New dynamic model for multimode chirp in DFB semiconductor lasers

Transcription

1 New dynmic model for multimode chirp in DFB semiconductor lsers A.J. Lowery, PhD, MlEE Indexing terms: Semiconductor lsers, Modelling Astrct: A new technique for modelling the dynmic spectrl chrcteristics of DFB semiconductor lsers ove threshold, which is sed on the trnsmission-line lser model, is descried. This includes the effects of index crrier dependence nd longitudinl index vritions. The timedomin responses nd spectr of qurter-wve shifted grting devices re compred with unshifted devices under trnsient conditions. 1 Introduction Distriuted feedck (DFB) semiconductor lsers offer improved spectrl chrcteristics over Fry-Perot devices ecuse of the use of frequency selective grting over their length (Fig. 1). Their ility to remin in single-longitudinl-mode while under modultion (dynmic single-mode : DSM) reduces pulse dispersion in long-hul fire-optic communictions systems. This llows higher dt rtes thn with Fry-Perot sources. However, dynmic single-mode opertion is difficult to chieve [l]. Even when single-mode opertion is chieved, y creful design of the lser's structure, the spectrum is rodened y chirping C2-41, cusing dispersion [5]. Although models re ville to predict the stedystte spectr of DFB lsers [&SI, few hve een extended to dynmic opertion. Hemni et l. hve studied the effects of multimode oscilltion in opticl systems including modulted DFB lsers [9]. However, lser chirp ws not considered. Bickers nd Westrook hve modelled chirp using simple, single-mode rteeqution pproch [ 10). However, longitudinl inhomogeneities were not considered. Kinoshit nd Mtsumoto fcet sustrte cldding wveguide I 1 ctive region Fig. 1 Typicl DFB structure, isected long the ctive region to show grting structure Pper (E13), first received 15th Novemer 1989 nd in revised form 14th Mrch 1990 The uthor ws formerly with the Deprtment of Electricl nd Electronic Engineering, University of Nottinghm, Nottinghm NG7 2RD, United Kingdom nd is now with the Deprtment of Electricl nd Electronic Engineering, University of Melourne, Prkville, Victori 3052, Austrli IEE PROCEEDINGS, Vol. 137, Pt. J, No. 5, OCTOBER I990 modelled trnsient chirping nd included longitudinl hole urning [l 11. However, their model ssumed tht the device oscillted in single longitudinl mode. Idelly, ny dynmic model should include oth chirping nd multiple modes. This would llow the dispersion penlities cused y oth spectrl rodening mechnisms to e ssessed. This pper presents such model, which is sed on previously descried scttering mtrix pproch [12] nd is one of fmily of lser models clled trnsmission-line lser models (TLLMs) [ Trnsmission-line lser models split the lser cvity longitudinlly into numer of sections. Ech section contins centrlly plced scttering mtrix which modifies forwrd nd ckwrd trvelling wves on trnsmission lines which connect the mtrices, Itertion in the time-domin gives the output wve from which spectr re found using Fourier trnsforms. Unlike trnsfer-mtrix models, which re solved in the frequency domin [18, 19, 63, TLLMs re suitle for dynmic simultions. Also, ecuse the time evolutions of oth the opticl field nd the crrier density re solved together, the models esily cope with gin sturtion cused y crrier depletion [SI. The model my e pplied to multicontct lsers, such s phse-tunle lsers [20], tunle lsers [21, 221, nd lsers designed to compenste for sptil hole urning [23]. The model my lso e pplicle to tunle DFB lser mplifiers [24], the noise properties of DFB lser mplifiers [19] nd to istle DFB switches [25]. 2 Model theory Much of the model's theory exists lredy. This is ecuse the TLLM lredy hs een pplied to DFB lsers without chirp [12] in model derived from Fry-Perot lser model [13]. As with ll TLLMs, the model is sed on the trnsmission-line modelling (TLM) method, which uses trnsmission lines s n intermedite model etween relity nd computer lgorithm [26]. A simple TLM consists of two repeted opertions; scttering nd connecting. These modify voltge pulses trvelling etween scttering nodes on trnsmission lines. The scttering opertion tkes voltge pulses incident on the nodes rvi, nd sctters them to give voltge pulses reflected from the nodes, kvr. It cn e written s scttering mtrix, s, operting on vectors V, i.e. kvr = s. kv' (1) where k is the itertion numer. The scttering opertion cn e derived from knowledge of the impednces of the trnsmission lines nd ssocited components, such s resistors, t the nodes. It 293

2 my lso include source terms, Vs so tht kv'= s' k Vi + kvs (2) The connection opertion descries how the reflected pulses propgte etween scttering nodes to ecome new incident pulses for the next scttering opertion. Agin, it cn e written s mtrix opertion, k+l Vi = c ' kvr (3) The connection mtrix cn e derived from the topology of the network nd is usully very sprse s only djcent nodes re connected. Note tht the trnsmission lines must hve equl delys, equl to the itertion timestep AT so tht ll pulses rrive t the nodes in synchronism. The numericl computtion consists of initilising the vlue of vector Vi nd then repeting eqns. 2 nd 3 to find the time evolution of the vector Vi or the vector V'. In most cses, however, the required output quntity is function of one of these vectors. In trnsmission-line lser models, the voltge pulses represent the opticl fields long the cvity. A chin of trnsmission lines form one-dimensionl model of the opticl cvity, from fcet to fcet. The scttering mtrices represent the opticl process of stimulted emission, spontneous emission nd ttenution. A rte eqution model of the locl crrier density sets the mgnitudes of these processes t prticulr mtrix. Such model hs een used to simulte Fry-Perot lsers [13-151, externl-cvity lsers [ 161 nd modelocked lsers [17]. The ddition of externl interfces hs llowed lser mplifiers to e studied [ The DFB model, presented in Reference 12, used rm sth f orword 4 A- 3 C reflection - line M 0 AT C Fig. 2 forwrd -+ stu circultor Two methods of dding phse delys to TLM models Using stu directly connected to the lines Using circultors nd seprte stus for the forwrd nd ckwrd wves modified connection mtrices to represent cross-coupling etween the forwrds nd ckwrds trvelling wves. However, ecuse the delys of the trnsmission line hve to e constnt, index chnges, cusing chirping, could not e modelled. The prolem of chirping in Fry-Perot TLLMs ws solved y plcing vrile impednce stu extensions t the ends of the lser cvity [ls]. These served to lter the phse-length of the cvity over limited ndwidth. The stus were plced t the cvity ends, rther thn long the entire cvity length, to prevent midcvity coupling etween the forwrd nd ckwrd trvelling wves. This intrcvity coupling would e result of the impednce discontinuities cused y the stus. Such coupling ws found to mke the Fry-Perot lser model ehve like DFB lser model [30]. A new pproch is introduced in this pper. Insted of connecting the stus in series with the trnsmission lines modelling the cvity (Fig. 24, circultors re used (Fig. 2). These send the wves, out of the stus, in the correct direction. For exmple, forwrd wve will enter the first, left-hnd, circultor (port 1) nd e directed to the stu port (port 2). Becuse the stu presents n impednce mismtch, prt off the wve will e reflected ck into port 2. The circultor then directs this reflected wve to port 3, where it continues on s forwrd wve. The reminder of the wve enters the stu to e delyed efore returning to port 2 to e directed to port 3. Bckwrd wves simply pss from port 3 to port 1 of this first circultor. A second set of three-port circultors is used to dely the ckwrd wves. This offers the possiility of hving direction-dependent index, s used in opticl isoltors. The phse dely cused y the stus is vried y ltering their impednce. For exmple, n infinite stu impednce gives reflection with zero phse shift; mtched cpcitive stu gives phse shift of (21t. AT.f) rdins; zero impednce stu gives 1t rdins; mtched inductive (shorted) stu gives (-271. AT. f) rdins, where f is the opticl frequency. Other phse shifts re ville, over limited ndwidth, y using other reflection coefficients. A complete DFB model is shown in Fig. 3. Here, scttering mtrices hve een inserted etween the circultors of ech section. Also, lternte sections' trnsmission-lines hve different impednces. This cretes impednce mismtches t the section oundries, which couple the forwrd nd ckwrd wves [12]. Ech section hs n ssocited crrier rte eqution model to enle the locl gin, refrctive index nd spontneous noise to e clculted from the injection current nd the crrier recomintion rtes [ 131. If two sections of the model were to e used to represent ech period of the DFB grting on the rel device, the numer of sections nd hence the computtionl tsk would e excessive. However, it is possile to represent crrier models fcet I D I I C! I I fcet, field model Fig. 3 " 1 section Complete DFB lser model I C P p is phse-shift stu, I nd c re gin-filter stus, i = injection current 294 IEE PROCEEDINGS, Vol. 137, Pt. J, No. 5, OCTOBER 1990

3 n odd numer of grting periods with single pir of model sections without compromising the model s ccurcy [12]. This technique relies on the model hving squre grting modultion. This cn e decomposed into numer of sinusoidl grtings t hrmonics of the grting period y Fourier techniques. One of these hrmonics models the rel device s grting period. Note tht the mplitude of ech hrmonic decreses with the hrmonic numer, e.g. the fifth hrmonic produces coupling of one-fifth of the mplitude of the fundmentl. For this exmple, the coupling of ech period of the squre grting hs to e incresed y fctor of five over the coupling of the rel lser s grting to compenste. A simpler nd much neter rule is tht the coupling K per unit length must e equl for model nd rel devices [ 123. If smll numer of sections is used, the opticl field will e smpled less thn once per wve period. This undersmpling is essentil for relistic computer times. Undersmpling hs een used in ll TLLMs nd does not compromise ccurcy if the smpling rte (section length/group velocity) is more thn twice the ndwidth of the opticl wve [13]. The use of two sections per grting period ensures tht the DFBs spectrum lwys lies ner the centre of the modelled spectrum. 3 Derivtion of the lgorithm from the trnsmission-line model Once the trnsmission line representtion of the device hs een derived, n lgorithm cn e produced. One of the dvntges of TLM is tht the lgorithm is lwys n exct representtion of the trnsmission-line model ; no inccurcies re introduced once the trnsmission-line representtion hs een formulted. This mens tht ll pproximtions hve physicl mening ecuse they re ssocited with the prmeters of the trnsmission lines. The terms in eqns. 1 to 3 will now e derived for the DFB lser model. Note tht the trvelling opticl fields (electric fields) re represented y voltge pulses A (forwrds) nd B (ckwrds) in the model. Thus, unity constnt m, with dimensions of metres, is used to convert etween electric field nd voltge to mintin dimensionl correctness. 3.1 Scttering mtrices, S The scttering mtrix cn e split into two scttering mtrices; one for ech wve direction. This is possile s there is no cross-coupling etween the wve directions in the scttering opertion. Scttering mtrices for cvity without phse shifting elements were derived in Reference 32. These hve een extended to include the circultors nd stus y considertion of the reflections t the stucvity interfces. The scttering process for the forwrd wve, with incident pulses from the previous section A (n), the gin filter s cpcitive stu &n), the gin filter s inductive stu Ai(n) nd the phse shifting stu A(n), is The scttering process for the ckwrd wve is simply the ove formul with ll wve mplitudes A replced y wve mplitudes B. The terms within this mtrix hve een derived previously [32], ut will e repeted here for clrity. Note tht ll the terms my vry from section to section nd, therefore, should techniclly hve suscripts n. Also, some terms re time-dependent nd vry with the itertion numer k. The spectrl dependence of the gin is modelled using trnsmission-line stu filters [13]. The sum of the gincurve filter s stu dmittnces y, is y = 1 + YL + r, (5) The stus dmittnces Yc (cpcitive) nd Yr. (inductive) re given in Reference 13. The field gin, resulting from stimulted emission, cross section of length AL is g = exp [ ALT(N(n) - N,)/2] - 1 (6) where is the gin cross-section, r is the confinement fctor, N(n) is the crrier concentrtion within section n nd No is the crrier density for trnsprency. The ttenution, cused y free-crrier sorption nd scttering, cross section is t = exp (-, AL/2) where,, is the ttenution per unit length. Spontneous emission is modelled with filtered Gussin (norml) distriution noise current I, with men-squre vlue of [ 141 <I:) = 2@~hf~[N(n)]~rn~/~, (8) where B is the spontneous emission coupling coefficient, L is the lser s cvity length, hf is the photon energy, B is the imoleculr (rditive) recomintion coefficient, rn is unit constnt with dimensions of metres nd 2, is the cvity wve impednce [ 131. The phse-djusting stu s impednces 2, re normlised to the cvity wve impednce nd re given y 2, = I cot (7$1ii,/c) I (9) nd 1 is the chnge in phse length cross section such tht 1 = r 7 AL [N(n)- N,] dn/dn e where N, is n ritrry crrier concentrtion for zero phse shift nd is usully set to the threshold crrier density [l5], ii, is the guide s group effective index (equl to the effective index in this dispersionless model) nd c is the velocity of light in vcuum. The ctive region s crrier index dependence dn/dn 1 cn e relted to Henry s fctor y c dn - 47rf 2tYL(2, - 1) 2y 1 (7) (4) 295

4 3.2 Connection equtions (C for the link-lines etween sections) The connection equtions in TLLM DFB models descrie the cross-coupling etween the two wve directions occurring t the section interfces. They were derived in Reference 12 nd re used lterntely long the lser model. They re [A(n+l)] - [I+KAL -KAL] k+1 B(n) KAL ~-KAL for low-high impednce oundry nd [A(n + 2)] = [ 1 - K AL K AL ] k+1 B(n + l) -KAL ~+KAL for high-low impednce oundry K, AL is the grting coupling per unit length for the device multiplied y the length of one modelling section. For stndrd DFB device (e.g. Reference 2), eqns. 2 nd 3 re pplied lterntely long the device length, i.e. n = (1, 3, 5, 7,...). For qurter-wve shifted grting devices (e.g. Reference 31), zero reflection interfce (identity mtrix) is inserted hlf wy long the cvity. There my lso e coupling t the fcets. For fcets plced t low-high impednce oundry simple resistive termintion cn e used giving k+lbi(s) = J(R). ka (s) t the front fcet k+lai(l) = J(R). kbr(l) t the rer fcet (14) where R is the power reflectivity of the fcets [13], nd s is the numer of sections. A more complex model, including phse-shifting stus etween the fcets nd the cvity, could e used to model the effects of fcet phse on mode-stility [33]. 3.3 Connection equtions C for the stus within section) There re lso equtions governing the reflections t the ends of the trnsmission line stus. These re hlf timestep long to ensure tht pulses rrive ck t the originting scttering mtrix fter dely of one timestep. For the inductive stus in ech section the reflection coefficient is negtive, giving For the cpcitive stus in ech section the reflection coefficient is positive, giving For the phse-djusting stus, which my e inductive or cpcitive, or 296 k+lagn) = - kagn) k + 1 B(n) = - kb( ) when the cotngent in eqn. 9 is negtive k + 1 Agn) = k + 1 B(n) = kb(n) when the cotngent in eqn. 9 is positive (17) 3.4 Crrier density rte eqution If we ssume tht diffusion long the cvity is negligile, then independent crrier density rte equtions my e used for ech section of the model. This is refinement over most lser models, which use single crrier density rte eqution to descrie the density verged over ll the cvity. These my not e ccurte for lsers with lowreflectivity fcets, including lser mplifiers. The rte eqution for crrier density cn e written -- dn(n) - - AN(n) - B[N(n)] - C[N(n)13 dt where A, B nd C re the monomoleculr, imoleculr nd Auger recomintion coefficients [34], respectively, wd is the cross-sectionl re of the ctive region, q is the electronic chrge nd Z(n) is the component of injection current injected into section n. The photon density, S(n), within section is relted to the incident wves from either side y S(n) = ([A (n)] + [B (n)] )~,/(hfcz,m ) (19) 3.5 Output power The power exiting the front fcet P, is relted to the wve incident on the fcet from the cvity, A (s) nd the fcet s power reflectivity R, y [13] P = [A (s)] (l - R)wd/(Z,m ) (20) This power is usully verged over numer of itertions to remove high frequency components. 4 Simultions of DFB devices The following numericl results serve to test the vlidity of the model nd then to illustrte its vlue. A 1550 nm device ws modelled [2]. Its prmeters re given in Tle 1 nd were otined from References 2, 34 nd 35. Note tht the comintion of ndnumer nd numer of sections gives centrl wvelength of nm. However, this restriction could e esed y modifiction of the lgorithm. Tle 1 : Lser prmeters Symol Prmeter nme Vlue Unit A0 L W d r e No rc R A B C B c s K I Ni M 0 U Gin-pek wvelength Lser cvity length Active region width Active region depth Opticl confinement fctor Lser group effective index Trnsprency crrier density Lser gin constnt Cvity ttenution fctor Lser fcet reflectivities Monomoleculr recomintion coefficient Bimoleculr recomintion coefficient Auger recomintion coeffficient Spontneous coupling fctor Vcuum velocity of light Numer of model sections Model ndnumer [13] Grting coupling per unit length Lser drive current Initil crrier density Gin pek offset from ndcentre Gin filters Q-fctor Henry s lph fctor x x x x lo- 4.0 x x x x 10l c~n-~ cmz cm- S- cm3 s- cm6 s- cm s- cm- ma nm IEE PROCEEDINGS, Vol. 137, Pt. J, No. 5, OCTOBER 1990

5 4.1 Effect of numer of model sections: devices without chirp The vlidity of using smll numer of sections for lrge numer of grting periods ws tested y compring the trnsmission responses of models with n incresing numer of sections. The crrier concentrtion ws fixed nd n impulse injected into the rer fcet. The impulse response, out of the front fcet, ws Fourier trnsformed to otin the trnsmission spectrum. Fig. 4 shows the trnsmission spectr for unshifted- DFB models with 23-, 96- nd 392-sections nd no phse-djusting stus operted just elow threshold. Only proportion of the ndwidths of the 98- nd 392- section models were plotted to llow comprison with the response of the 23-section model. The responses of the 98- nd 392-section models were in good greement over the entire ndwidth of the 23-section model. The 23-section model s response ws only good fit over the stop-nd. Thus, the 98 section model ws thought to e good compromise etween ccurcy nd computtionl effort. Exmintion of Fig. S shows tht the trnsmission peks re indeed shifted y ltering the impednce of the phse stus. Two unwnted effects occurred, however. The spcing etween the two modes decresed with incresing shifts from the centre of the nd. Secondly, when the modes were shifted down in frequency, other trnsmission peks ppered t the top-end of the modelled ndwidth. These effects were reduced in the 98-section model, with the disdvntge tht the computtion time ws incresed y fctor of out sixteen. Fig. 6 plots the error in the mode positions ginst the chnge in crrier concentrtion. Note tht the error ws symmetricl out the zero-shift position. This Figure cn e used s guide to the complexity of model required. It is not expected tht the secondry modes ppering t the nd edges will e prolem. This is ecuse the ginspectrum model will filter these out [13]. error in mode position, GHz 23 c 98 OZt I / I 23 lower mode ; : frequency, o THz o Fig. 4 Trnsmission responses of 23- (solid-line), 98- nd 960- (roken-line) section models with no stu phse sh$t, just elow threshold 4.2 Effect of numer of model sections: devices with chirp The vlidity of the phse-shifting stus ws checked y plotting the trnsmission response of 23-section cvity with different mounts of sttic shift (Fig. S). The test ws then repeted with 98-section model (Fig. S). l AN, ~ d ~ ~ ~ - ~ Fig. 6 Error in mode positions ginst the crrier density devition from N, for the 23- nd 98-section models CB A CB A - 5; %2 ZP 2% Fig. 5 Trnsmission responses 23- nd 98-section model 23-section model just elow threshold 98-section model (centre of nd shown) A no phse shift A no phse shift B -2.4 x lol7 CII-~ shift in crrier density B -2.4 x 1017 CII-~ shift in crrier density C -4.8 x lol7 CII- shift in crrier density C -4.8 x IO CIT-~ shift in crrier density IEE PROCEEDINGS, Vol. 137, Pt. J, No. 5, OCTOBER

6 4.3 Nonshifted DFB lser trnsient response Mny DFB models ssume tht the refrctive index is constnt long the cvity. However, if there is gin sturtion long the cvity s length, the index will lso e position dependent. Two simultions were used to investigte the effects of inhomogeneous index. The first ssumed homogeneous index, governed y the verge crrier concentrtion within the cvity. In the second, the index in ech section ws fixed y the crrier concentrtion within tht section. In oth simultions, the lser ws suject to step increse in injection current to 100 ma. This lrge vlue ws used to induce length-dependent sturtion nd lso to give short pulses nd hence lrge spectrl widths. Fig. 7 shows the trnsient responses of lser with homogeneous index. This shows clssic dmped relxtion oscilltion, common to ll lsers. Fig. 7 shows the spectr of the first nd second pulses in Fig. 7. The first pulse s spectrum (solid line) hd n verge width of 170 GHz for ech mode. The first pulse s width ws 12.5 ps. This gives timendwidth product of 2.12, less thn the vlue of 2.33 given y the formul for Gussin pulses, which hs een shown to e good pproximtion for Fry-Perot lsers [ls]. However, ecuse of the symmetry of the DFB spectr, it is difficult to define their FWHM width ccurtely. Note tht this symmetry, in prticulr the prominence of the red rit-er, is common to experimentl oservtions [2, 3,591. The model ws re-run without includmg index vritions to see whether homogeneous index vritions hd ny effect on the temporl responses of lsers. Only smll differences in the responses were oserved. These could e explined y phse shifts etween the power envelope nd the verging routine. Fig. 8 shows the response of lser llowing n inhomogeneous refrctive index. Although the first pulses re similr, there re noticele differences etween this nd the response using the homogeneous pproximtion. The differences included lower threshold crrier density, greter dmping nd smoother response. The first pulses were expected to e similr ecuse of the sence of gin sturtion in these erly times time, ps time, ps Fig. 8 pulses Trnsient response of DFB lser nd spectr ofjirst nd second Trnsient response llowing inhomogeneous index Spectr of first nd second pulses (multiply PSD scle y 2.5 for second spectrum) Fig. 7 Trnsient response of DFB lser nd spectr offirst nd second pulses Trnsient response ssuming homogeneous refrctive index Spectr of first (solid) nd second pulses (roken) (multiply PSD scle y 2 for second spectrum) 298 Fig. 8 shows the spectr of the first nd second pulses in Fig. 8. The first pulse s spectrum hd n verge mode-width of 210 GHz. The first pulse s width ws 11.4 ps, giving time-ndwidth product of 2.4, closer to tht of Fry-Perot lsers. Note tht the lser hs settled to single mode for the second pulse. This explins the smooth profile of the time-response. The second pulse s spectrum is not centred on the first pulse s spectrum, ut is shifted to the red. This is in greement with the lower vlue of verge crrier concentrtion thn in the homogeneous simultions. This effect ws oserved in Reference 3, ut ws explined y junction heting. This effect would hve importnt system consequences [36, 371. IEE PROCEEDINGS, Vol. 137, Pt. J, No. 5, OCTOBER 1990

7 4.5 Qurter- wve shifted lser trnsient response Qurter-wve shifted DFB structures hve single, dominnt oscillting mode. In contrst, unshifted devices usully support two modes, un!ess the fcet reflectivities nd phses re crefully chosen [31]. Thus, shifted DFB lsers re fvoured in communictions systems. It is esy to modify the TLLM for qurter-wve shifted DFB lsers. The order of the low nd high impednce sections is reversed in the middle of the model to give two djcent sections of the sme impednce. Fig. 9 shows the trnsient response of qurter-wve shifted device suject to the sme drive conditions s efore. As oserved in Reference 12, the dmping of the trnsient is etter thn for the unshifted device. Also, the crrier density settles to lower level thn for the unshifted devices Fig. 9 pulses time, ps h i c ld & Trnsient response of DFB lser nd spectr ofjrst nd second ~1 Trnsient response for qurter-wve shifted DFB lser Spectr of first nd second pulses (multiply PSD scle y 4 for second spectrum) The spectr of the two pulses in Fig. 9 re shown in Fig. 9. As expected, single mode domintes. The width of the first pulse s spectrum ws 205 GHz with corresponding temporl width of 15.6 ps. Thus, the timendwidth product ws 3.2. The spectrum gin shows predominnce of the red rit-er, more so thn in the unshifted device. Becuse this er domintes the spectrum, the spectrum ppers to shift to the lue s the relxtion oscilltions settle. This is in greement with Reference 1 1. The oscilltion in the power-spectrl density is proly result of interference etween the min ody of the IEE PROCEEDINGS, Vol. 137, Pt. J, No. 5, OCTOBER 1990 pulse (crrier concentrtion flling) nd the til of the pulse (crrier concentrtion rising). This interference is enhnced y the incresed dmping giving more power in the pulse s til. The second trnsform gives very nrrow spectrum, corresponding to the wide second pulse. Agin, this lies to the red side of the centre of the first spectrum. Further simultions, using different mount of sttic phse shift (y ltering NP) showed tht the model ws still vlid, even though the centre wvelength hd een shifted. This mens tht the form of the spectr re nerly independent of the centrl wvelength in reltion to the model s centre wvelength, s expected. If the numer of sections were to e reduced, then some differences might e seen. 5 Conclusions A new numericl modelling method for DFB lsers hs een developed. This is sed on trnsmission-line lser model with cross-coupling etween the forwrd nd ckwrd trvelling wves nd phse-shifting stus coupled to the cvity using circultors. Results from the model show tht it is importnt to consider longitudinl vritions in refrctive index s these ffect oth the temporl nd the spectrl ehviour of DFBs. The modelled trnsient spectr were in good greement with experimentl results nd show the highly symmetric nture of DFB spectr. One of the importnt qulities of numericl models is tht they should llow results to e gined fster thn from experimentl work. Certinly this model llows prmeters to e djusted more quickly thn in rel devices. The simultion times were of the order of 40min on sed mchine (pprox. 3x n 8 MHz IBM-AT). However, these cn e reduced y compromising ccurcy. This is simply chieved y reducing the numer of model sections; hlving the numer of sections cuts the computtionl tsk y 75%. Also, current work ims to implement the lgorithm on multiprocessor mchine with one section per processor. The modelling method is extremely flexile s it is sed on uilding-lock pproch ; ech scttering mtrix eing lock. The model hs een demonstrted on unshifted nd qurter-wve DFB lsers. However, simple modifictions to the injection-current profile would llow multicontct DFB lsers nd distriuted Brgg reflector (DBR) to e simulted. Interesting experiments include the effect of drive pulse-shpe on dynmic linewidth, the tuning speed of multicontct devices, comprison etween DFB nd DBR lsers nd the optimistion of the grting coupling coefficient. The uilding locks cn e extended eyond the lser to llow more complex lsers nd even opticl systems to e modelled. For exmple, the DFB lser could e included within n externl cvity to form tuning element in mode-locked lser. Alterntively, the model could e comined with time-domin fire model to clculte the dispersion penlty in long-hul systems. Also, the model cn ccept externl inputs. This would llow DFB lser mplifiers, useful s wvelength selectors, to e optimised. 6 References 1 SASAKI, S., CHOY, M.M., nd CHEUNG, N.K.: Effects of dynmic spectrl ehviour nd mode-prtitioning of 1550 nm distriuted feedck lsers on Git/s trnsmission systems, Electron. Lett., 1988, 24, pp

8 2 WESTBROOK, L.D., HENNING, I.D., NELSON, A.W., nd FIDDYMENT, P.J.: Spectrl properties of strongly coupled 1.5 pm DFB lser diodes, IEEE J., 1985, QE-21, pp BERGANO, N.S. : Wvelength discrimintor method for mesuring dynmic chirp in DFB lsers, Electron. Lett., 1988, 24, pp EISENSTEIN, G., TUCKER, R.S., nd RAYBON, G.: Opticl time-division multiplexed trnsmission t 8 Git/s using single lser nd semiconductor opticl power mplifier, Electron. Lett., 1989, 25, pp YAMAMOTO, S., KUWAZURU, M., WAKABAYASHI, H., nd IWAMOTO, Y.: Anlysis of chirp power penlty in 1.55pm DFB-LD high-speed opticl fier trnsmission systems, IEEE J., 1987, LT-5, pp WHITEAWAY, J.E., THOMPSON, G.H.B., COLLAR, A.J., ARMISTEAD, C.J.: The design nd ssessment of A/4 phse-shifted DFB lser structures, IEEE J., 1989, QE25, pp SODA, H., KOTAKI, Y., SUDO, H., ISHIKAWA, H., YAMA- KOSHI, S., nd IMAI, H.: Stility in single longitudinl mode opertion in GInAsP/InP phse-djusted DFB lsers, IEEE J., 1987, QE-23, pp McCALL, S.L., nd PLATZMAN, P.M.: An optimized 42 distriuted feedck lser, IEEE J., 1985, QE-21, pp HEMNI, H., KOIZUMU, Y., YAMAGUCHI, M., SHIKADA, M., nd MITO, I.: The influence of directly modulted DFB LD sumode oscilltion on long-spn trnsmission system, IEEE J., 1988, LT-6, pp BICKERS, L., nd WESTBROOK, L.D.: Reduction of trnsient lser chirp in 1.5 pm DFB lsers y shping the modultion pulse, IEE Proc. J, Optoelectron., 1986,133, pp KINOSHITA, J-I., nd MATSUMOTO, K.: Trnsient chirping in distriuted feedck lsers: Effect of sptil hole-urning long the lser xis, IEEE J., 1988, QE-24, pp. 216& LOWERY, A.J. : Dynmic modelling of distriuted-feedck lsers using scttering mtrices, Electron. Lett., 1989, 25, pp LOWERY, A.J.: A new dynmic semiconductor lser model sed on the trnsmission line modelling method, IEE Proc. J, Optoelectron., 1987,134, pp LOWERY, A.J.: A new timedomin model for spontneous emission in semiconductor lsers nd its use in predicting their trnsient response, Int. J. Numericl Modelling, 1988, I, pp LOWERY, A.J.: A model for picosecond dynmic lser chirp sed on the trnsmission line lser model, IEE Proc. J, Optoelectron., 1988,135, pp LOWERY, A.J.: A new dynmic multimode model for externl cvity semiconductor lsers, IEE Proc. J, Optoelectron., 1989, 136, pp LOWERY, A.J.: A new time-domin model for ctive mode-locking sed on the trnsmission-line lser model, IEE Proc. J, Optoelectron., 1989,136, pp BJORK, G., nd NILSSON, 0.: A new exct nd efficient numericl mtrix theory of complicted lser structures: Properties of symmetric phse-shifted DFB lsers, IEEE J., 1987, LT-5, pp. 14& MAKINO, T., nd GLINSKI, J.: Trnsfer mtrix nlysis of the mplified spontneous emission of DFB semiconductor lser mplifiers, IEEE J., 1988, QE24, pp MURATA, S., MITO, I., nd KOBAYASHI, K.: Frequency modultion nd spectrl chrcteristics for 1.5 pm phse-tunle DFB lser, Electron. Lett., 1987,23, pp YOSHIKUNI, Y., OE, K., MOTOSUGI, G., nd MATSUOKA, T. : Brod wvelength tuning under single-mode oscilltion with multielectrode distriuted feedck lser, Electron. Lett., 1986, 22, pp YOSHIKUNI, Y., nd MOTOSUGI, G.: Multielectrode distriuted feedck lser for pure frequency modultion nd chirping suppressed mplitude modultion, J. Lightwve Technology, 1987, 5, pp. 51& USAMI, M., nd SHIGEYUKI, A.: Suppression of longitudinl sptil hole-urning effect in 1/4shifted DFB lsers y non-uniform current distriution, IEEE J., 1989, QE-25, pp MAGARI, K., KAWAGUCHI, H., OE, K., nd FUKUDA, M.: Opticl nrrow nd filters using opticl mplifiction with distriuted feedck, IEEE J., 1988, QE-24, pp SHOJI, H., ARAKAWA, Y., nd FUJII, Y.: New istle wvelength switching device using two-electrode distriuted feedck lser, Electron. Lett., 1988,24, pp HOEFER, W.J.R. : The trnsmmission-line mtrix method - Theory nd pplictions, IEEE Trns., 1987, MTT-35, pp. 37C LOWERY, A.J.: New inline widend dynmic semiconductor lser mplifier model, IEEE Proc. J, Optoelectron., 1988, 135, pp LOWERY, A.J.: A comprison etween Fry-Perot nd trvelling wve lser mplifiers in n 8 Gps repetered opticl systems using time-domin model, J. Phys. D - Applied Phys., 1988, 21, pp. S177-S LOWERY, A.J. : Pulse compression mechnisms in semiconductor lser mplifiers, IEE Proc. J, Optoelectron., 1989, 136, pp LOWERY, A.J. : Trnsmission-line modelling of semiconductor lsers. PhD Thesis, University of Nottinghm, My HENRY, C.H.: Performnce of distriuted feedck lsers designed to fvor the energy gp mode, IEEE J., 1985, QE-21, pp LOWERY, A.J. : Trnsmission-line modelling of semiconductor lsers : the trnsmission-line lser model, Int. J. Numericl Modelling, 1989,2, pp BUUS, J.: Dynmic single-mode opertion of DFB lsers with phse shifted grtings nd reflecting mirrors, IEE Proc. J, Optoelectron., 1986,133, pp MOZER, A., HAUSSER, S., nd PILKUHN, M.: Quntittive evlution of gin nd losses in quternry lsers, IEEE J., 1985, QE-21, pp WESTBROOK, L.D., Mesurements of dg/dn nd dn/dn nd their dependence on photon energy in 1.5pm InGAsP lser diodes, IEE Proc. J, Optoelectron., 1986,133, pp CARTLEDGE, J.C., nd BURLEY, J.S.: The effect of lser chirping on lightwve system performnce, IEEE J., 1989, LT-7, pp CORVINI, P.J., nd KOCH, T.L.: Computer simultion of highit-rte opticl fier trnsmission using single-frequency lsers, IEEE J., 1987, LT-5, pp IEE PROCEEDINGS, Vol. 137, Pt. J, No. 5, OCTOBER I990