Injection Locking JQE

8/6/2019 Injection Locking JQE

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-.I688 IEEE JOURNAL OF QUANTUM ELECTRONICS, V O L . 21 , NO. 6. JUNE 1991

Injection Locking in Distributed FeedbackSemiconductor Lasers

R ongq ing Hu i , A le s s andro DOt ta v i , An ton io Me c oz z i , a nd P a o lo Spa no

Abstract-Injection locking properties of distributed feed-back semiconductor lasers are studied systematically. Due tothe high side mode suppression, these devices show differentlocking properties when compared to lasers having Fabry-Perotstructures. T he main result is the identification of four regimesfor different injection levels. In particular, a symmetrical lock-ing band at low optical injection level is confirmed. The pres-ence of this symmetrical band can be exploited in some appli-cations: as examples, the measurement of the linewidthenhancement factor a and the PSK modulation capability arereported.

I . INTRODUCTIONNJEC TION locking is a promising method to synchro-I ize one (or several) free running oscillators to a m asterlaser having, in general, a higher frequency purity. Injec-tion locking of semiconductor lasers can be usefully em-ployed in multichannel coherent optical transmission sys-tems, and it is also a good method to investigate laserproperties. Numerous studies on semiconductor laserswith external optical injection have been published so fa r

[1]-[8]. How ever, most of the experimental measure-ments were done on Fabry-Perot (FP) laser diodes, wherethe presence of longitudinal modes having a comparablevalue of gain prevents an extensive investigation of theinjection locking properties.This paper reports, for the first time to the authorsknowledge, a systematic experimental investigation of th einjection locking properties of distributed feedback (DFB)semiconductor lasers. In these lasers, the side longitudi-nal modes are highly suppressed by the distributed grat-ing, so that injection locking can be maintained even inconditions in which the phase relation between the elec-tric field present in the laser cavity and that injected fromoutside is such that the threshold gain is higher than thatfor the free running laser. These conditions cannot beachieved when using FP lasers due to the mode hoppingamong different longitudinal modes. Owing to this differ-ence, the experimental results show a symmetric stablelocking band in D FB lasers at low injection power, whereFP lasers display a typical asymmetric band [4]. As afunction of injection power, four different regimes have

Manuscript received October 18, 1990; revised February I I , 1991. Thiswork was supported by the Fondazione Ug o Bordoni and the Italian P. T.Administration.The authors are with the Fondazione Ug o Bordoni, 00142, Rome, Italy.IEEE Lo g Number 9100604.

been experimentally distinguished: 1) a symmetrical sta-ble locking band; 2) two stable locking bands for positiveand negative values of frequency detuning separated byan unstable region; 3 ) stable locking only for negativevalues of detuning; and 4) a bistable region. The mea-surements were performed by varying for more than 30dB the injected optical power level. To explain the ex-perimental results, a theory showing the importance of thenonlinear gain saturation term in stabilizing the injectionlocking has been developed.W e also propose a new method for measuring the line-width enhancement factor CY in DFB lasers based on thepresence of the symmetric stable locking band at low in-jection level. This technique is simple and accurate be-cause it does not require the knowledge of the value ofthe injected optical power, while similar methods previ-ously proposed do require such knowledge [8] .Moreover, the symmetric stable locking band allows usto achieve a relative phase detuning approaching a rad.This opens the possibility to use the injection-locked DFBsemiconductor lasers for optical coherent PSK modula-tion.

11. E X P E R I M E N TThe employed experimental setup is shown in Fig . 1 .Two identical DFB-BH laser diodes (Fujitsu FLD 150)having an emission wavelength of 1554 nm were used as

master and slave. Both of them had one facet antireflec-tion coated and the other facet cleaved. The master laser(ML) was biased at 2.5 times its threshold current withabout 8 mW of optical output power, and the slave laser(SL) was biased at 1.75 times its threshold, which cor-responds to 3 mW of optical output. Tw o diffraction lim-ited lenses with 0.65 numerical aperture were used forbeam coupling. Two optical isolators, inserted betweenM L an d SL, provided more than 50 dB of isolation, anda X/2 plate was used to match the polarization of the twolasers. The coupled optical pow er was roughly evaluatedfrom the photocurrent induced in the SL at zero bias. Th emaximum photocurrent obtained was about 150 pA which,for a unitary quantum efficiency and a perfect matchingof the laser mode, corresponds to about 120 pW . Thevariation of the injected optical power was obtained by aset of neutral density (ND) filters between ML and SL.Frequency matching and adjusting were accomplished bycontrolling the heat-sink temperature of the lasers . Both a

0018-9197/9 1/0600-1688$01 OO 0 99 IEEE


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1689HU I et al.: INJECTION LOCKING IN DFB SEMICONDUCTOR LASERS

TV camera

Fig. 1. Experimental setup.

monochromator and an FP scanning interferometer wereused for measuring the spectrum of SL output. An isolatorwas also used to prevent optical feedback from the inter-ferometer. The relative variation of the output power ofthe SL against the frequency detuning was indirectly mea-sured through the electric voltage across the diode junc-tion. T he relative increase of the voltage is in fact directlyproportional to that of the carrier density which is, in tum ,proportional to the relative decrease of the photon densityinside the laser cavity [ 2 ] . n this way, we were able toavoid the problem of field interference between the SLoutput and the directly transmitted or reflected light fromth e M L outside the SL's active waveguide.When locking was achieved, the free running slavemode was quenched effectively, and the oscillation fre-quency of the SL was locked to that of the master laser.The measured stable locking range is given in Fig. 2,where locking is defined to b e stable when the am plitudeof either the spurious free running slave mode or the re-laxation oscillation side bands are at least 20 dB belowthe locked main peak. This definition, in view of the ap-plications to the practical coherent optical communica-tions, seems more crucial and more relevant than thatconne cted to the visibility of the interference fringes [ 2 ] ,[4], [5]. In this last case, in fact, a small amount of un-locked power or weak excitation of relaxation side bandsis hard to be detected. In Fig . 2 and in the following, thepower ratio R is defined a s the ratio between the externallyinjected optical power and that em itted from the SL. Thetwo different detuning limits for stable locking are shownin the figure-one of them (open circles) determined bylock ingh nloc king , and the other one (points) by the onsetof dynamic instability revealed by the raising of the re-laxation oscillation side bands in the SL emission spec-trum. We call them static and dynamic limits, respec-tively. Four different regimes of injection locking areexperimentally well defined, as indicated in Fig. 2.

At low optical injection level (regime A), locking isunconditionally stable and no instability occurs. Th e moststriking feature in this regime is that the stable lockingrange is symmetrically centered around the frequency of

-204 8 """" ' ! . . . . I ! ' ' . . . , . I ! . ' . ' . JI o - ~ I o - ~ I o 3 1O 2 I O 'Optical Injection Ratio (R )Fig. 2. Locking bandwidth against optical power ratio R . The circles referto the measured dynamic limit, the points to the static limit, the diamondsto the onset of bistability. The curves represent the theoretical results: thesolid line is the dynamic limit; the dotted line is the static limit.

the free-running SL. Contrary to the general behavior ofFP lasers, in which the locked output power cannot be-come smaller than the free-running values [ ]-[4], wefound that the locked output power can increase for thenegative detuning or decrease for positive detuning whileneither relaxation-oscillation side bands nor free-runningslave modes appear at all. A typical result of the mea-surements of the voltage variation across the diode junc-tion and, hence, of the gain variation versus frequencydetuning is given in Fig. 3(a).In regime B, the stable locking range is split into twoparts by an interval of instability. The amplitude of th elocked main peak and the averaged amplitude of the twoside peaks due to relaxation-oscillation (the two relaxa-tion-oscillation sidebands usually have a different ampli-tude because of the phase-amplitude coupling [9]), mea-sured by means of an F P interferometer fo r two differentinjection levels in regime B, are reported in Fig . 4. Whenthe injection level increases, the range of positive detun-ings in which the stable locking is achieved gradually re-duces and finally disappears. In regime C, the systemshows a typical asymmetric locking, w hich has been stud-ied extensively in [11-[4]. With very strong optical injec-tion (regime D), bistability of locked output versus detun-ing is observed near the static boundary of the stable


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1690 IEEE JOURNAL OF QUANTUM ELECTRONICS. VOL. 27 . NO. 6, JUNE 1991300 1 t

i

03

O000 %

0

-300 4 L-3 -2 -1 0 1 2 3Detuning (Ghz)(a )

21 t

2 4 L-3 -2 -1 0 1 2 3Detuning (Ghz)

Fig. 3 . (a) Experimental values of the junction voltage variations versusdetuning; (b) relative photon density variation versus detuning obtainedthrough a computer s imulation.

-3 -2 - 1 0 1 2 3Detuning (GHz )

Fig . 4 . Experimental values of the amplitude of the main peak and relax-ation oscillation side peaks. Circles refer to R = -36 dB, d iamonds to R= -34 .5 dB.

locking range, as shown in Fig. 5 , where the stable lock-ing bandwidth is reported for a value of R equal to 3.5 xThis kind of bistable behavior was first found byKawaguchi et al. [7] when the SL was working very nearto i ts threshold, and w as found to disappear when the in-jection current was increased above 1.1 1 of i ts threshold.In our experiment i t is found , however , that the most im-portant parameter in determining the bistable behavior isthe power ratio between the externally injected opticalpower and that emitted from the S L. Systematic measure-ments indicate that the width of the bistable frequencyloop increases l inearly with the logarithm of the injectionoptical power ratio as shown in Fig. 6 . A bistable loopwas found even fo r bias of the SL as high as two times ofits threshold c urrent.

LB

-50 -45 -40 -35 -30 -25 -20 -15Frequency (GHz)

Fig. 5 . Measured values of the locked power emitted by the SL versusfrequency detuning for an optical power ratio R = - 14.6 dB. Closed andopen squares refer to the values obtained increasing and decreasing detun-ing, respectively.

r - 19P0

n /.0

4 0 24o- 1ooPower ratio

Fig. 6 . Measured bistability loop width versus optical injection power ra-t10.

111. ANALYSISIn this section, the stabil i ty properties of the injectionlocking process will be studied on the basis of a theoret-ical model. In this model, w e show the importance of thenonlinear gain saturation term to stabil ize the injectionlocking.In DFB semiconductor lasers, the side longitudinalmodes are highly sup pressed and the dynamic single modeoperation is ensured by the mechanism of distributedfeedback. T hus, i t is reasonable to base our analysis onthe well-known single mode Van der Pol equation and arate equation for the carrier density [ 11

In these equations, P ( t ) = exp [-i (wI t - $) I isthe normalized electric field of the SL inside the laser cav-ity, and P l ( t ) = Z:/* exp [-iwlt] s that coupled into theSL laser cavity from the M L ; I an d I , are the field inten-sities of S L , and that coupled from M L ; G is the materialgain; G N an d G I are the derivatives of G with respect to


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HUI er al.: INJECTION LOCKING IN DFB SEMICONDUCTOR LASERS 1691

N an d I ; wo is the modal frequency of the slave cavity; w1is the frequency of ML; N ( t ) is the carrier density; No isthe threshold carrier density; C ( t ) s the carrier injectionrate; 4 represents the phase difference between SL and th eML; and T~ an d T~ are the spontaneous lifetime of minoritycarriers and the group round-trip time of SL , respectively.G, accounts for the nonlinear gain saturation effect. Itshould b e m entioned here that the spatial hole-burning ef-fect is omitted in the set of (l ), and that our approach alsoneglects the noise due to the spontaneous emission eventsinside the SL cavity. The frequency and intensity noise ininjection-locked semiconductor lasers has been exten-sively studied in [6].In the stable locked state, the frequency of the SL islocked to that of the ML so that the stationary solutionsar e

(2a)(2b)

AG = -2 p COS 4Aw = p(sin 4 - a co s 4 )

where Aw = w 1 - wo is the frequency detuning; AG =GNAN + GIA I , A Z nd A N being the deviations of carrierdensity and photon density from their free running values;an d p = ( I I / Z ) ' I 2 / r is the normalized optical injectionlevel.The injection locking range is determined from (2b) bylAwl I p( 1 + CY^)'/^. This sets the static limit of thelocking range of Fig. 2 , which corresponds to the rangeof the phase detuning from the value of tan- ' (a) a / 2to tan-' (a) a / 2 .

All the points inside the two curves Aw = + p ( l +are stationary solutions of the set of ( l ), but theyare not always stable. Dynamic instability in injection-locked semiconductor lasers has already been studied [2]-[4]. Only recently, how ever, the nonlinear gain saturationhas been included in the evaluation of the dynamic sta-bility range [101. Physically, th e nonlinear gain dam ps therelaxation-oscillation and tends to stabilize the single-fre-quency laser oscillation. By using the sam e method of [2]-[4], but including the nonlinear gain saturation, (1) canbe linearized in terms of small deviations around the equi-librium values, namely, I ( t ) = Z + 6 I ( t ) , 4 ( t ) = +6 4 ( t ) ,N ( t ) = N + 6N ( t ) ,C(t) = C + 6 C ( t ) .The follow-ing linearized equations can then b e easily obtained:

d6+ p sin + aGNdt 21 2- 61 - p CO S 4 64 -- N (3b)where, for constant current injection, 6C = 0. The spon-taneous emission rate R has been phenom enologically in-troduced into (3a); the same equation, however, can beobtained from (la) when a proper Langevin noise term

accounting for spontaneous emission noise is introducedFollowing the standard treatment as in [2] and [3], afterthe Fourier transformation and the Routh-Herwitz crite-rion were applied to (3), the damping time of the relaxa-tion-oscillation can be obtained in the following simpleform:

[111.

1 1 R- = - + (GN- GI)Z+ - + p (cos 4 - a in 4 ) .7R rS Z(4)

The stable locking is achieved w hen, after a slight per-turbation of 6n, 6 4, an d 61, the system returns to its equi-librium state through a damped relaxation-oscillation.Quantitatively, this condition is verified when rR > 0.We define dynamic limit of the stable locking range thecurve rR = 0. This curve is plotted in Fig. 2 by using th efollowing laser parameters: GN = 5 .6 x lo3 s-I, G, =S - I , a = 6 , T , = 8 ps, QR = 2 a * 6 GHz, where QR(GGNZ)1/2.n order to compare the theoretical results tothe experimental data, we assumed a homogeneous fieldin the cavity an d an antireflection coating on the fron t facetof the SL so that Z l / Z is equal to R. In spite of the goodagreement between the theoretically evaluated dynamiclimit and the experimental data, on e should notice that ourtheoretical and operative definitions of dynam ical stabil-ity are different. The presence of spontaneous emissionnoise, in fact, increases the relaxation oscillation sidebands beyond the 20 dB limit we set as the experimentalthreshold for the stability, even when T~ is larger thanzero.By analyzing (4), one can observe that the term -G,Zcan be larger than both GNZa nd l / r s , so that GI is themain param eter affecting the stability proper ties, being theterm R / I important only for very low values of I . BothG,, which is always negative, and R ncrease the stablelocking range of injection locking. This can explain whythe stability analysis in [2], where both GIan d R were notaccounted for, gave results worse than those of the ex-perimental measurements.The use of (2) and (4) allows us to obtain the range ofinjection ratio where the laser is unconditionally stablewithin the whole locking band (regime A) and w here thestability region is divided into two parts by an instabilityinterval (regime B). The width of the regime A in Fig. 2is obtained from (4) to be 0 < p 5 1 / [ ~ ~ ~ ( 1The width of regime B can b e calculated by searching forthe cross point between static and dynamic limits, thusobta ining l / [ rm(l + I I / [ ~ ~ ~ ( fCY^)'/^sin 240], rR0= [(GN- GI)Z+ R/Z + l / ~ ~ ] -eing theintrinsic damping time of the SL without optical injection,an d +o = tan-' a.

It is worth noting that the symmetry of the stable lock-ing band in regime A [12], [13] and the existence of an-other stable locking range with positive detuning in re-gime B [12], have been experimentally observed only

-1.8 x io48, = 6. 4 x l o l l S-I , I / T ~= 3 x io9


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-.1692 IEEE JOURNAL OF Q U A N T U M ELECTRONICS. VOL. 27. NO . 6, J UNE 1991

recently in DFB lasers, while they have not been foundin FP lasers . In FP lasers , a symmetrical locking bandwas reported by Goldberg et al. [14]; but the definitionof this band, i .e., the frequency distance at which thebeating signal between ML and SL is reduced of 6 dBwith respect to its maximum value, does not assure thatthis band is stable. Intuitively, one could believe that inDFB lasers , in which the side longitudinal modes arehighly suppressed, the gain change expressed by (3a)makes the stable locking on the positive detuning rangeimpossible, because the positive values of A G may inducethe ris ing of the free-running main mode of SL. A com-puter simulation, carried out by integrating the set of ( 1 )by means of a fourth-order Runge-Kutta meth od, how-ever, shows that in regime A the stable locking is alwaysmaintained in the static locking range, as experimentallyobtained. T he simulated photon density at s teady state, infact, is time independent within the static locking range,and becomes oscillatory outside this range, which corre-sponds to the case of four-wave mixing [15]. The t imeaveraged relative photon density variation versus fre-quency detuning in regime A is reported in Fig. 3(b). Th ephoton density increases, with respect to the free runningSL, for negative frequency detunings, and decreases forpositive detunings. Within the static locking range, thephoton density variation, obtained by simulations, repro-duces what is predicted by the steady-state solution of ( 1 )an d (2), i . e . ,

11 + -A I 2p COS 4 G N I T ,- G 2p cos ( 1 + -&).GIE N

1 - -I

( 5 )Out of the static locking band, however, the photondensity gradually converges from both sides to the value

pertaining to the free-running SL . In order to compare tothe experimental measurement shown in Fig. 3(a), we re-call that the relationship between the junction electricvoltage variation A V and the photon density variation A iis A V = p A N = - p ( G + G [ l ) A I / ( G N I+ l/r,), wherep is a constant determined by junction dependence and theexternal electric circuits, as described in 1161. A qualita-tive agreement between theory and experiment [ Fig. 3(a)]is found. In FP semiconductor lasers , the symmetric lock-ing range cannot be found because the gain margin be-tween the main and the side longitudinal modes is rela-tively small. Hence, the gain decrease of the loched modewill result in multilongitudinal mode operation [3], [4].Moreover, the photon density decrease of the locked mainmode in the positive detuning will be compensated by thecontribution of the side longitudinal m odes, and no outputoptical power decrease can be found [l] , [3], [4].

IV. DISCUSSIONIn this section, we g ive two examples of the applicationof the particular characteristics of the injection locked

DFB lasers which have been discussed in the previoussections. Both of them are based on the property of sym -metric stable locking band at low injection levels.A . a Factor M easurement

The linewidth enhancement factor a is a special andimportant parameter in sem iconductor lasers. M any prop-erties that are unique to sem iconductor lasers can be tracedback to this a parameter which, unfortunately, is not pos-sible to b e m easured directly [8]. Up to d ate, the accuracyof the results of a measurement is not yet reliable. Lightinjection was proposed as a notable method to perform themeasurement of the a parameter [ l ] , [6]. In injectionlocked Fabry-Perot (FP) lasers , however, the multilon-gitudinal mode tendency prevents an easy measurementof the a parameter. Usually, the knowledge of the in-jected optical pow er is required, but this parameter is hardto precisely determ ine.The symmetric s table locking band at low injectionlevel in injection locked DFB lasers enables us to use asimple measurement technique for the a actor. Althoughbased on the principle of optical injection locking, it doesnot require the knowledge of the absolute amount of theinjection level [121.From (3a) and (3b), the half-locking bandwidth can befound as Aw,,, = p(1 + On the other hand, theoutput optical power is equal to that of the free runningSL, when 4 = a /2 , which corresponds to a detuning Aw o= p . T he a value can then be easily determined by

Experimentally, both values of Am , an d A o o can be mea-sured precisely if the stable injection locking is kept (re-gime A) . It has to be noted that the a value measured withthis technique is not the material linewidth enhancementfactor, but it is the structure dependent effective one asdefined in [171 an d [181. Several measurements of a, er -formed at different injection levels within the regime A ofFig. 2, using (6) are reported in F ig . 7 . From this figure,a an be estimated to be 5.5 f .6 in our case. This valueagrees rather well with the value of 5 which can be ob-tained using the relationship A o , = p(1 + al -though in this case the measurement suffers for the lackof precision in the evaluation of p .B . Optical PSK Modulation

The optical PSK (DPSK) modulation scheme achievesthe highest detection sensitivity in coherent optical com-munication systems [191. Optical phase modulation usingan injection-locked semiconductor laser was first pro-posed by Kobayashi et al. [20] in FP lasers . In that paper,a modulation of the current exciting the SL is shown toinduce, besides intensity modulation, phase modulationinstead of frequency modulation typical of free runninglasers . Despite good agreement between theory and ex-periment, the effect of the linewidth enhancement factor


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HUI er al . INJECTION LOCKING IN DFB SEMICONDUCTOR LASERS

4 1

Lockingbandwidth (GHz)Fig. 7 . Values of 01 measured at different optical injection levels.

CY was neglected, and both instability and asymmetriclocking band were not accoun ted for in this analysis.The presence of a symmetric stable locking range ininjection-locked DFB lasers opens the possibility of usingthese devices in optical PS K modulation. Although a the-oretical model accounting for the CY parameter is availablein the case of small signal an alysis [21], ap propriate re-sults for PS K modulation using injection-locked semicon-ductor lasers have not yet been found. In the following,we give the results of a small signal analysis obtained bymeans of a linearized theory and of numerical simulationsaccounting fo r the nonlinear effects, and predict some im-portant effects limiting the range of applications of thismodulation scheme.The small signal phase modulation efficiency can beobtained after applying Fourier transformation to (3), as

where(7 )

p(sin 4 - CY COS 6)+ CY2RI-i w - GJ + - + p cos 4

where A ( w ) = [C(w)/(C - Cth)], (w) an d +(U) are theFourier transformations of +(I) an d C(t) , espectively, andC,, is the carrier injection rate at threshold.The small signal phase modulation response given by(7) is reported in Fig. 8 for different levels of optical in-jection ratio. T he values of frequency considered in thisfigure are in the range 0.1-10 GHz. The results showncannot be extrapolated to lower frequencies because ofthermal effects which are not taken into account in (7).

0.1 1Frequency(GHz)

1693

0

Fig. 8 . Calculated small-signal phase modulation response versus modu-lation frequency at zero relative phase detuning for different optical injec-tion levels. The solid line refers to free-running condition; circles to R =-44 dB; points to R = -41 dB; triangles to R = -37 dB .

0.01 1 co.01-n12 4 3 4 1 0 n110 n13 -n12

Relative phaseFig. 9. Cutoff frequency and the relaxation-oscillation limit versus rela-tive phase detuning for different optical injection levels , ca lculated in thesmall-signal approximation. The long-dotted line refers to R = -44 dB ;the solid line to R = -47 dB: the short-dotted line to R = -5 1 dB .

Fig. 8 shows that the 3 dB modulation bandwidth slightlyincreases with the optical injection level, while the relax-ation-oscillation peak becomes more prono unced, endingup in the unstable region. Another feature shown by (7)is the strong dependen ce of the modulation bandwidth o nthe phase detuning. Th is dependence is presented in F ig.9, where the 3 dB modulation bandwidth is reported ver-sus the relative phase detu ning , defined as rl,= 6 an-' CY ,for several different optical injection ratios. It is worthnoting that a considerable decreasing of the modulationbandwidth is present w hen the relative phase detuning ap-proaches f 7 r / 2 . This limits the dynamic range of phasemodulation in practical use. In the same figure, the in-verse of the damping time of the relaxation-oscillations fc= (27r7,)-', which represents the o ther limit for the mod-ulation bandwidth, is also reported.

In practical PS K modulation systems, the relative phasedetuning rl, is usually shifted by a total amount equal to Rrad, so that the small signal analysis gives only a quali-tative understanding of the dynamical behavior of the


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HUI er al.: INJECTION LOCKING IN DF B SEMICONDUCTOR LASERS 1695

and 1990 he held a research fellowship at the Fondazione Ugo Bordoni,Rome, Italy, where his research interests were optical bistability, four-wave mixing, and optical injection locking of semiconductor lasers. He isnow with the Electronics Department, Politecnico di Torin o, Torino, Italy.He also holds a research fellowship from the Italian TelecommunicationResearch Center (CSELT), Torino, Italy. His main research interests aresemiconductor laser devices and coherent optical transmission systems.

Anton io Mecozz i , for a photograph and biography, see p. 34 3 of the March1991 issue of this JOURNAL .

Ales s andro DOttavi was born in Rome, Italy, onJanuary 29, 1962. He studied physics at the Uni-versity of Rome and received the degree in 1988He is currently working in the field of semicon-ductor lasers at the Fondazione Ugo Bordoni.

Paolo Spano, for a photograph and biography, see p. 34 3 of the March1991 issue of this JOURNAL .

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Injection Locking JQE