that thereis a region between 22 and 28km (11.5 and 16:5km)for maximum (minimum) EML power, where the tar-get BER can be achieved with two different SSG va-lues. This comes from the fact that each BER versusreceived optical power curve exhibits a minimum.Therefore, for each value of the fiber length withinthis interval there are two curves, corresponding totwo different amplifier gain values, that intersecteach other at the BER of 1 × 10−15. Each curve hasa slope of different sign. The implementation of theAGC scheme should therefore be able to distinguishone solution curve from the other, depending on thefiber length of interest.
The implementation to seek theminimumBER va-lue is simpler since there is only one possible valuefor each fiber length (optical power into the receiver).For long fiber lengths the minimum BER is achievedfor the maximum SSG of 23dB. This is particularlyevident in Fig. 9 for an EML output power of 0dBm.For fiber lengths shorter than 20km, the SOA gaindecreases monotonically, finally reaching 16dB. In
Fig. 7. (Color online) BER performance of the 100GbE link as afunction of fiber length for an EML output power of 0dBm. Simu-lations carried out with an unamplified link (squares), using anSOAwith a fixed gain of 18dB (stars), using the AGC preamplifiedreceiver with a target BER of 1 × 10−15 (triangles), and using theAGC preamplified receiver for the minimumBER. The dashed lineindicates the error-free threshold.
Fig. 8. (Color online) BER performance of the 100GbE link as afunction of fiber length for an EML output power of þ5dBm. Si-mulations carried out with an unamplified link (squares), usinga SOA with a fixed gain of 18dB (stars), using the AGC pre-amplified receiver with a target BER of 1 × 10−15 (triangles) andusing the AGC preamplified receiver for the minimum BER.The dashed line indicates the error-free threshold.
this case, SSG values lower than 16dB are practi-cally unnecessary. When an EML output power ofþ5dBm is utilized (Fig. 10), the curve bends towardlower gain values for fiber lengths shorter than ap-proximately 30km. This occurs because now the op-tical power injected into the SOA is higher for thesame fiber length. A SOAwith a lower SSG is herebynecessary to achieve the minimum BER. The re-quired SOA gain then decreases as the fiber lengthbecomes shorter, reaching the minimum SSG valueof 9dB.Finally, it is worth mentioning that cross-channel
SOA nonlinearities (mainly cross-gain modulation)are not expected to have a considerable effect on thepreamplified optical receiver behavior. Therefore, thesimulation results presented here (which includemost of SOA nonlinear effects such as cross-gainmodulation and four-wave mixing) are valid evenwhen a difference in the EML output power amongall four channels is present. For low cross-gain mod-ulation, it is mainly the total power impinging intothe SOA that determines its nonlinear response.Since we have analyzed the extreme cases of all fourchannels emitted with minimum (0dBm) power and
all four channels emitted with maximum (þ5dBm)power, the results of a system with all four channelshaving different EML output powers merely reducesto an analysis carried out between the two alreadyinvestigated extreme cases.
5. Conclusion
We have presented a numerical investigation of theperformance of an automatic gain-controlled SOApreamplified receiver in a 4 × 25Gbits=sWDM trans-mission systemwith a fiber length varying between 0and 40km. The simulations were carried out with awell-tested optical transmission system simulatordeveloped in a graphic programming language thatcan be used to capture the nonlinear response ofthe SOA and overload phenomenon of the photo-diode. It is shown that the use of the optical gain-controlled scheme effectively increases the inputpower dynamic range of the optical receiver, thus al-lowing the transmission system to operate error freeat a target bit error rate value of 1 × 10−15 for prac-tically every fiber length used. This represents asignificant improvement over a link with similarcharacteristics operated with a conventional pre-amplified receiver of fixed gain and hence reduceddynamic range, which does not exhibit error-free per-formance for all required fiber lengths. This studyrepresents a contribution to a better understand-ing, from a practical standpoint, of the nonlinearinteraction observed in an optical preamplified re-ceiver at low and high input powers. It is also an aidfor the design of the extended reach link of next-generation high-speed Ethernet technology.
We are grateful to Chris Cole and Yuri Vandyshevfrom Finisar Corporation for their helpful dis-cussions and suggestions. R. Gutierrez-Castrejonacknowledges support from Dirección General deAsuntos del Personal Académico, UNAM, throughthe Programa de Apoyo a Proyectos de Investigacióne Innovación Tecnológica (PAPIIT) project,IN103008.
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