Laser optimisation for dispersion supportedtransmission systems

J.A.P. Morgado and A.V.T. Cartaxo

Abstract: Ideal single-mode laser intrinsic parameters that optimise the performance of dispersionsupported transmission (DST) systems are investigated. Laser parameter optimisation is performedto accomplish two goals: maximising the back-to-back sensitivity (BBS) and the total dispersiontolerance (TDT), with fixed laser bias and modulation currents, thus avoiding the usual DST lasercurrent tailoring to the fibre length. Extensive numerical simulations reveal that significantimprovement of DST system performance can be achieved by optimising simultaneous,independently and without restrictions, four laser intrinsic parameters; namely, linewidthenhancement factor (a), photon lifetime, gain parameter and gain compression factor (1). Theoptimised laser shows good robustness of BBS and TDT to variations of those laser intrinsicparameters and a remarkable improvement in BBS and the TDT in comparison with the non-optimised DST system is achieved. It is shown that, to achieve the best DST performance at20 Gbit/s using fixed laser currents, lasers with low a (a < 0.8) and high 1 (1 < 10 £ 10223 m3)are required. The physical feasibility of the optimal laser intrinsic parameters is discussed from thestandpoint of current laser technology. It is shown that a suboptimal set of laser intrinsic parametersconsistent with strained multi-quantum well laser technology gives improved system performance.

1 Introduction

The use of directly modulated lasers (DMLs) as transmittersources has been proposed for optical transmission systems,due to their low cost, small size, low driving voltage andhigh output power when compared, with other transmittersusing external modulation schemes [1, 2]. However, DMLsexhibit the unwanted characteristics of frequency modu-lation (FM, chirp) in which the instantaneous opticalfrequency varies with time over the duration of theindividual bit pulses [3, 4]. In general, laser FM acts tobroaden the spectrum of the signal, and it can impose systemlimitations with regard to the maximum transmissiondistance due to fibre dispersion. The dispersion supportedtransmission (DST) technique has been proposed to achieveoptical transmission beyond the conventional dispersionlimit, by using a suitable combination of laser FM tointensity modulation (IM) conversion in dispersive opticalfibres with appropriate receiver electrical filtering [5, 6].Several experiments have demonstrated the practicalfeasibility of this technique as well as its excellent potentialcapabilities in field trials [6, 7]. However, in spite of itssimplicity and reliability [5, 6], as well as the improvementsthat have been proposed such as laser parameter optimis-ation [8], several drawbacks related to this technique havebeen indicated, namely the need to tailor the laser drivercurrent to the span length to tune the FM depth [6, 9] andthe need to optimise the cut-off frequency of the electrical

equaliser in order to reduce the sensitivity degradation fora given transmission dispersion [6].

Three regions have been identified in the operation ofDST systems [10]. One, which is dominated by laser IM,is located around the zero total dispersion, for positive(anomalous propagation regime) and negative (normalpropagation regime) dispersion. This region is designatedthe IM region. The other two regions are located to the right(positive total dispersion) and to the left of the IM region(negative total dispersion) and are dominated by DST.In [10], we call these regions respectively, positive-DST andnegative-DST regions. These regions are characterised by acombination of frequency shift keying modulation andresidual IM. It has been shown that the laser transient chirpcan have a tremendous impact on the DST systemperformance, mainly in the IM region [10]. In fact, in thisregion and in an anomalous propagation regime, a reductionof sensitivity exceeding 6 dB due to transient chirp has beenobserved [10]. On the other hand, in a normal propagationregime, the transient chirp can improve the systemsensitivity by about 5 dB [10]. In positive-DST andnegative-DST regions, the system performance is mainlyimpaired by the interaction of large fibre dispersion andlarge laser FM deviation or, in the case of reduced FMdeviation, by low extinction ratio.

These impairments are the main reason for the reductionof dispersion tolerance [10] and their effects should beproperly reduced. As a consequence, laser parameters thataffect both laser IM and FM responses should be taken intoaccount in laser optimisation for use in DST systems. Westress that only laser FM characteristics have beenconsidered in the laser optimisation presented in [8].

This work has two objectives. The first is to find an idealset of improved laser parameters so that, for the same laserbias and modulation currents regardless of total fibredispersion, maximisation of the back-to-back sensitivity(BBS) and of the total dispersion tolerance (TDT) areachieved. The ideal laser parameters are obtained with no

q IEE, 2005

IEE Proceedings online no. 20055043

doi: 10.1049/ip-opt:20055043

The authors are with the Optical Communications Group, Instituto deTelecomunicacoes, Department of Electrical and Computers Engineering,Instituto Superior Tecnico, Av. Rovisco Pais, 1049-001 Lisboa, Portugal

E-mail: j.morgado@lx.it.pt

Paper received 20th August 2004

IEE Proc.-Optoelectron., Vol. 152, No. 1, February 2005 49

restrictions due to, for instances, current laser technologylimitations. Thus we derive the best performance achievableby DST. The second objective is to examine and discuss, inthe light of current laser technology, the joint physicalfeasibility of the ideal laser intrinsic parameters. Theimpairments resulting from laser technology limitationsare assessed. Using these results, guiding principles for laserDST technology are outlined.

An optimisation approach similar to one used in [11],where optimisation of an uncooled directly modulatedlaser operating at 10 Gbit/s for metropolitan area net-works utilising negative dispersion fibres has beenperformed, will be used. Nevertheless, two majordifferences can be found in this work; the existence ofan electrical equaliser in the receiver, and both positiveand negative dispersions are considered. This will lead todifferent main conclusions about the optimal lasercharacteristics.

2 System description and performanceassessment

The DST system described in [10] is considered in ouranalysis, with minor changes described in the following.The binary DST system operates at B ¼ 20Gbit=s and usesa multi-quantum well-distributed feedback (MQW–DFB)single-mode laser. In order to assess the limitations imposedby the intrinsic laser dynamics on laser optimisation, laserparasitics and the ‘non-rectangular’ waveform of the sourcecurrent are neglected. The driver input current is defined byits average value [Note 1], the bias current Ib; and by theamplitude of the modulation current, Ip: the logical level ‘1’corresponds to I1 ¼ Ib þ Ip and the logical level ‘0’corresponds to I0 ¼ Ib � Ip: In the following, the definitionused for the extinction ratio is rext ¼ P1=P0 with P1 and P0

the stationary optical powers corresponding, respectively, tological levels ‘1’ and ‘0’.

From these definitions, assuming the eye diagram at thetransmitter output is completely opened, the extinction ratiocan be written as

rext ¼ ðIb þ Ip � IthÞ=ðIb � Ip � IthÞ ð1Þ

with Ith the laser threshold current.The single-mode laser dynamics is described by the

following three rate equations for the carrier density, N(t),photon density in the active region, S(t), and phase of theoptical field emitted by the laser, fðtÞ [3, 4]

dNðtÞdt

¼ �iIðtÞe �Vact

� RðNÞ � gðN; SÞ � SðtÞdSðtÞ

dt¼ GgðN; SÞ � SðtÞ � SðtÞ

tpþ RSðNÞ

dfðtÞdt

¼ aGg0

2½NðtÞ � �NN�

8>><>>:

ð2Þ

where I(t) is the injection current, �i is the internal quantumefficiency, e is the electronic charge, G is the opticalconfinement factor, tp is the photon lifetime, a is thelinewidth enhancement factor and �NN is the carrier densitycorresponding to Ib. R(N) is the recombination rate givenby RðNÞ ¼ AnrNðtÞ þ BrN

2ðtÞ þ CnrN3ðtÞ where Anr is the

non-radiative recombination coefficient, Br is the radiativerecombination rate and Cnr is the Auger recombinationcoefficient. The photon density dependence of the opticalgain is given by gðN; SÞ ¼ gðNÞ=ð1 þ eSÞ where e is thegain compression factor and a logarithmic carrier density

dependent gain (material gain) g(N) is assumed [12] and canbe written as [13]

gðNÞ ¼ gc � ln½RðNÞ=RðN0Þ� ð3Þ

where gc is the gain parameter, and N0 is the transparencycarrier density. RsðNÞ is the spontaneous emission ratedefined by RsðNÞ ¼ GbBrN

2 where the parameter b isreferred to as the spontaneous emission factor. Thedifferential gain is given by

g0 ¼ dgðNÞdN

����N¼ �NN

¼ ðgc � teÞ=ð �NN � tnÞ ð4Þ

where te is the carrier-recombination rate given by te ¼1=ðAnr þ Br � N þ Cnr � N2ÞjN¼ �NN and tn is the differentialcarrier lifetime given by tn ¼ 1=ðAnr þ 2Br � N þ 3Cnr �N2ÞjN¼ �NN : Laser intrinsic parameters and their values aresummarised in Table 1.

Although the laser model described so far is one of thesimplest possible mathematical descriptions of single-modelaser diodes, important DFB laser properties of directlymodulated lasers concerning the transmission systemperformance assessment, such as power overshoot, relax-ation oscillations, damping, and wavelength chirp, can bedescribed satisfactorily [2, 3]. In addition, its numericalimplementation is much more time efficient than other moreaccurate DBF laser models, based on transfer-matrixanalysis [4, 14, 15], namely in an optimisation context.Except for the carrier density dependent gain model, thislaser model has been accepted as satisfactorily valid for aDFB laser and a MQW–DFB laser in which the carriertransport effects are negligible [13].

We stress that the laser rate equations (2) assume uniformintensity and carrier distribution inside the laser cavity,therefore excluding from the optimisation, DFB lasersstructures with high spatial inhomogeneities due tolongitudinal carrier spatial-hole burning (SHB) [3, 16], orlaser structures where the transient time of the opticalwaveguide within the laser cavity is important totheir modulation characteristics, like mode-locked lasers[14, 17].

Table 1: Summary of laser parameters

Parameter Description Value

� Operating wavelength 1550.2 nm

N0 Carrier density at transparency 1:7 � 1024 m�3

Vact Quantum wells volume 29:2 � 10�18 m3

G Optical confinement factor 0.13

�i Internal quantum efficiency 1

� Differential quantum

efficiency per facet 0.139

gc Gain parameter variable

" Gain compression factor variable

�p Photon lifetime variable

� Linewidth enhancement factor variable

Spontaneous emission factor 2:5 � 10�5

Anr Non-radiative recombination

coefficient 5 � 107s�1

Br Radiative recombination

coefficient 4:6 � 10�16 m3=s

Cnr Auger recombination

coefficient 1:08 � 10�41 m6=sNote 1: In the following the laser average current is designated by laser biascurrent.

IEE Proc.-Optoelectron., Vol. 152, No. 1, February 200550

The transmission over the optical fibre and the receiverare modelled as described in [10]. In the receiver, a first-order equaliser whose �3 dB reference bandwidth is givenby [6, 10]

fref ¼c

2pjDLjl2EFMðIb � IthÞð5Þ

is used. In (5), c is the velocity of light in vacuum, DL isthe total dispersion, l is the operating wavelength and EFM

is the laser FM efficiency. Since the optimised �3 dBbandwidth depends on the total fibre dispersion and to avoidlong computation time, the ratio between the �3 dBbandwidth used in the optimisation procedure and thatgiven by (5) is assumed the same as that presented in [10].The impact of optimising the �3 dB equaliser bandwidth onthe system performance will be discussed in Section 4.3.

A semi-analytical method has been used in the perform-ance evaluation [10]. The bit error ratio (BER) is calculatedutilising the exhaustive Gaussian approximation methoddescribed in [10].

3 Problem statement

The objective of laser parameters optimisation is to achievetwo system performance goals. The first one consists inmaximising the BBS. The second one consists in maximisingthe TDT keeping the same laser bias and modulation currentsindependently of the fibre dispersion. Figure 1 shows thepower penalty due to fibre transmission against totaldispersion for a BER of 10�12 for the laser parametersconsidered in [10], and the target performance. The TDTrange is defined as the range of total dispersion for which thepower penalty due to transmission does not exceed 3 dB.

As a first guess, the optimisation of system performanceshould be accomplished with respect to all laser parameters.Nevertheless, for a matter of optimisation feasibility, and toobtain a set of acceptable laser intrinsic parameters and gaininsight to the physical reasons originating the impairments,the optimisation must be carried out as a function of areduced number of laser parameters. All the others shouldremain unchanged throughout the optimisation procedure.The laser intrinsic parameters selected to perform laseroptimisation for use in DST systems should control the laserIM and FM responses, for the reasons presented in Section1. This set of parameters should allow independent controlof the two laser responses, so that all possible laser IM andFM response combinations can be assessed during theoptimisation. However, most laser parameters affectsimultaneously both the IM and FM responses.

The theoretical reasoning presented in [11] points out thata; tp; gc and e allow control of the laser IM and FM responsesand may optimise effectively the single-mode laser.Extensive simulations have revealed that this conclusionholds also for laser optimisation in DST systems. Resultsshow that good trade-off between the two goals of laseroptimisation occurs close to a ¼ 0:8; tp ¼ 3 ps; gc ¼6:5 1012 s�1 and e ¼ 10 10�23 m3: For these laserintrinsic parameters, a laser threshold current of Ith �10mA; typical for MQW–DFB lasers [18, 19], is achieved.Bias and modulation currents of Ib ¼ 60mA and Ip ¼ 35mAhave been chosen initially, corresponding [from (1)] to rext ¼5:7: In this way, low rext is achieved in order to have low lasertransient chirp, reducing, therefore, the performance degra-dation at short distances in the anomalous dispersion regime.On the other hand, the BBS is not seriously penalised becauserext is still large. The impact of choosing other laser currentson system performance will be discussed in Section 4.2.

Laser optimisation has been investigated in depth for thefollowing range of parameters:

0:6 � a � 1 ð7Þ2 ps � tp � 4 ps ð8Þ

4 1012 s�1 � gc � 9 1012 s�1 ð9Þ

9 10�23 m3 � e � 11 10�23 m3 ð10ÞSince the objective in this part of the work is to find the idealset of laser intrinsic parameters that optimise the DSTperformance, we stress that no restrictions imposed by theinterdependence between a; tp; gc and e; as well as betweenthese parameters and the remaining ones, are considered.Thus, all those parameters are assumed easily controllableand will be varied independently without restrictions in theregions (7)–(10). With this assumption, the best theoreticalperformance of DST system is assessed. We stress that, inother work [20, 21], similar procedures have been reportedfor laser optimisation. In Section 5, the physical feasibilityof the resulting ideal set of laser parameters will bediscussed in the light of current technology.

4 Numerical results and discussion

4.1 Laser optimisation

This section presents the final results of system optimis-ation. First, the BBS is assessed for several tp values in theregion given by (8). Other variable laser intrinsic parametersare those given in regions (9) and (10). Since back-to-backoperation is assumed, no dependence on a exists. Figure 2shows the BBS for three different values of tp [(a) tp ¼ 2 ps;(b) tp ¼ 3 ps and (c) tp ¼ 4 ps]. These results show that thesensitivity is almost independent of tp: Therefore, theoptimisation of tp should rely only on the TDT. Figure 2shows also that the BBS improves strongly with increasinggc due to the wider IM bandwidth, leading to improvementin the opening of the eye diagram of the signal atthe decision circuit input. Figures 2b (b1) and 2b (b2)show back-to-back eye diagrams corresponding, respect-ively, to tp ¼ 3 ps; e ¼ 9:75 10�23 m3; gc ¼ 4 1012 s�1

and tp ¼ 3 ps; e ¼ 9:75 10�23 m3; gc ¼ 9 1012 s�1: Thenormalised eye openings of these sets of parameters are,respectively, 0.49 and 0.94. On the other hand, the BBSdegrades with increasing e due to a damped laser IMresponse. Nevertheless, this degradation is not so pro-nounced as that associated with the reduction of gc:

To perform tp optimisation, a is set in the middle of theregion defined by (7), and tp is varied within the region

Fig. 1 Power penalty against total dispersion for laser withparameters as [10], and target DST performance

IEE Proc.-Optoelectron., Vol. 152, No. 1, February 2005 51

defined by (8). Figure 3 shows the TDT for (a) tp ¼ 2 ps;(b) tp ¼ 3 ps and (c) tp ¼ 4 ps in the regions defined by (9)and (10), considering a ¼ 0:8: The results of Fig. 3 showthat the optimum tp is 3 ps because higher TDT is obtainedin the regions defined by (9) and (10).

In the following, optimisation of a is performed using thesame approach as for tp; with tp ¼ 3 ps: The value of a variesinside the region defined by (7). Figure 4 shows the TDT for

(a) a ¼ 0:6 and (b) a ¼ 1 in the regions defined by (9) and(10), considering tp ¼ 3 ps: The TDT for a ¼ 0:8 has alreadybeen shown in Fig. 3b. The results of Fig. 4 show that theoptimum a is 0.8, for which higher TDT is obtained. Weemphasise that, for a ¼ 0:6; higher TDT can be found, but foronly values of e and gc leading to a degradation in BBS ofalmost 3 dB (Fig. 2b). Additionally, these values were found ina very restricted zone, when compared with the case a ¼ 0:8:

The results of laser optimisation presented so far for theTDT have considered only discrete values of a and tp:

Fig. 2 BBS (dBm) for different values of photon lifetime

a tp ¼ 2 psb tp ¼ 3 ps ( - sub-optimum e ¼ 9:75 10�23 m3; gc ¼ 8 1012 s�1)c tp ¼ 4 ps

Eye diagrams in back-to-back at decision circuit for tp ¼ 3 ps;

e ¼ 9:75 10�23 m3 (b1) gc ¼ 4 1012 s�1 and (b2) gc ¼ 9 1012 s�1

Fig. 3 TDT ðps=nmÞ for a ¼ 0:8 and different values of photonlifetime

a tp ¼ 2 psb tp ¼ 3 ps ( - sub-optimum e ¼ 9:75 10�23 m3; gc ¼ 8 1012 s�1)c tp ¼ 4 ps

IEE Proc.-Optoelectron., Vol. 152, No. 1, February 200552

To determine whether further improvement of TDT can beachieved by choosing other a and tp; TDT was computedfor the regions 0:6 � a � 1 and 1 ps � tp � 4 ps; keepinge ¼ 9:75 10�23 m3 and gc ¼ 8 1012 s�1: Figure 5 showsthe results obtained and reveals that the optimal region forlaser intrinsic parameters (the OLIP) is given by a ¼ 0:8;tp ¼ 2:5 ps; e ¼ 9:75 10�23 m3 and gc ¼ 8 1012 s�1:

With these values, Ith; BBS and TDT are about 10.1 mA,�26:6 dBm and 1460 ps=nm; respectively. Comparison ofFigs. 3a and 3b reveals that no substantial improvementscan be obtained by optimising further gc and e; becausethese figures correspond to tp ¼ 2 ps and tp ¼ 3 ps andsimilar TDT is obtained in the optimum region of theparameters.

The TDT obtained corresponds to a remarkable perform-ance improvement relative to the one reported in [10], whichis about 800 ps=nm (Fig. 1). Furthermore, a dispersiontolerance of 900 ps=nm in the anomalous dispersionpropagation regime was achieved, which is similar to theone reported in a practical experiment [7]. Additionally,the BBS is much improved compared with the �17:8 dBm(for a BER of 10�9) reported in [7]. We stress that in ourwork, fixed laser bias and modulation currents are used,which was not the case for [10] and [7], where the drivercurrents were tailored to fibre dispersion to optimise systemperformance.

4.2 Impact of laser currents optimisation onsystem performance

After optimising the laser intrinsic parameters for theprescribed current levels, the question of further performanceoptimisation by adjustment of the laser currents still remains.This point is very important because, when assessing anysignificant improvement for other laser currents, the OLIP forthe new laser currents can be significantly different from theone achieved in Section 4.1. Figure 6 shows TDT and theBBS versus Ib; at the OLIP achieved in Section 4.1. Ip waschosen to set a current of 95 mA for logic level ‘1’. Steps of1 mA have been considered in this analysis. These resultsreveal that Ib ¼ 60mA and Ip ¼ 35mA gives an excellentcompromise between BBS and TDT. In fact, Ib lower than60 mA, although improving the BBS, lead to a strongreduction of the TDT. This is due to the increase in rext;whichincreases laser transient chirp, causing a power penaltyexceeding 3 dB in the anomalous IM region. On the otherhand, increasing Ib above 60 mA, although improving theTDT, strongly decreases the BBS. This is mostly due to thereduction in rext; which increases the power penalty. Theseresults allow one to conclude that no substantial performanceimprovement is obtained for other laser currents.

4.3 Impact of equaliser bandwidthoptimisation on system performance

The arguments concerning the need to assess the impact oflaser current optimisation also hold for equaliser bandwidth

Fig. 4 TDT (ps/nm) for tp ¼ 3 ps and different values oflinewidth enhancement factor

a a ¼ 0:6b a ¼ 1

Fig. 5 TDT (ps/nm)

e ¼ 9:75 10�23 m3 and gc ¼ 8 1012 s�1 ( - optimum a ¼ 0:8;tp ¼ 2:5 ps)

Fig. 6 (a) TDT and (b) BBS versus laser bias current, for laser withintrinsic parameters a ¼ 0:8; tp ¼ 2:5 ps; e ¼ 9:75 10�23 m3;gc ¼ 8 1012 s�1: The modulation current has been chosen in orderto have a current of 95 mA corresponding to logical level ‘1’

IEE Proc.-Optoelectron., Vol. 152, No. 1, February 2005 53

optimisation. Figure 7 shows system sensitivity versus totaldispersion for the OLIP achieved in Section 4.1. Curve (a)assumes that the ratio between the �3 dB bandwidth of theequaliser and that given by (5) is equal to that of [10]. Curve(b) considers the optimised �3 dB bandwidth of theequaliser. These results reveal that sensitivity improvementsnot exceeding 0.5 dB are achieved by optimising theequaliser �3 dB bandwidth for all fibre dispersions, exceptfor �470 ps=nm; where 1 dB is observed [Note 2].

These results and those of Section 4.2 show that nofurther improvement is achieved by choosing drivercurrents and equaliser �3 dB bandwidths other than thoseused in Section 4.1.

5 Analysis of the OLIP from the standpoint ofjoint physical feasibility

Over the last decade, single-mode semiconductor lasertechnology has developed a large set of techniques toimprove the performance of MQW–DFB lasers for directlymodulated long-wavelength ð1:55 mmÞ optical fibre tele-communications, allowing achievement of a very broadrange of combinations of laser intrinsic parameters [3, 4, 17,22–25]. To discuss the physical feasibility of the OLIP, it isnecessary to determine which of these improvementtechniques can achieve simultaneously such parameters,particularly low a and high e; in a consistent way with otherlaser intrinsic parameters.

It has been shown both theoretically and experimentallythat strained (tensile and compressive) multiple quantumwell (S-MQW) laser technology gives lowest a and high e;[17, 23, 26–33]. Therefore, the physical feasibility of theOLIP is discussed assuming the use of this laser technology.

In spite of some theoretical studies foreseeing thepossibility of achieving a 1 using S-MQW lasertechnology [17, 25–28], for the time being, the optimuma ¼ 0:8 seems not to be physically feasible using current S-MQW laser technology. To the authors’ knowledge, a � 1is the lowest experimental value reported hitherto concern-ing S-MQW lasers emitting at 1:55 mm [29, 30]. However,among the experimental a values reported in [29, 30] a ¼

1:1 is the lowest for which further information required toassess the change in the real part of the refractive index as aresult of a change in the carrier density ðdnr=dNÞ and thedifferential gain g0; is presented. (See the informationindicated in [30] regarding the laser there designated as laserB.) This information is crucial to get a set of simultaneouslyphysically feasible laser parameters. From the experimentalresults indicated in [30], corresponding to a ¼ 1:1; weobtain: dnr=dN � 3:2 10�26 m3 and differential gainnormalised by group velocity ðg0

0 ¼ g0=vgÞ of g00 � 23:6

10�20 m2: To determine vg; a typical value of the groupeffective index for 1:55 mm S-MQW-DFB lasers of ng ¼ 3:2[14] is assumed. These values are obtained using theexpression for the KIM-factor given by KIM ¼ 4p2ðtp þe=g0Þ [4], and the relationship between a and g0

0 givenby a ¼ ð4p=lÞ � ðdnr=dNÞ=g0

0 [4]. Some theoretical studies[28, 34] considered also dnr=dN values for S-MQW lasersmaterials similar to the previous one.

To determine the best system performance under the

condition a ¼ 1:1; the optimisation of e and tp was

performed considering dnr=dN � 3:2 10�26 m3 andg0

0 � 23:6 10�20 m2: Figure 8 shows the TDT achievedfor a ¼ 1:1; in the ranges 1:5 ps � tp � 3:5 ps and 6:5 10�23 m3 � e � 9 10�23 m3; assuming Ib ¼ 60mA andIp ¼ 35mA: The inset of Fig. 8 shows the correspondingBBS. The results of this sub-optimisation allow one toconclude that the optimal laser intrinsic parameterswith restrictions (OLIP-restricted) are a ¼ 1:1; tp ¼ 3 ps;e ¼ 7:25 10�23 m3; and gc ¼ 20 1012 s�1 for Ib ¼60mA and Ip ¼ 35mA; resulting in g0

0 ¼ 23:5 10�20 m2;Ith ¼ 8mA; BBS ¼ �26:5 dBm and TDT ¼ 900 ps=nm:A strong reduction of about 600 ps=nm in TDT, relative tothe optimum one, is observed. Nevertheless, improvementsin TDT and BBS of about 100 ps=nm and 1.5 dB,respectively, relative to the non-optimised DST system,are achieved, with the additional advantage of fixed lasercurrents.

To discuss the simultaneous physical feasibility of theOLIP-restricted, the arguments considered in [20] toperform the laser bandwidth optimisation of a strainedquantum well laser are followed. In [20] it is shown that theappropriate choice of S-MQW laser technology featuresallows to set independently the parameters tp; e and g0:From the photon lifetime relationship given by [4, p. 39]

Fig. 7 Sensitivity against total dispersion for laser with intrinsicparameters a ¼ 0:8; tp ¼ 2:5 ps; e ¼ 9:75 10�23 m3; gc ¼ 8 1012 s�1

a Ratio between �3 dB bandwidth of equaliser and that given by (5), equalto the one presented in [10]b �3 dB bandwidth of optimised equaliser

Fig. 8 TDT (ps/nm) for a ¼ 1:1; tp ¼ 3 ps ( - optimum withrestrictions e ¼ 7:25 10�23 m3; gc ¼ 20 1012 s�1); and insetsBBS (dBm) for tp ¼ 3 ps ( - optimum with restrictions e ¼7:25 10�23 m3; gc ¼ 20 1012 s�1)

Note 2: This difference of 1 dB is mainly due to the rough bandwidthestimate presented in [10] and not to the actual improvement obtained byoptimisation of the �3 dB bandwidth of the equaliser.

IEE Proc.-Optoelectron., Vol. 152, No. 1, February 200554

tp ¼ 1

ðc=ngÞfai þ ð1=LcavÞ � ln½1=ðr1r2Þ�gð11Þ

it is possible to adjust the laser cavity length Lcav or the facetfield reflectivities r1 and r2; to set tp independently of theother laser intrinsic parameters. Assuming an intrinsic lossby unit length of ai � 10 cm�1 [22, pp. 440], r1 � r2 ¼ 0:35;and Lcav ¼ 390 mm; results tp ¼ 3 ps: All these are typicalvalues indicated for S-MQW lasers [20].

For the OLIP-restricted, KIM ¼ 0:25 ns is obtained. Thisfig. has been reported for S-MQW lasers in [33, 35]. Thissuggests that the relation (e=g0) is physically feasiblesimultaneously with tp ¼ 3 ps; using S-MQW lasers.References [30–33] indicate that the gain compressioncan be strongly enhanced in the presence of strain,originating experimental e much larger than in bulkmaterials. References [30, 33] indicate values of e in therange of 4–10 10�17 cm3 using S-MQW lasers. Noticethat a e parameter of 9:56 10�23 m3 is presented in [30] forthe laser with a ¼ 1:1: Since this value is close to the sub-optimal value of e it seems that it will be physically feasible.This procedure ensures that the OLIP-restricted a; gc; tp ande are jointly physically feasible.

To discuss the physical feasibility of the OLIP-restrictedwith the remaining laser intrinsic parameters of Table 1, themain laser extrinsic parameters were assessed, namely: Ith;the �3 dB IM bandwidth ð f�3dBÞ; the damping ratio of theIM response ðÞ and EFM: Values within feasible rangesreported for S-MQW DFB laser technology were attained:Ith � 8mA (values in the range 6mA � Ith � 15mA werereported in [18, 19]), f�3dB � 27:6GHz for Ib ¼ 60mA(values higher than 28 GHz were reported in [19, 36]), �0:5 for Ib ¼ 60mA (values in the range 0:25 � � 0:9 havebeen indicated as typical in [20]) and EFM � 175MHz=mA(values lower than EFM ¼ 60MHz=mA have been reportedin [37] for a laser frequency relaxation oscillation higher than10 GHz, suggesting the possibility of obtaining simul-taneously EFM � 175MHz=mA and f�3 dB � 27:6GHz).Therefore, we believe that the set of fixed parameters inTable 1 are consistent with the OLIP-restricted, from thepoint of view of physical feasibility.

Figure 8 allows one to conclude that good performancerobustness to variation of laser parameters is achievedaround the OLIP-restricted. Nevertheless, it has beenconcluded that a is a very stringent parameter. For example,a small reduction of a to 1, would allow a large increase inTDT, to about 1250 ps=nm:

6 Conclusions

General laser optimisation for use in DST systems has beenpresented. Laser optimisation has been performed toaccomplish two goals: maximising BBS and TDT. Fixedlaser bias and modulation currents have been assumed toavoid undesirable DST laser current tailoring to fibre length.It has been established that the objectives can be obtained byadjusting suitably the laser intrinsic parameters a; tp; gc ande: The OLIP have been obtained for prescribed laser currentsand equaliser bandwidth. It has been shown that nosignificant improvement is achieved by further optimisationof these prescribed quantities.

These results thus reveal that a set of laser parametersoptimised under constrained circumstances can providegeneral laser optimisation.

Compared with the experimental data reported in [7],significant improvement in BBS and TDT is observed in theanomalous dispersion propagation regime. We also stressthat fixed laser bias and modulation currents are used, in

contrast to [10] and [7] where driver currents were tailoredto fibre dispersion to optimise system performance.

The physical feasibility of the OLIP using state of the artS-MQW laser technology has been discussed. It has beenconcluded that the optimum a ¼ 0:8 is the most question-able factor concerning physical implementation, given thata � 1 is the minimum experimental value reported to date.Nevertheless, laser suboptimisation with the restrictiona ¼ 1:1 has shown that improvements relative to thenon-optimised DST system performance are still achieved,with the additional advantage of fixed laser currents.

Unlike the results achieved in [11], the OLIP and OLIP-restricted lasers lead to strong adiabatic chirp. For the OLIPlaser, a steady-state frequency deviation of about 12.4 GHzis observed for a peak-to-peak frequency deviation of about17.6 GHz. This can easily be explained by the intrinsic needof the DST technique for large adiabatic chirp [6] and of thedeleterious impact of transient chirp on DST systemperformance in the anomalous propagation regime [10].

This work provides valuable input information todesigners of lasers for use in DST systems, who need toknow the best target laser parameters. It has been shown thatto achieve the best DST performance at 20Gbit=s usingfixed laser currents, lasers with low a ða � 0:8Þ and high eðe � 10 10�23 m3Þ are required.

Future work, will address the assessment of how changesof those laser parameters kept constant in this work, affectthe optimised parameters.

7 Acknowledgments

This work was supported, in part, by Fundacao para aCiencia e Tecnologia from Portugal, POSI and FEDER,within the project POSI/CPS/35576/1999-DWDM/ODC.

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