Mesurements of reltive intensity noise (RIN) in semiconduct lsers Irène Joindot To cite this version: Irène Joindot. Mesurements of reltive intensity noise (RIN) in semiconduct lsers. Journl de Physique III, EDP Sciences, 1992, 2 (9), pp.1591-1603. <10.1051/jp3:1992201>. <jp-00248828> HAL Id: jp-00248828 https://hl.rchives-ouvertes.fr/jp-00248828 Submitted on 1 Jn 1992 HAL is multi-disciplinry open ccess rchive f the deposit nd dissemintion of scientific reserch documents, whether they re published not. The documents my come from teching nd reserch institutions in Frnce brod, from public 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 lbtoires publics ou privés.
of reltive intensity noise (RIN) in Mesurements lsers semiconduct CNET-LAB/OCM, route de Tr6gstel, BP 40, F-22301 Lnnion, Frnce intensity noise (RIN). In this pper very ccurte mesurement technique is presented reltive results re given on some components. RIN mesurements on isolted longitudinl modes nd electric field ffected by mplitude intensity noise (the topic of this pper), nd phse system. BRefly speking, intensity fluctutions re me imptnt in direct detection prmeter which describes the intensity noise is clled RIN (Reltive Intensity Noise). The ought to pper now in dt sheets. The reson f this new interest hs been brought bout It the im of noise investigtions s function of frequency is to know the intrinsic Finlly, without the prsitic elements circuit. bndwidth 1. Theeticl re.clls on intensity fluctutions of opticl sources. illuminted by n opticl source is the sum of two terms [2] : J. Phys. III Frnce 2 (1992) 1591-1603 SEPTEMBER 1992, PAGE 1591 Clssifiction Physics Abstrcts 42.60 Irbne Joindot (Received 14 November 1991, ccepted 30 Mrch 1992) Abstrct. The intensity fluctutions of the lser diodes light re chrcterized by the so-clled cn explin how the energy is shred between the modes. Introduction. Like other electronic devices, semiconduct lsers exhibit noises. A semiconduct lser is n imperfect opticl oscillt, emitting wves, the results of which re described by n noise. The igin of these noises must be sought in the discontinuous nture of the frequency bsption nd emission, nd the crrier genertion nd recombintion processes. photons The intensity fluctutions of the light bem emitted by lser diode, even when it is CW bised in very stble mnner, impress n ultimte limit to ny opticl communiction while phse fluctutions re me imptnt in coherent systems especilly when systems, heterodyne receiver is used to cncel the locl oscillt intensity noise. blnced recent ide of using semiconduct lsers in lightwve multi-chnnel nlog mplitude the video distribution systems, in the lo MHz-800 MHz bnd. The necessry signl- modultion to-noise rtio requires RIN vlue s low s 155 db/hz [I]. In this pper, the described mesurement technique cn rech RIN vlues s low s -170 db/hz. The noise spectrl density of the photocurrent fluctutions t the output of detect wf) =2,q.I+1).RIN if) (1)
where RIN mens «Reltive Intensity Noise» : j (2) () is by mplitude stbilized perfect lser, the power spectrl When detect illuminted of the light intensity is equl to zero nd the noise of the fluctutions the of density to mesure pure shot noise, becuse with such source, the second term of the right sy, of eqution (I) is much lower thn the first term : shot noise is much higher thn member must not exceed 100 200 LA. photocurrent superluminescent diode (SLD) is n incoherent source with n inteml gin [4]. Its A output power is much higher thn the LED opticl power nd its opticl spectrl opticl much lower thn the LED bndwidth. Thusfr, when detect is illuminted by bndwidth SLD, excess noise cn be observed bove the pure shot noise, s it will be shown lter. So we obtined by dding to the well-known rte equtions, Lngevin fluctutions operts usully shot noise chrcter [9] : fn(t) f electrons nd fs(t) f photons. In hypothesis, the hving shot noise. They re uncrelted noise sources nd their vrinces dd. Rte equtions re 1592 JOURNAL DE PHYSIQUE III N 9 RIN if = is the verge vlue of the output photocurrent, q is the electron chrge, (3) is the I intensity of the opticl field, Wj if is the power spectrl density of the opticl verge intensity fluctutions. The first term of reltion (I), well known s «shot noise», is the result of the discontinuous nture of electrons nd photons. In the second term the one-sided power spectrl density of the reltive fluctutions of the opticl source clled RIN, ppers : it is prmeter of the source nd not of the detect. And so, to know me bout RIN, it is necessry to opticl the opticl source. exmine is pure shot noise. Let us exmine some other opticl sources. photocurrent light emitted by incoherent therml sources consists of the superposition of elementry The fields which rise when different toms spontneously emit light [3]. The RIN is independent to the coherence time rc of the source. Light emitting diodes (LED) re therml equl Gussin sources. The opticl bndwidth AA of surfce emitting LED lies between 400 nd 600 h round I Lm emitted wvelength : I/ jr rc = 30 AA IA ). So surfce emitting LED will be used to clibrte our RIN mesurement set-up, tht is to excess noise due to the opticl source. But ccding to the opticl bndwidth, the cnnot mesure pure shot noise with SLD. In the erly seventies, semiconduct lser diodes were considered s crude devices, but now, buffed structures (BH) nd distributed feedbck structures (DFB) cn compete with solid stte gs lsers. The next prgrphs will be devoted to noise properties of semiconduct lser diodes. 2. Modelistion of intensity noise in semiconduct lsers. The spectrl density of the quntum fluctutions of the photons nd electrons popultion is noise sources f(t) et fs(t) re Gussin rndom processes nd their uto- nd crossreltion functions re proptionl to Dirc distributions. Ech process such s bsption emission of photon, rrivl deprture of n electron from the conduction bnd is source of ssuming smll increment round sttionry vlue nd s; being the totl number linerized, photons in the I-th mode t wvelength Ai, we will write : of s, it) = S + As, (t) (3) At first we will consider single mode lser. In the frequency domin, it is esy to clculte
N 9 RELATIVE INTENSITY NOISE IN SEMICONDUCTOR LASERS 1593 = 2 wf, f being the bsebnd frequency t which the noise is nlysed (f further detils, see [2]). The expression of ( [As ill )]) contins denomint which cn be written s f f( ) + ( &/2 w), f nd revels resonnce frequency f nd dmping fct &. fct in simple mnner. This prmeter is defined s follows : Pop This prmeter equls to I in totlly inverted lser nd lies between 2 3 in =. P P i) j5) r is the spontneous rditive recombintion lifetime. f( is proptionl to I/I I. dmping fct is dominted by extr effects like crriers diffusion [5] gin The by the photons of the powerful mode [6] : gin compression increses the compression Deriving the exct expression of RIN is rther tedious nd cumbersome but crude nd injected into the mode : 4 p r n) (III s 1) RIN decreses like (I/Is 1) like the output power to the minus 3 (the output power NoisE MEASUREMENT EXPERIMENTAL SET UP. Mesurements of reltive intensity 3.I hve been crried out, in our lbty f mny chips on submount lsers, emitting in noise by n opticl ttenut, slightly tilted off xis, nd is collected through long reduced distnce microscope objective (MO). The photodiode (PIN) photocurrent is wking frequency (800 MHz to 10 GHz) noise mesurement chnnel with locl oscillt. The low the two-sided power spectrl density of the fluctutions of photons number ([As(J2)]), where J2 nd & hve the sme expression s the resonnce frequency nd dmping fct of the f response modelistion. modultion The inversion popultion prmeter helps to express resonnce frequency nd dmping Ns (4) where N is the electron number t threshold nd No the electron number t trnsprency. semiconduct lser. So bove threshold (me thn 20 fb), simplified expression of the resonnce frequency cn be derived : f( 4, w T4 Ts Is where I is the injection current, I the threshold current, r is the photon lifetime, nd fct. dmping simple pproximtion cn be found [2] t zero frequency nd between 20 nd 30 fb bove very (with n err less thn lo fb), where p is the frction of spontneous emission threshold ( RIN 2 = (6) S being proptionl to I/Is 1). 3. Experimentl techniques. single trnsverse mode, using the well-known single-detect technique. The experimentl is shown in figure I. To lower the opticl feedbck, the light output power is first set-up fed into lock-in mplifier either through I kq resistnce, either through low sequentilly (30 MHz with I MHz bndwidth) noise mesurement chnnel, through high frequency
1594 JOURNAL DE PHYSIQUE III N 9 ser cmer grting oudroti etection ( ) frequency mesurement chnnel consists of Trontech L30B mplifier followed by 3 db ttenut, 30 MHz Telonic filter, SCD Nucldtude mplifier nd lo db ttenut. A mplifier. desk computer drives the sequences, selects the lock-in best scle, gthers nd verges A electronics, fter stepping up the lser current. 1 r%j s # l 3 fij' j ' jf Attenut Bttery q ' supply nochromt Fig. I. ExpeRmentl set-up. Nucldtude widebnd mplifier is the first stge of the high frequency mesurement chnnel. Then the locl oscillt is lunched through RF mixer. This chnnel is ended by 30 MHz Telonic filter nd 6 db ttenut. Finlly, the 30 MHz chnnel is used s the intermedite frequency the photocurrent, the cresponding noise level vlues nd the zero (drkness) noise of the
shown t the end of this pper. 3.2 RIN (RELATIVE INTENSITY NoisE) MEASUREMENTS. At first we clibrte our experimentl set-up using n incoherent source : surfce light emitting diode t 0.85 1.3 Lm. ppers bove the shot noise, especilly t lser threshold. With this clibrtion process, RIN Noise dt nd photocurrent dt re ccumulted s long s the required ccurcy mplifier. not obtined. With this experimentl technique we cn mesure RIN vlues s low s is Lo f A. Fig. 2. - oise N 9 RELATIVE INTENSITY NOISE IN SEMICONDUCTOR LASERS 1595 Jobin-Yvon opticl spectrometer (HRS1000) is used to select one two Eventully, modes to perfm prtition noise cross-reltion mesurements, s will be longitudinl check tht, t ech frequency, pure shot noise with power spectrl density proptionl We the photocurrent I is obtined. Then the LED is replced by the lser nd excess noise to mesurements results re only dependent on the exct vlue of the photocurrent, s shown by the following expression ' ( RIN l (8) = Ih (Ai) is the noise spectrl density when the detect is illuminted by the lser nd (Ai) when it is illuminted by the LED. The rtio between the two noise terms cncels the (Ai() conversion fct between noise level nd voltge level t the output of the synchronous 170 db/fiz with 20 fb err if the photocurrent is higher thn 200 LA nd if there re 200 ccumulted dt. figure 2, we cn see the noise spectrl density when the detect is illuminted by LED, In SLD nd lser (LD) : the noise obtined with SLD is different from pure shot noise. lo Noise spectrl density, A. A. + '..', lo li - diode (SLD) superluminescent
4. Globl noise mesurements. Globl noise mens tht ll the modes re gthered on the detect, while when the modes 4. I GENERAL FEATURES OF THE NOISE. the end the decresing steepens. The pek frequency increses with the injection current P just bove the threshold (in greement to reltion (7)) nd like P fr from the tht moment its RIN increses with its coherence time, this coherence time being inversely t to the opticl bndwidth. The smll gin just befe the threshold reduces the proptionl the opticl mode to the stripe vicinity. By contrst in index guiding lsers the opticl confines confinement occurs through lterl vrition of the refrctive index of the ctive lyer. mode p cn be up to 25 times greter in gin guiding lsers compred to index guiding prmeter [7]. lsers cvity is fmed by cleved fcets t ech end of the device, the multimode emission is 1596 JOURNAL DE PHYSIQUE III N 9 re seprted by dispersive medium (f instnce spectrometer), the noise induced by the shre of intensity is clled «mode prtition noise». 4.I.I Noise s function of frequency. At low frequency, from 0 to round 50 khz, the noise hs I/f behviour s in ny semiconduct device. Then, up to some hundreds of the noise exhibits flt, nd beyond lghz pek with mximum meghertz, the relxtion frequency between photons nd electrons in the cvity, nd t cresponding bove the threshold. 4.1.2 Noise s function of injection current. In the flt region of the spectrum (50 khz- MHz), the reltive intensity noise reches its smllest vlue. As function of the injection 300 the RIN increses s the output power P under the threshold, then decreses like current, threshold. It is possible to explin this behviour s follows : under the threshold, the lser cn be considered s n incoherent therml light source with nrrow opticl bndwidth nd spectrum nd so increses the noise without bringing ny stbility. Then bove the opticl the gin sturtion leds stbiliztion of electrons fluctutions nd then of threshold, reltive fluctutions. The light stimultion effect is to synchronize the emission of the photons Consequently, the noise pek t threshold shows the turning of light properties electrons. when stimulted emission overcomes spontneous emission. 4.2 AT MIDDLE FREQUENCY. -Noise mesurements t middle frequency, tht is to sy in the flt region (30 MHz), revel the lser stbility : the weker the RIN is, the higher the is. In the two following sections we will set gin guiding lsers over ginst index stbility lsers, then multimode lsers over ginst singlemode lsers. guiding I Gin guiding nd index guiding lsers. In gin guiding lsers, the current is injected 4.2. nrrow centrl region using stripe contct. The lterl vrition of the opticl gin over The opticl mode structure no longer depends on the injection current. guiding lsers exhibit very high RIN t threshold, but RIN decreses me bruptly Index index guiding thn in gin guiding devices, in terms of reltive current nmlized to the in threshold current (Fig. 3). F the best index guiding lsers, RIN vlues lie between I x 10 nd 8 x 10 (l/hz) t twice the threshold. In gin guiding lsers, gin sturtion nd intensity stbility re me difficult to obtin. (7) cn give rough justifiction of those experimentl results t lest f Eqution currents higher thn 1.2 times the threshold current. The spontneous emission injection 4.2.2 Multimode nd single mode lsers. In conventionl lsers when the Fbry-Perot (FP)
RIN (l/hz) 4 0 $ ii io io 3. RIN t 30 MHz versus injection current f gin guided lser () (*) nd n index guided Fig. (b) lser (o). : fibres, there is need f single longitudinl mode opertion of lser diodes. A dispersive incpted long the length of the gin region, replces the mirrs of the Fbry- grting lbl when I/Is I is between 10 nd I, s predicted by reltion (7). With our experimentl setup we cn mesure RIN vlues f DFB lsers, s low s 10? (1/Hz) (tht is to sy level [8]. As shown in figure 5, RIN vlues less thn 155 db/hz re esily obtined with n nd DFB types), hving pproximtely the sme ctive volume nd emitting t (Fbry-Perot Lm, crefully voiding feedbck reflections. Their structure re BH (buried heterostruc- 1.3 BR (buried ridge), BC (buried crescent) nd DCPBH (double chnnel plnr BH). ture), RIN mesured t 20 fb bove threshold, tht is to sy f current vlue where no Their RIN vlue nd lser structure. N 9 RELATIVE INTENSITY NOISE IN SEMICONDUCTOR LASERS 1597 ii o o o o o io II lis of the reltively brod spectrum of stimulted emission s compred to the mode consequence In some pplictions like long distnce opticl communiction systems using spcing. Perot cvity nd provides wvelength selective filter leding to single mode opertion. But the complex building of distributed (DFB) lsers obliges mny users to wk with FP lsers. In well-behved DFB single mode lsers, RIN is smooth nd decreses like (I/Is 1) 170 db/hz) (Fig. 5). But RIN increse of sometimes me thn one decde occurs when DFB lser gets two modes (Fig. 4) when the envelope spectrum of Fbry-Perot lser exhibits dip. In both cses competition between two modes settles nd cuses n increse of totl photon number fluctutions. So there is shrp creltion between longitudinl mode distribution nd noise index guiding DFB lser. Noise mesurements hve been crried out on set of 26 InGASP index guiding lsers mode competition occurs, re gthered in tble I. There is no obvious creltion between
10 10 10 ls)l's ii -n 10 10" 10 lo ' 10' Fig. 5. RIN of low noise iidex guidbg DEB lser, versus injection current, t 30 MHz. 1598 JOURNAL DE PHYSIQUE III N 9 R.>.N 1/Hz i I o o ". NJ i o Fig. 4. RIN plots of DEB with two modes versus injection current (III 1). R.I.N (I/Hz) 10'" *, -ll *»»»» 10'» io- 10"* II -(sins
current f different lser structures I f grooved mes, 2 f buried ridge, 3 f threshold crescent, 4 f buried heterostructure PPIBH, 5 f DCPBH, 6 f double chnnel buried FR nme Structure Cvity I 20 fb 20 fb Lser type (ma) 10-'4 (GHz) n (Hz-) n 77 5 PF 25 3 2.3 Philips n 79 5 PF 23 0.5 2.2 Philips A10 5 DFB 16 3 1.5 Fujitsu M5 5 DFB 7 1.9 Fujitsu M17 5 DFB 8 2.5 1.9 Fujitsu 7902/187 4 DFB 26 0.8 1.2 Mitsubishi current ccding to the simplified reltion [5]. injected of the intrinsic frequency response of semiconduct lsers is of bsic Knowledge imptnce in mny pplictions [9]. If the frequency response is mesured using direct N 9 RELATIVE INTENSITY NOISE IN SEMICONDUCTOR LASERS 1599 Tble I. Mesured vlues of threshold current, RIN nd resonnce frequency t 1.2 the buried mes. Cviy ypes re Perot,Fbry (PF) nd DFB. RIN ThCSF 302A5D 2 PF lo 4 1.6 ThCSF 304868 2 PF 12 0. 8 2, I ThCSF 304H7G 2 PF II 3 1.8 ThCSF 302H3D 2 PF 12 4 1.8 LdM 1383/96M PF 21 2 Hitchi HL1341FG DFB 32 3 3.5 ATT 172 7 PF 14 3 2,I CIT 82 PF 34 0.6 2.3 370 5 DFB 12 2 1.7 Fujitsu 371 5 DFB 12 2 2 Fujitsu NEC 5600/17 6 DFB 19 3 2.4 NEC 5600/21 6 DFB 32 3 2.6 ThCSF RIBD9/09 2 PF 18 2.5 2.1 ThCSF R10Al/11 2 PF 13 2.5 3 ThCSF R181/20 2 PF 24 3 1.9 NEC 6F391 6 PF 22 6 1.9 NEC 6F4160 6 PF 27 3 2.5 Mitsubishi 7902/192 4 DFB 12 2 1.9 Mitsubishi 7901/81 3 PF 11 3 2 Mitsubishi 7901/82 3 PF 8 2, In term of cvity length, f set of Fbry-Perot lsers built from the sme wfer, we hve observed tht RIN vlues decrese s the length of the lsers increses, s shown in figure 6. An verging of intensity fluctutions cn be imgined in long cvity lser. So to lower the noise we cn think to build long lsers but the RIN improvement is rther slim : only 4 5 db between loo Lm nd 400 Lm length. 4.3 AT HIGH FREQUENCY. Using our experimentl set up, we follow noise vritions up to lo GHz. In figure 7, we cn notice the resonnt pek, the frequency of which depends on the current modultion, the lser diode's intrinsic response is usully msked by electricl
I x w. w 7 c w. 6. RIN versus lser length (L in Lm) f I I. I x I. (.) mesurements t 30 MHz, (-) Fig. curve with spontneous emission fct: () p= (0.026JL(Lm)). (b) p= theeticl -12 (d) 1.l19 (g) l211 Frequency (MHz) -14 lee? 1500 Zoo? 2500 3000 3500 4000 500 Fig. 7. RIN versus frequency f different vlues of injection current. nd dmping fct re the sme in intrinsic frequency response nd in intensity frequency Since the noise is intemlly generted nd is not filtered through the prsitic elements, noise. 1600 JOURNAL DE PHYSIQUE III N 9 lq) ' o (b) Z 0 loo 200 300 (00 Lse Length lpml (0.013JL Lm ) ) RIN (I/Hz) l ( ) -I I l ) 1.1327 (b) 1.1357 (c) 1.1388 ) l.149 (f) 1.181-13 lo elements including ctive lyer spce chrge cpcity, substrte elements, bond wire prsitic nd stub prsitic cpcitnce [10]. Accding to rte eqution nlysis, resonnce elements, noise mesurements give the true intrinsic pek frequency nd the true dmping fct.
N 9 RELATIVE INTENSITY NOISE IN SEMICONDUCTOR LASERS 1601 There is simple reltion between the dmping fct & (relted to the width of the resonnce pek) nd the squred resonnce frequency [6]. This rtio only depends on mteril prmeters nd is two three times higher in conventionl double heterostructure lsers (DH) thn in multiple quntum wells lsers (MQW), ccding to our mesurements : m * ** / M m f C C7 C- 1c m cn O Fig. 8. Resonnce frequency (o) nd dmping (*) versus injection current. prtition noise. RIN of the I-th mode is defined by : RIN, = clculted using rte equtions. nd min mode hs smller RIN thn ny one of its neighbours. Among its closest The coefficients re defined by : (As, ill As c = I las, in ) j) jas in ) j) ns f DH lsers nd 0.6 ns f MQW lsers. This high nonliner dmping due to spectrl 0.2 buming cn limit the mximum bndwidth of MQW lsers. Resonnce frequency nd hole fct re plotted in figure 8. Discrepncy from reltion [5] lw is explined by non dmping gin nd gin compression. liner io ** -> X X c9 c9 l' o 10 DO OJ o O ' w C $ C - -u $ -z -1 10 -j o l10 10 10 10 (1-Is)/Is 5. Prtition noise nd cross-creltion coefficients between mode fluctutions. In multimode lsers, the energy emitted by the lser is shred between the different modes. The totl rdited power fluctutions re 000 times smller compred to the fluctutions of n isolted mode power. This extr noise induced by the shre of intensity is clled lser mode ) (9) 2 S, the two hving the highest mplitude show lso the highest RIN. neighbours, cross-colteltion coefficients of the fluctutions between two modes, we cn From understnd the wy in which the energy is shred between the modes. Cross-creltion ill )) ii o) nd derived from rte equtions.
«numbered nd one of the subsidiry modes numbered, «2 o 3.., is negtive.»», tht ll these subsidiry modes lose get energy from the min centrl mode. mens This mode cross-creltion coefficients re smll nd positive. This mens tht ll Subsidiry subsidiry modes exhibit in-phse intensity fluctutions between ech other, exchnging these with the lsing mode essentilly. energy the longitudinl modes re seprted by spectrometer [III. The Experimentlly, I z 9. Cross-creltion coefficients s function of the injection current f four mode pirs. Solid Fig. theeticl curves, ix) mesurement f (0-1) mode pir. (+) mesurement f II -2) mode pir. lines frequency nd how they depend on the lser structure, the mteril properties nd high behviour. irregulr From our mesurements we hve shown tht, in nlog mplitude modultion systems, it is to use DFB single mode lser to rech RIN vlue less thn 155 db/hz nd to necessry feedbck reflexions. void energy is shred between the different modes. - II Is 1602 JOURNAL DE PHYSIQUE III N 9 As shown in figure 9, the cross-creltion coefficient between the min centrl mode output slit is opened up to let two modes go through. Then the slit width is spectrometer to let only one of the two modes through. Cross-creltion coefficients mesure- reduced ments, t 30 MHz, re shown in figure 9 : (x) f (o-i ) mode pir nd (+) f (1-2) mode pir. (2-3) < 10-7 cn 10-1) i x x c ij -.3 2 3 LASER CURRENT Conclusion. We hve presented here noise mesurement results on semiconduct lsers t middle nd noise mesurements cn still give quite Intensity lot of infmtions. F instnce, if we high frequency up to 20 GHz, we will see the ultimte intrinsic bndwidth without exple electricl prsitic elements. Intensity noise of isolted mode shows the wy in which the totl Acknowledgments. We wish to thnk C. Boisrobert f fruitful discussions nd M. Dontenwille f technicl ssistnce.
DARCIE T. E., BODEEP G. E., Lightwve multichnnel nlog AM video distribution systems, [Ii 89 ppier 32.4. I, p. 1004, p. 1007. ICC [2] JOINDOT I., Bruit d'intensitd reltif des lsers k semiconducteur, Ann. Tdldcommun. 46 (1991) 191- BORN W., WOLF G., Principes of optics (2Cddition Pergmon Press, 1964). [3] JOINDOT I., BOISROBERT C., Peculir fetures of InGASP DH superluminescent diodes, IEEE J. [4] Electron. QE 25 (July 1989). Quntum BRossoN P., FERNIER B., LECLERC D., BENOiT J., Crrier diffusion effects on quntum noise [5] nd dmping rte of 1.3 Lm InGASP semiconduct lsers, Appl. Phys. Lett. 50 frequency 1987). (Mrch PETERMANN K., Clculted spontneous emission fct f double heterostructure injection lsers [7] gin induced wveguiding, IEEE J. Quntum Electron. QE15 (1979) 566-570. with [8] JOINDOT I., BOISROBERT C., Opticl spectrum irregulrities nd their influence on semiconduct PETERMANN K., Lser diode modultion nd noise Advnces in Optoelectronics (Kluwer [9] Publishers, KTK Scientific Publishers, Tokyo, 1988). Acdemic [lo ANDREKSON P., ANDERSON P., ALPING A., ENG T., in situ chrcteriztion of lser diodes from bnd electricl noise mesurements, IEEE J. Lighnvve Technol. LT-4 (July 1986). wide JOINDOT I., BOISROBERT C., Anlysis of cross-creltion between mode fluctutions in [ll] N 9 RELATIVE INTENSITY NOISE IN SEMICONDUCTOR LASERS 1603 References 204. in long wvelength BH lsers, IEEE J. Quntum Electron. QE 21 (1985) 700-706. spectr OLSHANSKY R., HILL P., LANzISERA V., POWAzINIK W., Universl reltionship between resonnt [6] lser intensity noise, EFOC. LAN.85 (4-4, June 19-21, 1985) Montreux Switzerlnd, pp. 77-80. semiconduct lsers, IEEE J. Quntum Electron. QE 23 (1987) 1059-1063.