Reduction of pulse distortion in travelling wave semiconductor optical amplifiers

REDUCnON OF PULSE DI!jTORTION IN TRAVELLING WAVE SEMICONDUCTOR OPTICAL AMPLIFIERS M. J.Sonei a. J.F.Gonzalez, S.Ruiz-Mo eno & J.Gui a Dp o. Teo ia de la Se lal y Comunicaciones. ETSIT-BARCELONA, UPC c/Jo ge Gi ona Salgado s/n. 08034 BARCELONA. SPAIN. ABSTRACT- The nonlinea phenomenon inhe- en in a elling wa e semiconduc o op- ical ampli ie s can p oduce se e al ha m- ul e ec s in ansmission sys ems such as pulse dis o ion in mul i-Gbi /s in en- si y-modula ion sys ems. In his communi- ca ion, is pasan ed a heo e ical in es- iga ion o he possibili y o educing he gain sa u a ion du ing he pulse am- pli ica ion p ocess by means o he com- pensa ion o he ca ie densi y a ia- ions. This should be e y use ul in many op ical sys ems and, specially, in high speed communica ion sys ems. 1. INTRODUCTION T a elling wa e semiconduc o op ical am- pli ie s (TWOA) a e eme ging as p ac ical componen s o use in op ical communica- ions sys ems. using bo h di ec and cohe en de ec ion. Se e al wo ks [11,[21 ha e shown ha hey posses many ad an- ages, being i s high gain o e a e y wide bandwid h one o he mos ou s anding cha ac e is ic. Because o i s la ge band- wid h TWOA a e specially sui able o am- pli y na ow op ical pulse [31. The de ice gain can be signi ican ly educed du ing he pulse p opaga ion and, in consequence, he ailing pulse edge can ecei e less gain han he leading edge causing he pulse dis o ion. This is due o he gain sa u a ion om dec ease o ca ie densi y. On he o he hand, in a high bi a e ansmission sys em is hinkable ha he ime in e al be ween wo consecu i e sig- nals is compa able o o e en smalle han he ca ie li e ime o he de ice. As a consequence, he ca ie densi y will no be enough ime o eco e . Clea ly, he gain expe ienced by each indi idual pulse will be di e en om each o he and de- penden on he o egoing signals. In his communica ion we s udy he possibili y o educing he a ia ions o he ca ie densi y and so he sa u a ion gain unde dynamic condi ions. The me hod p oposed o educe he sa u a ion gain akes in o ac- coun he p opaga ion coo dina e because he ca ie densi y diminu ion is la ge a he end o he ampli ie . In Sec ion 2 we s ablish bo h he basic equa ions which go e n he dynamics o he ampli ica ion p ocess and he heo e ical base o he compensa ion scheme o he ca ie den- si y. Some esul s a e p esen ed in Sec- ion 3. whe e we discuss he e ec s o compensa ion on he ampli ied pulse and on he ca ie densi y. The main conclusions a e d awn in Sec ion 4. 2. NONLINEAR MODEL OF A TWOA 2.1 Basic Equa ions In he s udy o pulse p opaga ion in TWOA, he ampli ie is modeled as a se o wo le el sys ems wi h ansi ion ene gies ex ending o e he whole ange o he con- duc ion and alence bands. The basic equa ions which go e n pulse p opaga ion in semiconduc o op ical ampli ie a e (3) whe e (1) and (2) come om he wa e e- qua ion and hey gi e he longi udinal a- ia ion o powe , P, and phase, #, o he pulse. Gp and Lp a e he powe gain and he losses in he medium espec i ely, F is he phase gain and N is he ca ie densi y. The equa ion (3) is he ca ie densi y a e equa ion which go e n he ca- ie densi y wi hin he ac i e egion. Ne CH2964-5/91/0000-0186$01.00 01991 IEEE 186 is he ca ie densi y due o bias cu- he i s e m is cons an and ep esen s en , TS is he ca ie li e ime, h is he pumping ca ie densi y necessa y o he Plank cons an , U is he op ical e- ob ain he small signal gain, ha is, (9) quency and wad is he ac i e egion c oss and he second e m is he compensa ion as a ea. The gain unc ions can be exp essed Go = GplN=N~~, p=O Gp(N,P)= TG(N)[l-Kp(P)I (4) e m de ined by whe e is he con inemen ac o . G(N) wi h his, he solu ion o equa ion (3) can con ains he dependence wi h he ca ie be app oxima e as Nc Neo when pulse wid h is much sho e han he ca ie li e ime. densi y, which is ep esen ed by a polynoi Bu equa ion (10) p esuppose o know he mica1 app oxima ion gi en by G(N) = ZAIN supp esion unc ions which a e de ined I41 o he ampli ie which is un hinkable. wi h i4-04. KP(p) and a e he gain gain and he op ical powe a each poin P/P s (6) Howe e , i we assume ha exi s an ideal compensa ion he gain can app oxima e as Kp(P)= Gp(N) Go (11) (Go-Lpl~ (12) ha is, (11) and (12) a e easonable ap- p oxima ions as o en as N(z. )=NBo. Then, subs i u ing in equa ion (10) we ob ain and so, P(z, ) I PIN( 1.e (7) being 13 and phenomenological and ps a no malized powe which depends on he semiconduc o medium. The pa ame e s TS Go (GO-LP)Z.~~~(~) alues used in he simula ions a e hu w*dWe NBC(Z,~) = - summa ized in Table I. wd L A Ao Ai A2 A3 A4 LP a 13 Ps NBO 7s 0.3 pm2 300 pm 1.55 pn 0.3 -1.92.1 o5 2.42- 10' -8.47 * 1 O5 1.55. lo; -1.06- lo1 4000 m- 0.3 ns 5.0 4.5 420 mW 2.5 - 10 "65 Table I 2.2 Theo e ical compe n s a ion o In he same way han [SI, in o de o com- pensa e he diminu ion o he ca ie den- si y we ha e sepa a ed Ne in o wo e ms (8) non1 inea i y i n TWOA Ne(z. ) = NBO + Nec(z, ) (13) he e o e, he compensa ion unc ion de- pends on he inpu op ical signal and he z-coo dina e by a exponen ial unc ion. I is possible o app oxima e his unc ion by sec ions di iding he ampli ie in o a numbe m o equal sec ions. In each o hese he pumping ca ie densi y akes he mean alue o Nec(z, ), hen we can ob ain whe e i=l,..,m is he sec ion numbe and L is he ampli ie leng h. I m=l (only one sec ion) he esul is he same ha [51 doing Lp x GO. So hen he scheme p oposed o compensa e he ca ie densi y is d awn in igu e 1. 3. RESULTS AND DISCUSSION The se o equa ions (11, (2) and (3) can 187 _ %--x I’nu (0 II 1 7II-1 _- PI11 -- (I) I --I lWOA ]---- Figu e I: Compensa ion scheme. no be sol ed analy ically and, in conse- quence, is necessa y i s nume ical solu- ion. In he simula ions we ha e consi- de ed a Gaussian pulse o which whe e Ein is he inpu pulse ene gy and o is ela ed o he ull wid h a hal maxi- mum (FWHM) by p=1.665 o. In igu e 2 is ep esen ed he ca ie densi y as a unc- ion o he p opaga ion coo dina e z o he pulse peak when he e is no compen- sa ion, cu e (c), and when he e is he- o e ical compensa ion (131, cu es (b) and (3. The di e ence be ween hese las cu es is ha (b) does no ake in o ac- coun he sup ession gain e ms in con- as o (a) whe e hey a e aken in o ac- coun . O cou se, when he e is no compen- sa ion he ca ie densi y dec ease along ampli ie leng h when pulse is passing. Ne e heless, when compensa ion is ope a- ing he ca ie densi y is ap oxima ely cons an i he gain sup ession e ms a e no aking in o acoun (K~(P)=KF(P)=O). On he con a y, when hey a e aking in o accoun exi s a ligh inc emen a he end o he ampli ie . The alue o ca ie densi y gi en by (13) is la ge han he alue gi en by (10) because he i s does no look a he gain disminu ion due o op ical powe in he medium (sup ession phenomenon). In igu e 3 is shown he e olu ion o ca- ie densi y along ampli ie leng h when he e is compensa ion conside ing he he- o e ical case (cu e (a)), only one sec- ion (cu e (b)) and ou sec ions (cu e (cl). We can obse e ha he a e age o he ca ie densi y in each sec ion is app oxima ely cons an and equal o he ca ie densi y ob ained in he heo e- ical compensa ion case. This is he main eason om wha he shape and phase o he ampli ied pulse a e independen o he N (m-’) 2.55E Q24 3 Z.SOE+O24 2.48 024 2.4OE 024 2.35E 024 2.3JOE 024 Figu e 2: Theo e ical compensa ion. 2.45€+024 2.4OE+024 1 2.3=+024 Figu e 3: E olu ion o ca ie densi y o sec ions numbe used as we will see in i- gu es 4 and 5. Howe e , he sec ion numbe has in luence on he inal le el achie ed o he ca ie densi y and, he e o e, on he ecupe a ion ime o ini ial s a e (be o e he pulse ampli ica ion) o he ampli ie . I his ime dec eases, he se- pa a ion be ween wo consecu i e pulses can dec ease, being he gain o each in- di idual pulse he same. The inpu pulse phase ep esen ed by equa- ion (15) is equal o ze o, ne e heless will be modi ied du ing he ampli ica ion p ocess. The di e ence be ween he ins an aneous equency and he op ical equency can be ob ained as di e en sec ions. 1 ddJ 2n d A ec = - - - (16) 188 (Pd Figu e 4: Ampli ied pulse powe . A ec . 0.03 -0.12 3 20 40 80 1 Figu e 5: Ou pu equency displacemen . In igu es 4 and 5 a e shown he shape and equency displacemen , A ec, o de am- pli ied pulse, espec i ely. The cu es (e) ep esen he si ua ion whe e he e is no compensa ion and he o he s a e o he compensa ion si ua ion. The cu es (a) and (b) ep esen he heo e ical compensa ion wi hou and wi h sup ession gain, and (c) and (d) ep esen he compensa ion case wi h sup ession gain o one and ou sec ions espec i ely. The igu e 4 shows as he ampli ied pulse wi hou compen- sa ion is ligh ly assyme ic ( he pulse maximum shi s o he leading pulse edge) as a consequence ha he ailing pulse edge ecei e lowe gain han he ailing edge. In a Compensa ion si ua ion (cu es (b),(c) and (d)) he shape o ampli ied pulse is independen o he numbe o ampli ie sec ions. This is due o each sec ion has he same a e age gain along he ampli ie leng h. In igu e 5 can be obse ed ha whi hou compensa ion he equency displacemen inc eases almos linea ly o e he cen al pa o he pulse. Such a linea cha ac e is ic im- plies ha he pulse can be comp essed in a dispe si e medium. Like he shape, he equency displacemen is independen o he numbe o sec ions. On he o he hand, he displacemen maximum is lowe in a compensa ion si ua ion. No ed ha in a compensa ion si ua ion wi hou sup ession (cu e (a)) A ec is almos equal o he inpu one. This esul con i ms ha he compensa ion o he ca ie densi y dimi- nu ion is mo e e ec i e a leas impo - an is he sup ession phenomenon. 4. CONCLUSIONS In his communica ion we ha e p esen ed heo e ical esul s ela e o dynamic compensa ion o he sa u a ion gain in semiconduc o op ical ampli ie s. The me- hod o educe he sa u a ion gain con- sis s o a inhomogeneous pump o he ampli ie . This inhomogenei y can be achi- e ed using a mul isegmen ampli ie . The ob ained esul s show ha when he numbe o sec ions inc ease, he ime in e al be ween wo consecu i es pulses can de- c ease being dynamic gain equal o each indi idual pulse. On he o he hand, his compensa ion me hod is alid o low a ia ions o he ca ie densi y in ela ion o he injec ed ca ie densi y (NBo). Unde his condi ions, he dynamic gain is close o small signal gain o he ampli ie . 5. REFERENCES 189 1-- IT I II J.C.Simon, "Semiconduc o Lase Ampli- ie o Single Mode Op ical", J. 0p .Comm.. .4, no.2, 1983. T. Sai oh & T. Mukai, "1,s pm GaInAsP T a el 1 ing-Wa e Semiconduc o Lase s Amp1 i ie s", IEEE J. Q.Elec on., V. 23, no.6, 1987. I. E. Ma shall, e al."Picosecond Pulse Response o a T a elling-Wa e Op ical Ampli ie ", Elec.Le ., .24,no.l6,1987 G. P. Ag awa1,"Spec al Hole-Bu ning and Gain Sa u a ion In Semiconduc o La- se s: S ong-Signal Theo y", J. Applied Physics, . 63, no.4, 1988. 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