Picosecond and sub-picosecond pulse generation in semiconductor lasers

Transcription

1 Picosecond nd sub-picosecond pulse genertion in semiconductor lsers J.-M. Lourtioz, L. Chusseu, N. Stelmkh To cite this version: J.-M. Lourtioz, L. Chusseu, N. Stelmkh. Picosecond nd sub-picosecond pulse genertion in semiconductor lsers. Journl de Physique III, EDP Sciences, 1992, 2 (9), pp < /jp3: >. <jp > HAL Id: jp Submitted on 1 Jn 1992 HAL is multi-disciplinry open ccess rchive for the deposit nd dissemintion of scientific reserch documents, whether they re published or not. The documents my come from teching nd reserch institutions in Frnce or brod, or from public or privte reserch centers. L rchive ouverte pluridisciplinire HAL, est destinée u dépôt et à l diffusion de documents scientifiques de niveu recherche, publiés ou non, émnnt des étblissements d enseignement et de recherche frnçis ou étrngers, des lbortoires publics ou privés.

2 nd sub-picosecond pulse genertion in Picosecond lsers semiconductor prtique pour un nombre croissnt d'pplictions. EIIe pr6sente ussi un intdrdt fondmentl de pr s reltion 6troite vec les dtudes de l dynmique du milieu semiconducteur. Apr6s une semiconducteur. Nous discutons finlement quelques perspectives de d6veioppements nouveux. of gin-switching, Q-switching nd mode-locking techniques. The comprison is performnces by experimentl results s well s by lser modelling, some of which re new. A specil illustrted nd solid-stte lsers) for electro-optic smpling [6, 7], time-resolved spectroscopy, lser dye nd metrology in the time-domin. In ddition to their compctness, semiconductor rnging J. Phys. III Frnce 2 (1992) SEPTEMBER 1992, PAGE 1673 Clssifiction Physics Abstrcts 42.55P 42.60F 42.80W J.-M. Lourtioz, L. Chusseu nd N. Stelmkh Institut d'electronique Fondmentle, URA 22 du CNRS, Universitd Pris XI, Bit. 220, Orsy Cedex, Frnce (Received 5 December I99J, ccepted 20 Februry 1992) R4s1m4. L g6n6rtion d'impulsions courtes dns les lsers h semiconducteurs est d'int ret revue introductive, nous comprons les performnces des techniques de commuttion de gin, de commuttion de penes de cvitd et de blocge de modes. L comprison est ussi bien illustr6e pr des r6sultts exp rimentux que pr des r6sultts de moddlistion. Certins de ces rdsultts sont nouveux. Un ccent prticulier est mis sur [es spects de modultion de phse dns Ie milieu Abstrct. Genertion of short opticl pulses in semiconductor lsers is of prcticl interest for n incresing number of pplictions. It is lso of fundmentl interest becuse of its tight reltion with the field of semiconductor lser dynmics. After n introductory review, we compre the is given on the spects of phse modultion in the semiconductor lser medium. Finlly, emphsis discuss some perspectives for further developments. we 1. Introductory review. semiconductor light sources generting short pulses in the picosecond nd subpicosecond High-speed time scles re essentil for lrge vriety of pplictions. To dte, the strongest demnd for picosecond lser diodes remins in the field of opticl communictions where exists need of sources for soliton trnsmission in opticl fibers [1-3] s well s for high bit rte extemlly modulted trnsmission systems nd for time-division multiplexed trnsmission [4, 5]. (Sub)-picosecond lser diodes re lso expected to serve s clock genertors in systems prllel processors. On the other hnd, high-power pulsed semiconductor lsers ll-opticl re n interesting ltemtive to more conventionl lser systems of lrger sizes (e.g. YAG, lsers hve the evident dvntge of being comptible with integrted electronic circuits.

3 pulse chrcteristics re desired ccording to the ppliction which is envisged. Different instnce, long-distnce soliton trnsmission in fibers require Fourier trnsform-limited For of djustble length, while studies of nonliner phenomen in vrious mterils pulses need high peks powers. For ech ppliction, different techniques nd opticl essentilly semiconductor lsers in pulsed regime operting I) gin-switching (I.e. pulsed pumping), it) : iii) mode-locking. These three techniques were investigted erly on in the Q-switching, of semiconductor lsers. Moreover, the first lser emission from development homojunction n diode structure ws chieved in 1962 with the injection of current pulses [8]. Two yers ccomplished in the following decde obviously followed the technologicl Progress of semiconductor mterils. Better ccurcy ws lso chieved in pulse developments first time, subpicosecond pulses (0.65 ps) were mesured in semiconductor lsers. This ws by the work of Yokoym et l., where similr performnces were chieved (0.58 ps) followed n ged lser [17]. Gin-switching experiments in double heterostructure GAs lsers with crried out in prllel, which gve output pulses of 15 ps [18]. All these experimentl were represented decisive improvements in terms of short pulse durtion. results of relizing coherent emission for opticl communiction [19-21]. These investigtions were out in prllel with the development of single-mode distributed-feedbck (DFB) crried lsers emitting in spectrl regions ner 1.3 m nd 1.5 cm. In 1986, Tkd et l. InGASP trnsform-limited picosecond pulse genertion t 1.3 m by fiber compression of reported DFB lser pulses [22]. The efficiency of this novel technique ws further gin-switched confirmed by severl uthors for the spectrl region ner 1.5 m schemes bsed on grtings nd interferometers were used to compenste for compression effects in mode-locked lsers. Trnsform-limited pulses were obtined by Silberberg chirping repetition rtes scling from 16 GHz to 40 GHz were reported in different works on ctive 1674 JOURNAL DE PHYSIQUE III N 9 schemes must be explored. As for other lsers, there re bsiclly three techniques for lter, Lsher proposed n inhomogeneous pumping of the ctive medium to relize the conditions for regulrly pulsed emission [9]. Q-switching ws effectively demonstrted in 1966 Kumosov et l. with two-section lser geometry [10]. Mode synchronistion in n by semiconductor GAs lser with n exteml cvity ws climed by Morozov et l. in injection [1il. All these first experimentl investigtions were performed with homojunction 1968 operted t low temperture below 77 K. The shortest pulses were lredy found structures to be less thn 100 ps, with pulse repetition rtes of severl gighertz [12]. mesurements. In 1970, E.P. Hrris clerly demonstrted ctive mode-locking in semiconductor lser [13]. In the sme yer, Glodge nd Lee reported ccurte mesurement of Q-switched GAs lser pulses by utocorreltion [14]. After long period devoted to the for new lsing mterils s well s to the improvement of CW lser spectrl properties, serch Ho et l. reported in 1978 the first mode-locking experiments with double- P.T. heterostructure lser operted t room temperture [15] : 20 ps pulses were obtined. Pssive with sturble bsorber ws demonstrted three yers fter by Vn der Ziel et mode-locking [16] : the bsorber ws creted by proton implnttion through the diode fcets. For the l. From the yer 1982, the reserch work ws pursued in new directions. The min direction ws certinly the investigtion of chirping effects in modulted nd pulsed lsers with the gol 24]. Fiber compression [23, lso successfully pplied to single-mode Q-switched lser where strong chirping effects ws led to the genertion of very short (lps) nd powerful (3W) pulses [25]. Other et l. [26] nd Kuhl et l. [27] using pssive nd ctive mode-locking, respectively. A second importnt improvement of (sub)-picsecond lser diodes during the lst decde concemed the increse in pulse repetition rte. For gin-switching s well s for ctive mode- progress resulted from the use of lsers with lrge modultion bndwidths. A locking, rte of 12 GHz ws chieved with gin-switched DFB lser in 1986 [22]. Pulses repetition

4 to 350 GHz [34]. up n incresing number of studies ws directed t pek-power optimiztion. In few Finlly, source ws gin-switched DFB lser in one cse [39] nd synchronously pumped surfce- InGAs lser in the other cse [40]. Extremely short pulse durtions of 0.46ps, emitting nd 21fs were reported in references [38, 39] nd [40] respectively, but the 0.2ps lser chrcteristics were for little in these performnces. semiconductor this introductory review, the rest of the pper is orgnized in four sections. The Following three techniques for short pulse genertion, I-e-, gin-switching, Q-switching nd mode- re presented in sections 2, 3 nd 4, respectively. Experimentl results nd locking, from lser modelling re used to illustrte these techniques. Specil emphsis is clcultions on the spects of phse modultion (chirping) which re of prime importnce in given lsers. We finlly discuss some perspectives of further developments in semiconductor is chieved with fst excittion of the lser medium. Under this condition, Gin-switching popultion inversion nd thus high gin level cn be reched before the lser strts. In strong roundtrip times (w10ps). These two fetures give the possibility of short pulse cvity t high repetition rtes by gin-switching. genertion The simplest mthemticl description of the gin-switching process is provided by the two fmilir rte equtions for the crrier density N nd the photon density S : n p n The three terms on the right-hnd side of eqution (I) represent the crrier injection rte, spontneous recombintion rte nd the stimulted recombintion rte, respectively. the on the right-hnd side of eqution (2) re respectively the totl cvity-loss rte, the Those rte nd the stimulted-emission rte. Prmeters entering spontneous-emission (I) nd (2) re listed in tble I. equtions mplitude exceeds threshold current, the lser output exhibits relxtion oscilltions step reching stedy-stte vlue different from zero. Actully, the lser response is tht of before N 9 (SUB)-PICOSECOND PULSES IN SEMICONDUCTOR LASERS 1675 [28-31], the highest performnce being chieved in 1989 by Tucker et l. with mode-locking extended cvity InGASP lser [31]. More recently, pssive mode-locking ws monolithic demonstrted in lsers without extended cvities [32, 34], leding to ultimte repetition rtes pek powers exceeding I W were directly obtined from solitry diodes [25, 35- experiments, However, in most cses, high-power performnces were ttined by complementing the 37]. lser diode with severl mplifier sections nd nonliner compression stges. A pek power of 70 W ws reported by Delfyett et l. for n elborte system comprised of mode-locked AlGAs lser diode with n externl cvity, grting compressor nd two trvelling-wve semiconductor mplifiers [38]. Pek powers scling from 100 W to I kw were chieved in two recent experiments by using high-order soliton effects in fiber compression stges : the lser section Gin-switching. turn, s soon s lsing tkes plces, the emitted light is very intense nd the popultions of the lser level rpidly decrese below threshold. The lser emission then ceses nd n upper pulse is obtined. Semiconductor lsers re chrcterized by high gin vlues nd short opticl A (I ES) (N No) S (1) " + + ra (i es j (N Noj s. (2j Exct solutions of equtions (I) nd (2) cn only be found numericlly. Results of numericl simultions re shown in figures I nd 2 for prticulr cses of excittion. The first cse (Fig. l) corresponds to n idel step excittion with n infinitely short risetime. If the

5 1676 JOURNAL DE PHYSIQUE III N 9 (L r spontneous crrier lifetime I ns photon lifetime I ps r liner gin coefficient 2 A 10-6 cm3/s x cse (Fig. lb) corresponds to rectngulr pulse excittion. A single gin-switched second is emitted when the bck edge of the current pulse nerly coincides with the end of the pulse of the injection current, this sitution being of prcticl interest for high-bit-rte modultion communiction. Figures 2, 2b nd 2c represent the simultneous time-evolutions of opticl the time-evolution of the crrier density since the gin is ssumed to linerly depend on (1/4 T) Ag (t). Since the c An (t)/n1), the lser frequency evolution cn be described by : Au it) fi Ag(t) nd t the end of the pulse. Consequently, pulse compression cn be relized by beginning the downchirped pulses through linerly dispersive medium such s n opticl fiber pssing I + (Within the ssumption of Gussin pulses, the mximum compression rte is given by Tble I. List of prmeters entering into rte equtions (left) ; prmeter vlues used for clcultions in figures1, 2 nd 3 (right). Prmeters 1.5 m DFB lser 400 m) V ctive volume 170 m3 F nonliner gin coefficient I x 10-? cm3 N o crrier density t jrnsprency I x 10 ' 8 cm-3 r confinement fctor 0.5 p spontneous emission fctor 2 x 10-5 linewidth enhncement fctor 4 1 lser quntum efficiency 0.4 second-order filter whose time evolution is govemed by two differentil equtions. The first relxtion oscilltion. The lst cse (Fig. 2) corresponds to strong microwve the gin, output power nd lser frequency, respectively. Note tht figure 2 lso represents N in equtions (I) nd (2). Figure 2c will be discussed lter. As seen, the lser pulse is fter the lser gin hs reched its mximum. This is the norrnl sitution where only emitted pulse is emitted per period. The mximum-gin to threshold-gin rtion is presently close one to 1.2. It rrely exceeds 1.5 under microwve modultion [41]. The instntneous lser frequency evolution reported in figure 2c merits further comments. It is implicitely ssumed tht the lser is single-mode. In the semiconductor lser theory, the nd refrctive index vritions re interrelted vi dimensionless prmeter gin known s the linewidth enhncement fctor [19] : An (t), vritions re lso directly relted to refrctive index vritions frequency (t) (Av $ (ra ii ES) (N No) I/r), (3) where the reference frequency is tken t the lser threshold. From eqution (3), liner decrese of the gin is ccompnied by liner decrese of the lser frequency (downchirp). This sitution is illustrted in figures 2b nd 2c. Pulses emitted from semiconductor lsers exhibit qusi-liner downchirp. Non-linerities occur t the [42]. 3 shows the results of pulse compression experiments recently performed with Figure DFB lser t 1.52 m nd I km dispersion-shifted fiber with totl dispersion gin-switched

6 N 9 (SUB)-PICOSECOND PULSES IN SEMICONDUCTOR LASERS 1677 _ 0.2 o 5 Time (psi " 2 I Z I ' 200 Fig. I. Fig- 2. I. Lser responses under strong electricl excittion. ) single-step excittion, b) rectngulr Fig. excittion. pulse Under strong microwve modultion f 2.I GHz, l 400 E loo ( Time Ins) o, j D-1 ( > 0 $ O-OS ( D-S Time (ns)i oo i Sfl M ' 5? o loo 0 0 o o 600 j Time Ins) 2. Time-evolutions of the gin ), output power b) nd emitted frequency c) for 1.5 m DEB Fig. under strong microwve modultion. Lser prmeters re those reported in tble I. The dc bis, lser modultion mplitude nd modultion frequency re I 80mA, l150ma nd f 3GHz, respectively. The dotted line in figure 2 represents the threshold gin. of 20 ps/nm [24]. Clcultions from rte equtions (1-3) re presented for comprison. The prmeters (Tb. I) re determined from set of mesurements including the lightcurrent lser chrcteristics, the lser spectr under threshold, the opticl mesurement of the lser resonnce frequency nd the smll-signl modultion chrcteristics t vrious bises [43]. 200mA), the lser spectmm is to over GHz 120 (Fig. 3, bottom) nd the pulsewidth before compression mesured spred be 18ps from utocorreltion mesurements (FWHM, full-width hlf- to deduced is Clcultions gree with experiments. The clculted spectrum (Fig. 3, top) is mximum). GHz wide nd exhibits pek on the low-frequency side, the ltter being relted to the 120 til of the downchirped pulse. The clculted pulse (Fig. 3b) is symmetricl nd hs pulse of 18ps (FWHM). Figure 3c shows the utocorreltion trce of the pulse fter width

7 j 0 i i so $ fl So 3 i. loo 0 loo Frequency (GHz) Time (psi 3 '00 E X 0 So modultion frequency re I Time (ps) T;me (ps) 90 ma, I y o 200 ma nd f Agin, experiments (bottom curve) re well reproduced by clcultions (top compression. The trce width is 8ps (FWHM). The existence of extended wings in the curve). curve revels some devition from either Gussin or secnt hyperbolic utocorreltion pulse. Actully, chirp non-linerities in the pulse before compression give rise to smll shped pumping in equtions (I) nd (2) during gin-switching, nlyticl expressions re found for 1678 JOURNAL DE PHYSIQUE III N 9 l b) E 0 0 c) d) 2 ] p c $ f 3. Fiber compression of gin-switched DFB lser pulses t 1.5m (experiments nd Fig. Lser prmeters re those reported in tble I. The dc bis, modultion mplitude nd clcultions). 2. I GHz, respectively. The fiber is -20ps/nm. ) lser spectrum mesurements (bottom) nd clcultions (top) b) dispersion pulse before compression ; c) utocorreltion trce of the compressed pulses mesure- clculted ments (bottom) nd clcultions (top) ; d) clculted pulse fter compression. side-lobes in the compressed pulse (Fig. 3d). Owing to the overll fit between clcultions nd pulsewidth of 5.5 ps cn be estimted fter compression, which leds to timebndwidth experiments, product At. Au of 0.6. The compression rte (3) is close to the vlue estimted for ( 4). The pek power t the fiber output (350 mw) is more thn one order of higher thn the CW power delivered by the lser. mgnitude shorter pulses scling from 2 to 4ps hve been obtined by pplying the sme Still to different lsers [44]. Ultimte performnces of gin-switching cn be evluted technique n nlyticl pproch of rte equtions. Ignoring spontneous emission nd electricl from the totl number of emitted photons, S dt, nd the pek photon density, S, respectively 45]. The pulsewidth is then deduced from these quntities. If gin non-linerities re [41, into ccount, it is shown tht for very high initil-inversion-rtios the minimum tken

8 pulsewidth is given by : where r is the photon lifetime nd f e/ar. f-1 liner nd nonliner gin coefficients, The nd e, entering into f re priori mteril prmeters while r is cvity prmeter. In the A semiconductor lser terminology, 4 T e/a is known s the K-fctor nd f mximum modultion bndwidth chievble with given lser mteril [46]. the limits of eqution (4) cn be esily understood. In most cses, e/a is much lrger thn The Complementing the gin-switching technique with fiber compression, gin-non-linerities. pulse genertion thus ppers to be fesible for semiconductor lsers with sub-picosecond physicl limit insted of r. of ions through the diode fcets [48-50]. The second one is the reliztion of implnttion lser geometries, where some of the sections re unbised or reverse-bised [9, multi-section 4. Bsic scheme of semiconductor lser with sturble bsorber. r, r nd r re respectively Fig. bsorber relxtion time, the gin recovery time nd the cvity roundtrip time. the JOURNAL DE PHYSIQUE III -T 2, N'9, SEPTEMBER N 9 (SUB)-PICOSECOND PULSES IN SEMICONDUCTOR LASERS 1679 f (4) P is / Al T e (I,e., f is much lrger thn I in Eq. (4)) so tht the ultimte pulsewidth is close to r This vlue is obviously relted to the smllest period of lser relxtion oscilltions. The e/a. minimum K-vlue reported to dte for long-wvelength lsers is 0.17 ns [47], which gives F/A 4 ps. Still smller vlues re expected for short-wvelength lsers wich exhibit weker lrger thn 5. A different limit is predicted for lsers with very long cvities since f becomes less thn I in (4). The minimum pulsewidth identifies in tht cse with the photon lifetime, eqution However, this result must be tken with cre since propgtion effects cnnot be neglected r. so fr in rte eqution models. Indeed, the cvity roundtrip time, r, ppers to be the true 3. Q-switching. in semiconductor lsers is chieved by creting regions of sturble bsorption in Q-switching with the gin medium (Fig. 4). Two min solutions re used. The first one is the series 5 Iisturble bsorber ctive medium

9 time. The ltter must be lwys shorter thn the gin relxtion time in order to obtin emission. However, it my be shorter or longer thn the cvity roundtrip time, pulsed on the cvity length nd the bsorber mteril. The first sitution my priori led depending to mode-locking. The lser dynmics in the second sitution re similr to those of ginswitching. us focus on the second sitution. One difference with gin-switching is the possibility of Let opticl pulses with dc lser bis. In this pure Q-switching cse, the pulse generting is fixed by the recovery time of the gin medium. Another difference is relted to periodicity popultion in the bsence of light, r The stimulted bsorption term must be included s loss term in eqution (2). cross-section. solutions of rte equtions hve been proposed in reference [49]. Approximte difficult due to the presence of the sturble bsorber. The simplest pproch is to ssume n vlue for the -prmeter (Eq. (4) in Sect. 2). Under this ssumption, the chirp verge during the pulse is proportionl to the gin vritions s well s to the electron mplitude to be proportionl to pulse energy. expected 5 shows the results of time-resolved spectroscopic experiments perforrned with Q- Figure AlGAs lsers of different pulse energies [52]. The lsers re operted in singlemode switched with the injection of smll CW monochromtic rdition in the cvity [53]. The pulse is vried by chnging the ion-implnttion conditions, I.e., by chnging the sptil energy of the sturble bsorber in the cvity. Electricl pumping is chieved with 2 ns extension pulses t repetition rte of 40 MHz. Opticl pulse mesurements re mde with strek energy (13 pj), the chirp mplitude (15 A) is bout four times the cvity mode highest spcing. with electricl pumping. Beyond the performnce, one my notice the extremely high lser of the compression rte (17), the ltter being directly relted to. Such result vlue 1680 JOURNAL DE PHYSIQUE III N 9 The mechnisms involved in diode lser Q-switching depend on the bsorber relxtion shpe. Q-switched pulses exhibit shorter tils thn gin-switched pulses due to the pulse recovery t pulse end. However, the mjor interest of Q-switching stems from the bsorber chievement of very intense pulses under electricl pulse excittion. Absorber sturtion effects re simultneously combined with gin switching nd the gin t mximum my be two times higher thn the sturted cvity losses. As for gin-switching, good mthemticl description of Q-switching is provided by rte models. Equtions (I) nd (2) of section 2 re ccompnied by third eqution for eqution bsorber popultion density N. the dn N N A N S (5) The two terms on the right-hnd side of this eqution represent the spontneous crrier relxtion nd the stimulted bsorption, respectively. N is the equilibrium bsorber is the bsorber relxtion time nd A is the bsorber The precise description of phse modultion effects in the Q-switching regime is somewht vritions, liner reltion existing between g nd N. Since the number of emitted density is pproximtely equl to the number of lost electrons, the totl chirp mplitude is photons cmer. As seen, the chirp mplitude is found to regulrly increse with pulse energy. For the 6 shows results obtined in fiber compression experiments with the lser of highest Figure The pulsewidth mesured by utocorreltion is 22ps before compression. The energy. mesured fter compression is l.3 ps, which grees with previous mesurements pulsewidth strek cmer [25]. This result is the best reported to dte for Q-switched semiconductor by with semiconductor lser models which include gin non-linerities nd predict n grees of the forrn o I +P/P for high-power lsers [54]. However, the evolution

10 300keV proton implnttion -E2.5 pj c) HLP 1400 Hitchi lser with 11 MeV oxygen with -E5.8pJ; d) gin-guided AlGAs structure with 20MeV oxygen implnttion implnttion 0.6 d d I ' Dely, ps 6. Second-hrmonic utocorreltion trces of Q-switched pulses emitted by the gin-guided Fig. lser with 20 MeV oxygen implnttion. The trce width (FWHM) is 38 ps without exteml AlGAs contribution of the sturble bsorber should be explicitly tken into ccount for more The previous experimentl illustrtions clerly revel the possibility of very lrge phse- in single-mode Q-switched lsers. Due to high power levels resulting in strong modultion non-linerities, the ultimte performnces of Q-switching my be different from those lser 38 ps N 9 (SUB)-PICOSECOND PULSES IN SEMICONDUCTOR LASERS Time-resolved spectroscopic imges of single-mode gin-iq-switched lser pulses t Fig. m. ) HLP 1400 Hitchi lser without implnttion E 1.2 pj b) HLP 1400 Hitchi lser 0.83 E 33 pj ps 0.4? 2 o It becomes 2ps fter compression by 200m long fiber with totl dispersion of compression. ps/nm. A fctor of 0.65 is used to deduce the lser pulsewidths in the text. 24 complete nlysis. previously estblished for gin-switched lsers. In principle, the ultimte limit of chirp

11 mplitude is given by the gin-bndwidth. More relisticlly, chirp mplitudes of bout 40 h is known s the most efficient technique to produce extremely short opticl Mode-locking from lser sources. For semiconductor lsers, mode-locking is effectively superior to pulses the gin- nd Q-switching techniques concerning the mplitude nd timing jitter [30, 55] s well s the minimum width of the obtinble pulses [16, 17, 29, 38]. However, it is lso more Bsiclly, mode-locking is chieved by introducing mechnism inside the lser cvity to is to modulte the lser gin t frequency close to or multiple of the frequency mens between the longitudinl modes. This technique is referred to s ctive mode-locking. spcing conditions imposed to the bsorber relxtion time, r nd to the cvity supplementry time, r. The most fvourble sitution for pssive mode-locking occurs when : roundtrip cvity (Fig. 7b). On the other hnd, pssive mode-locking my lso occur when: r m r r. In principle, no exteml cvity is needed in tht cse, but very fst bsorbers implnttion in the first cse [33] while three-section lser with one reverse-bised section of the diode cvity, the longitudinl modes of the extended cvity cn be gthered presence different clusters, ech cluster being centered round one of the diode cvity resonnces. into 1682 JOURNAL DE PHYSIQUE III N 9 cn be expected t 0.8 m for pulse energy of 30pJ, which should correspond to 240 fs pulses fter compression. 4. Mode-locking. Among the lrge vriety of effects observed in mode-locked semiconductor lsers, complex. of them still remin unexplined. some cuse the longitudinl modes to interct with one nother thereby locking them in phse. One for stndrd semiconductor lser devices, the cvity mode spcing is beyond However, GHz nd it is very difficult to modulte the lser gin t these frequencies. Active mode- 100 requires the extension of the lser cvity. The most current solution consists of using locking exteml reflector, the inner diode fcet being ntireflection (AR) coted (Fig. 7). The n second solution is to relize specil devices such s monolithic extended-cvity lsers where the gin region is coupled to low-loss pssive wveguide [31, 56]. In both cses, the minimum pulse repetition rte is fixed by the cvity mode spcing wheres the mximum rte is limited by the lser modultion bndwidth. repetition other mens of chieving mode-locked lser pulses is to use sturble bsorber in the The lser cvity. This technique which is referred to s pssive mode-locking is best described in time domin. As for Q-switching (see Sect. 3), the sturble bsorber serves to shrpen the the pulse risetime while gin sturtion effects combined with fst bsorber recovery bring up bout n brupt termintion of the pulse [57-59]. The difference with Q-switching lies in the r r, r being the recovery time of the gin medium. Since r is of the order of I ns in r lsers, the previous condition cn be only fulfilled if the cvity length exceeds semiconductor few centimeters. As for ctive mode-locking, the experimentl solution is to use n externl be used. Mode-locked pulses were recently reported in two experiments without using must exteml cvity [33, 34] : the region of sturble bsorption ws relized by ion n ws used in the second cse [34]. Interest of such configurtions stems from the chievement very high pulse repetition rtes. The mjor drwbck is the wek level of emitted pek of As the gin medium cnnot fully recover between two successive pulses, the power. inversion rte lwys remins t low vlue. popultion complexity of the mode-locking process in semiconductor lsers mostly results from the The use of n exteml cvity. Even if the residul reflectivity of the AR coting is very low, sy 10-, the existence of the smll lser diode cvity cn never be ignored. In fct, the modelocked lser must be treted s two-cvity system. This sitution ws first nlyzed by Hus in 1980 [60, 61]. Figure 8 gives schemtic representtion in frequency-domin. Due to the

12 7. Bsic schemes of mode-locked semiconductor lser with extended cvity. ) ctive modelocking, Fig. b) pssive mode-locking. h I / $) """'j """" _/ locked modes 8. Mode-locking of nonidelly ntireflection coted lser diode in n exteml cvity. The Fig. of the diode cvity resonnces is simulted by influence periodic gin profile (compound gin) [60]. this simple picture, one imgines tht the different modes of given cluster cn esily Using together. In contrst, modes from neighboring clusters re not necessrily in phse with lock which gve the stedy-stte conditions for ech longitudinl mode [60, 61]. The eqution cvity resonnces were simulted by using periodic profile for the lser gin (see diode Fig. 8) nd the pulsewidth limits were evluted in this condition. N 9 (SUB)-PICOSECOND PULSES IN SEMICONDUCTOR LASERS 1683 ) b) bsorber _.- -., -. ' ' compound cvity gin cluster of Jl/ext r is the roundtrip time in the exteml cvity while r is the roundtrip time in the diode sub-cvity. Modes from neighboring clusters re not necessrily in phse with one nother. one nother. Mode-locking is then only prtilly relized nd the emitted pulses re fr to be trnsforrn-limited. The theoreticl description proposed by Hus ws bsed on single mster

13 1684 JOURNAL DE PHYSIQUE III N 9 equtions were lmost identicl to those given in section 2, except tht delyed feedbck lser instbilities where shown to occur when the roundtrip time in the externl cvity ws thn the period of recurrence for the current pulses [64]. For the short pulse regime shorter «r), the rte equtions were modified to include propgtion effects in the diode cvity (AT Trnsverse effects my be lso of some importnce s reveled by recent experiments on of oxygen ions through the rer fcet of the diode. The other fcet is used for implnttion to the externl cvity. The bsence of AR coting in the present experiments plces coupling of n AR coted microscope objective for bem collimtion nd n end-mirror comprised totl reflection. Under norrnl conditions, the lser diode is dc bised. A modultion with tht the mode-locked lser output is composed of pulse trins, the pulse spcing being cler roundtrip time in the semiconductor mplifier ( 8 ps). For most of the experimentl the 0.7ps, which pproximtely corresponds to phse-locking of five clusters of modes The pulsewidth, AT, is lrger thn the roundtrip time in the diode cvity, r. () zj is the roundtrip time in the externl cvity while k determines the rte of opticl feedbck. (*) the erlier work of Hus, mode-locking of semiconductor lsers in n exteml Following ws further nlyzed in time-domin by severl uthors [30, 62-67]. Except for one cse cvity nlyses were directed t ctive mode-locking nd numericl simultions were [63], from rte eqution models. For the long pulse regime (AT performed r) (*), the bsic term of the form k. S (t r) (**) ws included in the photon density eqution to ccount for the effect of the exteml cvity [64, 65]. In greement with experimentl observtions, with the boundry conditions t both the inner diode fcet nd the externl reflector together 66-68]. In contrst, gin non-linerities were ignored for the ske of simplicity. The [30, existence of non-idel AR coting t the inner diode fcet ws found to result in the emission of lser pulse trins insted of regulr mode-locked pulses, the time seprtion between successive pulses of given pulse trin being the roundtrip time in the diode cvity. In with mesurements [29, 30], pulse trins consisting of three pulses greement utocorreltion for residul reflectivities s low 10-. s clculted were in spite of these theoreticl fits, lser models still remin undpted to predict However, trnsition from the long pulse regime to the short pulse regime, I-e- from prtil mode- the to full mode-locking. Experimentlly, this trnsition bruptly occurs for certin locking of the exteml cvity nd/or for creful djustment of the feedbck coupling [29]. tuning The behviour is indifferently observed in pssive nd ctive mode-locking. In view of results in sections 2 nd 3, it is cler tht chirping effects ply n importnt role in reported lsers. Improved models must then necessrily tke them into ccount. semiconductor other mode-locked systems such s Ti Spphire lsers [69, 70]. Experimentl nd theoreticl should be crried out in this direction for better understnding of investigtions lser dynmics. semiconductor 9 shows recent results obtined by the uthors on pssively mode-locked AlGAs Figure The experimentl scheme is close to tht presented in figure 7b. A commercil lser. HLP1400 Hitchi lser diode is used. The sturble bsorber is creted by n lo MeV the fcet reflectivity to stndrd vlue of 30 fb. The exteml cvity is 15 cm long nd is source cn be dditionlly used to synchronize the pulses on n exteml reference clock. The utocorreltion trces reported in figure 9b well illustrte the previous discussion. It is conditions, the contrst between pulses is moderte : the modultion rtio is less thn 60 fb curve). However, n brupt chnge is observed for certin tunings of the exteml (dotted nd the modultion rtio increses up to 90fb (solid curve). Simultneously, the cvity emitted spectrum is shifted towrds shorter wvelengths nd the spectrl width is incresed from 25 to 45h (Fig. 9). The minimum pulsewidth deduced in these conditions is

14 N 9 (SUB)-PICOSECOND PULSES IN SEMICONDUCTOR LASERS I Ml Wvelength, nm Dely, ps (Al 15 A). The verge output power is 4 mw, thereby indicting pek-powers round I W. The perforrnnces re comprble to those previously published by Vn der Ziel et [16]. l. for Q-switching, the minimum pulsewidth obtinble by mode-locking is, in principle, As developments cn be expected in severl directions. One importnt direction is to go Future femtosecond pulses. Reserch in this field is not only motivted by pplictions, but towrds lser medi. From discussions in sections 1, 2 nd 3, it is cler tht pulsewidths semiconductor 300fs lredy pper to be fesible. Recent results obtined by opticl pumping below pulse genertion, but optimized AR cotings (R10) re needed to eliminte short effects in extended cvities. On the other hnd, gin or Q switching in verticl prsitic cvity surfce emitting lsers (VCSEL) offers gret promise [71]. Interest of VCSEL structures stems from tile wek opticl thickness of the gin medium ( l m) leding in tum to very short cvity lengths ( 10 m). Sub-femtosecond pulse-to-pulse timing jitters cn be io 8pS o-g s fi ) b) 9. Mesured spectrum ) nd utocorreltion trces b) of pssively mode-locked AlGAs lser Fig. 15 cm long exteml cvity. Dotted curve nd solid curve in b) respectively correspond to two with different tunings of the exteml cvity (see text). determined by the inverse of the gin-bndwidth. This should priori led to femtosecond ( 20 fs) since the gin-bndwidth typiclly scles from 20 to 60 nm in semiconductor pulses On the other hnd, some recent clcultions from rte-eqution models plced the lsers. limit just below I ps in the cse of ctive mode-locking [68]. Note tht the uthors finlly bout the existence of pure «ctive mode-locking». A more direct estimtion cn questioned mde from the spectrl width of the lser emission. In pulsed regime, lser diodes cn emit be to 30 modes of resonble mplitude (15 modes re obtined in Fig. 9). In the cse of up lsers t 0.8 m, this pproximtely corresponds to spectrl width of 90 A nd AlGAs trnsform-limited pulses of 100 fs cn be envisged. 5. Prospects of further developments. it is lso of fundmentl interest for better knowledge of trnsient phenomen in confirm this ssertion [40]. Mode-locking remins the most efficient technique in terms of when spontneous emission is loclized in n ctive region of such smll thickness. expected VCSEL structures consisting of wells of different widths lso pper Multiple-quntum-well

15 require Fourier trnsform-limited pulses of djustble length t 1.55 m. Perhps, one of the long pulses re needed to minimize pulse distorsions nd dispersive wve rdition, Actully, resulting from the use of lumped mplifiers regulrly spced long the opticl link [72]. both technique for relizing such pulses is to use mode-locking in n exteml selective cvity One the pulsewidth being djusted with spectrl filtering in the cvity. However, solutions [73], bsed on monolithic cvities re preferble for opticl communiction pplictions. Investi- re presently crried out in this direction. A first solution is to chieve mode-locking gtions very long monolithic cvities with integrted Brgg reflector [56]. A second solution is to in lsers with smll phse-mplitude coupling fctors must be designed in order to Single-mode the length of the dispersive fiber needed for compression. Strined-lyer multiple- limit DFB lsers re good cndidtes [74]. quntum-well semiconductor lsers ble to deliver picosecond pulses of high energy re desired Finlly, with lrger emitting surfces. Severl solutions cn be considered : I) brod stripe lsers it) lser diode rrys, iii) lsers with stripe of lrge thickness (1-2 m), iv) verticl lsers, surfce emitting lsers (VCSEL). The two first solutions re commercilly vilble, cvity trnsverse mode control is difficult. Solution iii) presents the dvntge of output bems but could not be specificlly treted in this context. Actully, the development low-dimensionlity low-dimensionlity lsers s other recent developments is not necessrily motivted by of 1686 JOURNAL DE PHYSIQUE III N 9 to be n interesting solution for the reliztion of semiconductor lsers with wide ginbndwidth. importnt evolution of picosecond semiconductor lsers is dictted by the rpid Another in the field of opticl soliton trnsmission. Long-hul soliton trnsmission in fibers progress most surprising chllenge is the reliztion of coherent semiconductor lser pulses with durtions of severl tens of picoseconds nd repetition rtes scling from 2.5 to 10 Gbit/s. extend the fiber compression technique to the cse of gin-switched pulses of long durtion. for lrge number of pplictions. For instnce, 200pJ pulses re typiclly required for triggering of fst electronic circuits. Up to now, the output energy of semiconductor opticl rrely exceeds 30 pj in the short-pulse regime nd there is room for improvement. The lsers mximum intensity which cn propgte in the lser medium is determined by the two-photon threshold. A typicl vlue is 109 W/cm2. For lser stripe of stndrd trnsverse bsorption (0.2 x 2.5 m), the mximum pek-power is then round 5W nd the dimensions mximum energy emitted in lo ps pulse is 50 pj. Further improvements require the use of with wek trnsverse ellipticity. However, CW opertion is excluded. Solution iv) priori the lrgest emitting surfces. A quick estimte indictes tht pek powers up to provides W should be obtined with solutions I), it) or iii). Still one order of mgnitude could be 100 gined with solution iv). 6. Concluding remrks. This pper hs reviewed the current understnding of short pulse genertion in semiconductor The different methods used to generte short pulses hve been nlyzed in detils, lsers. of the results presented for illustrtion being new. Possibilities of further improvements some hve been lso discussed. However, some importnt spects relted for instnce to lsers of to short pulse genertion nd high-speed modultion. Moreover, the lser pplictions re not relted in performnces simple mnner to the mteril prmeters. For instnce, it is now estblished tht quntum well wveguide lsers do not exhibit better perforrnnces thn bulk lsers of the sme geometry. In contrst, progress complished in the growth of thin semiconductor lyers llows the reliztion of new geometries such s verticl cvity lsers which re of gret promise for high-power short-pulse genertion.

16 MOLLENAUER L.F., NYMAN B. M., NEUBELT M.J., RAYBON G., EVANGELIDES S.G., Ill of soliton trnsmission t 2.4 Gbit/s over km, Elecn.on Lett. 27 (1991) Demonstrtion [3] IWATSUKI K., SusuKI K., NISHI S., SARUWATORI M., Observtion of 10 Gb/s opticl soliton over 000 km using gin-switched DFB-LD pulse source, 17th Europen Conference on Opticl 10 ECOC'91 (Pris 1991) Post-dedline pper, pp Communictions TAKADA A., SARUWATARI M., 100 Gbit/s opticl signl genertion by time-division multipliction [4] modulted nd compressed pulses from gin-switched distributed feedbck (DFB) lser of Electron Lett. 24 (1988) diode, TUCKER R. S., EISENSTEIN G., KOROTKY S. K., Opticl time-division multiplexing for very high- [5] bit-rte systems, Conference on Lser nd Electro-Optics CLEO 88 (Anheim 1988), pper DUVILLARET L., CHussEAu L., LouRTioz J.-M., Electro-optic Smpling of GAs circuits using [6] lsers, 3rd Europen Conference on Electron nd Opticl Bem Testing of semiconductor Circuits (Como 1991), Conf. Digest, pp Integrted WIESENFELD J. M., TAYLOR A. J., TUCKER R. S., EISENSTEIN G., BuRRus C. A., Electro-optic [7] using injection lsers, SPIE Proc. 795 (1987) smpling HALL R. N., FENNER G. E., KINGSLEY J. D., SOLTYS T. J., CARLSON R. O., Coherent light [8] LASHER G. J., Anlysis of proposed bistble lser, Solid Stte Electron. 7 (1964) [9] V.D., MAGALYAS V. I., PLESHKOV A.A., RIVLIN L.A., TRUKHAN V.G., [IOjKURNOSOV [I Ii MoRoZov V. N., NIKITIN V. V., SHERONOV A. A., Self synchroniztion of modes in GAs ZAKHAROV Y. P., KOMPANETS I. N., NIKITIN V. V., SEMENOV A. S., Synchroniztion of gllium [12] lser light pulses, Sov. Phys. JETP 26 (1968) rsenide GLODGE D., LEE T. P., Study of self-pulsing GAs lser by intensity correltion in Lithium [14] J. Appl. Phys. 42 (1971) Iodte, VAN DER ZIEL J. P., TSANG W. T., LOGAN R. A., MIKULYAK R. M., AUGUSTYNIAK W. M., [16j Sub-picosecond pulses from pssively mode-locked GAs buried opticl guide T.P., YOKOYAMA H., ITO H., INABA H., Genertion of sub-picosecond coherent opticl pulses by [17] mode-locking of n AlGAs semiconductor diode lser, Appl. Phys. Lent. 40 (1982) pssive ASPiN G. J., CAROLL J. E., PLUMB R. G., The effect of cvity length on picosecond pulse [18] with highly rf modulted AlGAs double heterostructure lsers, Appl. Phys. Lent. genertion N 9 (SUB)-PICOSECOND PULSES IN SEMICONDUCTOR LASERS 1687 Acknowledgment. The uthors cknowledge the vluble nd expert ssistnce of D. Pscl in the course of experiments. References [2] NAKAzAWA M., Opticl soliton communiction using Erbium-doped fibre mplifier, 17th Euro- Conference on Opticl Communictions ECOC' 91 (Pds 1991) Invited pper, pp pen l55. TUKS. emission from GAs junctions, Phys. Rev. Lett. 9 (1962) TsvETKov V. V., Self modultion of emission from n injection semiconductor lser, JETP Lett. 4 (1966) semiconductor injection lser, JETP Lett. 7 (1968) HARRIS E. P., Spiking in current-modulted CW GAs exteml cvity lsers, J. Appl. Phys. 42 [13] (1971) [15] Ho P. T., GLASSER L. A., IPPEN E. P., HAus H. A., Picosecond pulse genertion with CW GAlAs lser diode, Appl. Phys. Lett. 33 (1978) semiconductor lsers, Appl. Phys. Lett. 39 (1981) (1981)

17 1688 JOURNAL DE PHYSIQUE III N 9 HENRY C. H., Theory of the linewdith of semiconductor lsers, IEEE J. Quntum Electron. QE-18 [19] (1982) [20] KOCH T, L., BowERs J. E., Nture of wvelength chirping in directly modulted semiconductor KOCH T. L., LINKE R. A., Effect of nonliner gin reduction on semiconductor lser wvelength [21] Appt. Phys. Lent. 48 (1981) chirping, [22] TAKADA A., SUGIE T., SARUWATARI M., Trnsform-limited 5.6ps opticl pulse genertion t GHz repetition rte from gin-switched distributed feedbck lser diode by employing 12 compression technique, Electron. Lent. 22 (1986) pulse CHUSSEAU L., XIE J.M., DUVILLARET L., LOURTIOZ J.-M., ACCARD A., HEBERT J.-P., [24j 0.3 W picosecond pulses (4 ps) from Bndwidth-limited 1.53 m microwve modulted DFB STELMAKH N., LouRTIoz J.-M., BARTHELEMY A., Ultrshort pulse genertion from Q-switched [25] lser with CW injection, Appl. Phys. Lent. 59 (I99I) , AlGAs SILBERBERG Y., SMITH P. W., Subpicosecond pulses from [26] mode-locked semiconductor lser, J. Quntum. Electron. QE-22 (1986) IEEE EISENSTEIN G., TUCKER R. S., KOREN U., KOROTKY S. K., Actively mode-locking chrcteristics [28] InGASP-single mode fiber composite cvity lsers, IEEE J. Quntum Electron. QE-22 of mode-locked GInASP lser with Subpicosecond output, Appl. Phys. Lett. 52 (1987) Actively BowERs J. E., MORTON P. A., MAR A., CORzINE S. W., Actively mode-locked semiconductor [30] IEEE J. Quntum Electron. QE-25 (1989) lsers, II TUCKER R. S., KOREN U., RAYBON G., MILLER B. I., KocH T. L., EISENSTEIN G., Active modelocked [3 in 1.5 m monolithic extended cvity lser, Electron. Lent. 25 (1989) VASIL'EV P. P., SERGEEV A. B., Genertion of bndwidth-limited 2ps pulses with I00GHz [32] rte from multisegmented injection lser, Electron. Lett. 25 (1989) repetition ZARRABI J. H., PORTNOI E. L., CHELNOKOV A. V., Pssive mode locking of multistripe single [33] well GAs lser diode with n intrcvity sturble bsorber, Appl. Phys. Lent. 59 quntum (I99I) CHEN Y. K., Wu M. C., TANBUN-EK T., LOGAN R. A., CHIN M. A., Subpicosecond monolithic [34] mode-locked multiple quntum well lsers, Appl. Phys. Lett. 58 (1991) colliding-pulse l255. TSUCHIYA Y., MIWA M., KoisHi M., Direct observtion of picosecond light pulses from pulsecurrent [35] pumped semiconductor lser, J. Appl. Phys. 53 (1982) VASIL'EV P. P., Picosecond injection lser : new technique for ultrfst Q-switching, ieee J. [36] Electron. 24 (1988) Quntum (1989) DELFYETT P. J., LEE C. H., FLOREZ L. T., STOFFEL N. G., GMITTER T. J., ANDREAKIS N. C., [38j G. A., CONNOLLY J. C., Genertion of sub-picosecond high-power opticl pulses ALPHONSE hybrid mode-locked semiconductor lser, Opt. Lent. 15 (1990) I37I from XIANG W. H., FRIBERG S. R., WATANABE K., MACHIDA S., SAKAI Y., IWAMURA H., [40j Y., Sub-100 femtosecond pulses from n exteml-cvity surfce emitting YAMAMOTO lsers, Electron. Lett. 20 (1984) TAKADA A., IwATsuKi K., SARUWATARI M., Picosecond lser diode pulse mplifiction up to [23] W by lser diode pumped erbium-doped fiber, ieee Photon. Technol. Lent. 2 (1990) l24. lser with fibre compression, Electron Lett, 26 (1990) KUHL J., SERENYi M., GOBEL E. O., Bndwidth-limited picosecond pulse genertion in n [27] mode-locked GAs lser with intrcvity chirp compenstion, Opt. Lett. 12 (1987) ctively (1986) CORZINE S. W., BOWERS J. E., PRZYBYLEK G., KOREN U., MILLER B. I., SOCCHOLICH C. E., [29j PORTNOI E. L., STEL'MAKH N. M., CHELNOKOV A. V., Chrcteristics of heterostructure lsers [37] sturble bsorber fbricted by deep ion implnttion, Sov. Tech. Phys. Let'. 15 with NAKASAWA M., SusuKi K., YAMADA E., Femtosecond opticl pulse genertion using [39] lser diode, Electron. Lett. 26 (1990) distributed-feedbck

18 InGAs/InP multiple quntum well lser with soliton-effect compression, Appl. Phys. Lett (1991) LAU K., Short pulse nd high frequency signl genertion in semiconductor lsers, J. Lighnvve [41] Buus J., Propgtion of chirped semiconductor lser pulses in monomode fibers, Appl. Opt. 24 [42] (1985) sinusoidl current modultion: modeling nd experiments t 1.3m, ieee J. strong Electron. 26 (1990) Quntum TUCKER R. S., High-speed modultion of semiconductor lsers, J. Ligthwve Technol. LT-3 (1985) [46] NAGARAJAN R., FUKUSHIMA T., BowERs J. E., GEEL R. S., COLDREN L., High-speed [47] strined multiple quntum well lsers with low dmping, Appl. Phys. Lett. 58 InGAs/GAs (1991) ] VAN DER ZIEL J. P., TSANG W. T., LOGAN R. A., AUGUSTYNIAK W. M., Pulsting output of confinement buried opticl guide lsers due to the deliberte introduction of seprte loss, Appl. Phys. Lent. 39 (1981) sturble KUZNETSOV M., Pulstions of semiconductor lsers with proton bombrded segment welldeveloped [49] pulstions, ieee J. Qunt. Electron. QE-21 (1985) ALFEROV Zh. I., ZHULAREV A. B., PORTNOI E. L., STELMAKH N. M., Picosecond pulses from Q- [50] injection heterostructure lsers, Sov. Tech. Phys. Lent. 12 (1986) switched TSANG D. Z., WALPOLE J. N., Q-switched semiconductor diode lsers, ieee J. Qunt. Electron. [51] (1983) QE-19 STELMAKH N., LOURTIOZ J.-M., Anlysis of modl chirp in Q-switched semiconductor lsers, 152] Lett. 27 (1991) Electron. [54] AGRAWAL G. P., Intensity dependence of the linewidth enhncement fctor nd its impliction for DERICKSON D. J., MAR A., BowERs J. E., Reltive nd bsolute timing jitter in ctively modelocked [55] semiconductor lsers, 12th IEEE Intemtionl Semiconductor Lser Conference 1990) Conf. Digest, pp (Dvos RAYBON G., HANSEN P. B., KOREN U., MILLER B. I., YOUNG M. G., CHIEN M., BURRUS C. A., [56j HAus H. A., Theory of mode-locking with slow sturble bsorber, ieee J. Quntum Electron. [58] (1975) QE-11 HAus H. A., Theory of mode-locking with fst sturble bsorber, J. Appl. Phys. 46 (1975) [59] HAus H. A., Theory of ctive mode-locking of semiconductor lser in n exteml cvity, J. Appl. [60] 51 (1980) Phys. HAus H. A., Mode-locking of semiconductor lser diodes, Jpn J. Appl. Phys. 20 (1981) [61] l020. N 9 (SUB)-PICOSECOND PULSES IN SEMICONDUCTOR LASERS 1689 Technol. LT-7 (1989) [43] HEMERY E., CHussEAu L., LouRTioz J.-M., Dynmic behviours of semiconductor lsers under [44j CAVELIER M., STELMAKH N., XIE J.-M., CHUSSEAU L., LOURTIOZ J.-M., KAZMIERSKI C., BOUADMA N., Picosecond (2.sps) wvelength-tunble (20nm) semiconductor lser with repetition rtes up to 12 GHz, Electron. Lett. 28 (1992) pulses WAGNER W. G., LENGYEL B. A., Evolution of the gint pulse in [45] lser, J. Appl. Phys. 34 (1963) STELMAKH N., LouRTioz J.-M., JULIEN F. H., Injection-locking of Q-switched AlGAs lser with [53] sturble bsorber, Electron. Lett. 27 (1991) fst semiconductor lsers, ieee Photon. Technol. Lett. 1(1989) ALFERNESS R. C., A monolithic extended-cvity lser with n integrted Brgg reflector for ctive mode-locking t 8.3 GHz, 17th Europen Conference on Opticl Communictions ECOC'91 (Pris 1991) Postdedline pper, pp KRYUKOV P. G., LETOKHOV V. S., Fluctution mechnism of ultrshort pulse genertion by lser [57] sturble bsorber, ieee J. Quntum Electron. QE-8 (1972) with VAN DER ZIEL J. P., AcIive mode-locking of double heterostructure lsers in n exteml cvity, J. [62] Phys. 52 (1981) Appl.

19 HAus H. A., SILBERBERG Y., Theory of Mode-locking of lser diode with multiple-quntumwell [63] structure, J. Opt. Soc. Am. B 2 (1985) CHESNOY J., KLEIN M. C., CHussEAu L., LouRTIoz J.-M., Period-doubling nd periodqudrupling [65] for n ctively mode-locked lser diode with extended cvity, J. Appl. Phys (1990) DEMOKAN M. S., A model of diode lser ctively mode-locked by gin modultion, Int. J. [66] SCHELL M., WEBER A. G., BnTTCHER E. H., SCHOLL E., BIMBERG D., Theory of sub-picosecond [67] genertion by ctive modelocking of semiconductor lser mplifier in n exteml pulse limit for the pulsewidth, IEEE J. Quntum Electron. QE-27 (1991) cvity SCHELL M., WEBER A. G., SCHOLL E., BIMBERG D., Fundmentl limits of sub-ps pulse [68] [69] NEGUS D. K., SPINELLI L., GOLDBLATT N., FEUGNET G., Sub-100 fs pulse genertion by Kerr Postdedline pper PD ) SALIN F., SQUIER J., MouRou G., PicHt M., MCCARTHY N., Mode-locking of Ti A120 using [70] self-focusing, Advnced Solid Stte Lsers Conference (Hilton Hed 199I) Postdedline KARIN J. R., MELCER L. G., NAGARAJAN R., BOWERS J. R., CORZmE S. W., MORTON P. A., [7ij R. S., COLDREN L. A., Genertion of picosecond pulses with gin-switched GAs GEELS lser, Appl. Phys. Lett. 57 (1990) surfce-emitting MOLLENAUER L. F., EVENGELIDES S. G., HAus H. A., Long-distnce soliton propgtion using [72] mplifiers nd dispersion-shifted fiber, J. Lighnvve Technol. 9 (1991) lumped LUNDQVIST S., ANDERSSON T., ENG S. T., Genertion of tunble single-mode picosecond pulses [73] KANO F., YosHiKuNi Y., FUKUDA M., YOSHiDA J., Linewidth enhncement fctor of 1.3 m [74] strined-lyer multiple-quntum-well DFB lsers, IEEE Photon. Technol. Lent. InGAsPflnP 1690 JOURNAL DE PHYSIQUE III N 9 [64] GARSIDE B. K., KEMPF P., Influence of diode fcet reflectivity on the dynmics of ctively modelocked semiconductor lsers, Appl. Opt. 25 (1986) Electron. 60 (1986) by ctive modelocking of semiconductor lsers the spectrl gin width nd the genertion reflectivities, IEEE J. Quntum Electron. QE-27 (1991) fcet Lens mode-locking InTi A1203, Advnced Solid Stte Lsers Conference (Hilton Hed pper PDS. from n AlGAs semiconductor lser with grting feedbck, Appl. Phys. Lent. 43 (1983) (1991)