Threshold and Above-Threshold Performance of Various Distributed Feedback Laser Diodes

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1 Threshol n Aove-Threshol Performne of Vrious Distriute Feek Lser Dioes C. F. Fernnes Instituto e Teleomunições, Instituto Superior Ténio, Liso, Portugl Astrt A omprtive nlysis of the threshol hrteristis of ifferent istriute feek (DFB) lser ioes (LDs) using mtrix tehnique known s trnsfer mtrix metho (TMM) will e presente. For high urrent level injetions, omintion of the TMM with the photon n rrier rte equtions emphsizes the sptil hole-urning (SHB) effet, tht is the mjor rwk of the DFB LDs in the ove-threshol regime. A summry of the results otine for ifferent phseshifte (PS) or istriute oupling oeffiient (DCC) DFB strutures, suh s the threshol urrent, the moe seletivity, the sie moe suppression rtio (SMSR) n the tuning rnge, will e referre. I. INTRODUCTION The DFB lser ioes re the most ommonly use strutures in optil ommunition systems. When ompre to FP lsers, DFB lsers le to n inrese in the moe seletivity, ue to the perioi vrition of the refrtive inex of the semionutor meium. The min lser fetures re seen to e strongly influene y the orrugtion properties, nmely the oupling oeffiient, the grting perioiity, the vity length n the onitions ssume t the vity ens. These re very iffiult to ontrol ue to the tolernes inherent to the frition proess. To suppress their influene it is quite usul to hve nti-refletive otings on the lser fets of the DFB strutures. Due to the symmetry involve, the emission ptterns eome ouly egenerte, thus preventing the neessry single longituinl moe (SLM) opertion tht minimizes the effet use y the ispersive property of optil fiers. In orer to overome this prolem, severl solutions hve een opte, ll of them orresponing to lk of symmetry in the overll longituinl lser struture. Nmely, the introution of one or severl phse-shifts in the orrugtion [1] or the onsiertion of non-uniform grting epths hve een mentione. When properly hosen these ltertions my inue importnt itionl improvements in the lser performne [2]. Sine the perioiity of the orrugtion is roken ue to the presene of struturl hnges in the vity, the nlysis se on the eigenvlue pproh [3] is iffiult to e implemente. Inste, when eling with those ses, where gret mount of ounry onition must e tken into ount, the use of mtriil tehniques [4] is seen to gretly improve the numeril proeure. In setion II rief esription of the numeril simultion moel will e presente, together with the vrious DFB lser strutures uner stuy. These orrespon to single qurterly wvelength-shifte (QWS), multiphse-shifte or/n istriute oupling oeffiient in mirrorless DFB lser strutures. Results of the simultion nlysis re inlue in setion III n orrespon to the threshol n ove-threshol regimes. In the ltter, sptil hole urning effets re pprent n some remrks out the strutures will e onsiere in orer to minimize their influene on the lser performne. Finlly, some onlusions will e presente with omprtive nlysis of the strutures uner stuy. II. THE MODEL Inste of trying to solve omplite nlytil eigenvlue equtions, the present moel uses the trnsfer mtrix formlism [5]. Its flexiility is losely relte to the use of generl mtrix eqution, mening tht the lulte lgorithm n e pplie to stuy ifferent lser strutures. In this moel, herefter lle TMM, the lser vity is esrie y finite numer of longituinl setions or ells, where ll the prmeters re kept onstnt. The fiel istriution is ssoite with two ounter-running wves tht my e erive y two liner equtions, eh ell eing represente y 2 2 omplex mtrix. The orrugtion orrespons to perioi vrition of the refrtive inex with perio Λ=2l, with eventul phse isontinuities of vlue φ. The orrugtion prmeters re: l = λb 4n eff n 1 = n eff K Cλ B 4 n 2 = n eff + K Cλ B 4 where λ B is the Brgg wvelength, K C is the oupling oeffiient n n eff is the effetive refrtive inex. The whole vity (orrugtion plus fets) is represente y mtrix [M] tht is simply the prout of the suessive mtries relte to eh ell [M] = M 11 M 12 = [M R ][M or ][M L ] M 21 M 22 where [M R ], [M or ] n [M L ] re the mtries relte to the right fet, the orrugtion n the left fet, respetively. Therefore, the following reltion hols etween the running wves t oth sies of the vity: (1) (2) (3) (4)

2 u R v R = [M] u L v L (5) n r k = n r0 + Γ n r n (n k n th ) (10) ur, vr or ul, vl eing the right n left going wves t the right n left fets, respetively. [M or ] is evlute s the prout of the suessive mtries relte to the ifferent ells [M i ] n the eventul phse shift mtries [Mφ i ]. For n i perios of the orrugtion insie the ith setion, [M i ] is given y: [M i ] = [M Λ i ] n i where [MΛ i ] is the mtrix relte to one perio of the orrugtion. Aove threshol, stimulte emission uses sptil holeurning of the rrier ensity profile long the lser. The onsiertion of hole-urning effets mkes the effetive refrtive inex epenent on the longituinl o-orinte, mening tht [M i ] my iffer from ell to ell. Phse shift grtings re esily inlue using the mtrix formlism. If it is ssume tht the eletri fiel isontinuity is smll long the plne of the phse shift, the nlysis of φ k phse shift (PS) lote t the z k plne is strightforwr. It is given y [Mφ k ] where: uz k + v z k+ = [M φ k ] uz k v z k = ejφ k 0 0 e jφ k uz k v z k The osilltion onition orrespons to the vnishing of u L n v R n les to the following requirement: M 22 (δβ, γ) = 0 Eqution (8) is solve y Newton-Rphson metho in the omplex plne [5]. The solutions orrespon to the etuning δβ n to the mol gin γ for eh moe tht propgtes insie the vity. The normlize gin seletivity γl orrespons to the ifferene etween the normlize gins relte to the lsing moe n to the most prole sie moe of the DFB lser. Another lser figure of merit is relte to the uniformity of the fiel istriution. It is the prmeter F (for fltness) n it quntifies the non-uniformity of the fiel istriution. For generl N-setion DFB lser vity it is given y: (6) (7) (8) where nr k represents the refrtive inex of the kth ell, n k its rrier ensity, n th the threshol rrier ensity n Γ is the optil onfinement ftor. The emission properties of the lser ioe is ltere y the non-uniformity of n r, inuing quik egrtion of the lser performne in the ove-threshol regime. It represents the mjor rwk in DFB lser strutures n hene, it is speilly isvntgeous when F is high. For lsers of hunres Angstrom length, it is epte tht: (i) the gin seletivity shll e greter thn, in orer to ensure the SLM opertion; (ii) the fltness shll e kept uner 5, in orer to otin stle SLM opertion in the high power regime. III. EXAMPLES In this work, numeril results otine for the threshol n ove-threshol regimes of n AR ote inex-guie Q-5 InGAsP will e presente. In orer to voi the rnom influene of the fet phse-shifts on the lser emission, we only hve onsiere mirrorless (R R =R L =0) lser vities. Altertions in the orrugtion of these onventionl DFB strutures shll e inlue, to rek the oule egenery in the fiel ptterns tht prevents the SLM opertion. In the following exmples QWS, 3PS or DCC lser strutures hve een onsiere, whose shemti igrms re represente in Fig. 1. Mteril n struturl prmeters re the sme s referre in [6]. φ L L 1 L 1 φ () () z N F = 1 L z 0 I(z) 1 2 z I v (9) () where I(z) is the longituinl eletri fiel istriution n I v is its men vlue. A non-uniform photon istriution les to non-uniform rrier istriution, tht inues importnt hnges in the refrtive inex oring to: L 1 Fig. 1 Shemti representtion of the DFB strutures. () QWS DFB; () 3PS DFB; () QWS DCC DFB. L 1

3 For omprison purposes, n verge normlize oupling oeffiient hs een efine in DCC strutures. It is given y: < KC >= K C1 pk + K C2 (1 pk) (11) =2L 1 /L eing the frtion of the vity ssoite with oupling oeffiient of vlue K C1. Fig. 2 shows the gin seletivity versus phse shift position for QWS DFB struture. Figures 3 to 6 show the fltness n the moe seletivity for 3PS (φ,φ,φ) DFB lser ioe s funtions of φ n. Results show tht the introution of more phse isontinuities long the orrugtion flttens the fiel istriution, lowering F, while the gin seletivity my show erese fe to the QWS se. A stle SLM opertion is hieve for: pφ ]5; 0.3[ ]0.48; 0.66[ when φ= π/3 ; pφ ]0.22; 0.26[ ]; 0.65[ when φ= π/4 ; pφ ]3; 0.66[ when φ= π/6. 5 Seletivity Seletion riterium Fltness Phse Shift Position Fig. 2 Moe seletivity versus phse shift position in QWS DFB lser ioe with K C L=2. The Brgg moe, lwys present in the QWS struture, orrespons to the lsing moe when the phse isontinuity is in the viinity of the enter. The results show tht SLM opertion is me possile only if 2 < pφ 1. These lsers present high moe seletivity, smll threshol urrents n zero-frequeny etuning. However, the fiel istriution is highly non-uniform, egring the lser performne in the high power regime. In strutures with multiple phse isontinuities, the min lser hrteristis re strongly epenent on the vlues ssume for φ n. Moe seletivity Fig. 4 Fltness versus for: ) φ=π/6; ) φ=π/4; ) φ=π/3 in 3PS(φ,φ,φ) DFB lser with K C L=2. phse shift position Fltness phse shift (egrees) Fig. 5 Moe seletivity versus φ for: ) =0.25; ) =; ) =0.75 in 3PS(φ,φ,φ) DFB lser with K C L= phse shift (egrees) Fig. 3 Fltness versus φ for: ) =0.25; ) =; ) =0.75 in 3PS(φ,φ,φ) DFB lser with K C L=2. In the struturl esign of DCC DFB lsers, the threshol hrteristis epen strongly on the rtio r=k C1 /K C2 n on the position of the oupling hnge. Fig. 7 shows the fltness of QWS DCC DFB lser with (K C L) v =2.0 s funtion of for ifferent vlues of r. It is pprent the iffiulty of hieving vlues of fltness tht my oey the seletion riterium, owing to the typil strong vlues for the eletri fiel ner the enter of the vity in QWS strutures.

4 Moe seletivity phse shift position Fig. 6 Moe seletivity versus for: ) φ=π/6; ) φ=π/4; ) φ=π/3 in 3PS(φ,φ,φ) DFB lser with K C L=2. As it is pprent from the results, the moe seletivity my e strongly improve fe to the QWS se if r is me lower thn 1 n tkes vlues ner. The optiml solution to hieve SLM opertion is otine for r=1/3 (highest γl) when is greter thn (smllest F). The omine effets of hving multiple phse shifts in non-uniform oupling oeffiient grting is investigte in the 3PS(φ,φ,φ) DCC DFB lser ioe. Tle I summrizes the investigtion unergone on those strutures tking into ount the possiility of SLM opertion. Severl vlues of φ hve een onsiere for DCC DFB lser with r=1/3 n (K C L) v =2. The strutures tht fll within the seletion riteri, oth for γl n F when n vry long its entire rnge, hve een signle y the symol X. Tle I Seletion riteri for SLM opertion in 3PS DCC DFB LDs. 0.2 Fltness Fig. 7 Fltness of QWS DCC DFB lser s funtion of when (K C L) v =2. () r=3; () r=2; () r=1/2; () r=1/3. Fig. 8 shows the seletivity of QWS DCC DFB s funtion of for ifferent vlues of r. Notie tht the vlues otine for =0 or =1 oinie, irrespetive to the vlue of r, orresponing to the QWS DFB se with K C L=(K C L) v. Moe seletivity oupling hnge position Fig. 8 Moe seletivity s funtion of for the sme set of lsers of the previous figure when (K C L) v =2. oupling hnge position φ = π/ X X φ = π/4 X X 0.7 X X X X X X X X X 0.8 X X X X X 0.9 X X X X 0.2 X 0.3 X X X 0.4 X X X X X X X X X X 0.7 X X X X X X X X 0,8 X X X X X 0.9 φ = π/ X 0.2 X 0.3 X X X X X 0.4 X X X X 0.7 X X X X X X X X X 0.8 X X X X X 0.9

5 As it is pprent, the hnging of oupling oeffiient in multiphse shift strutures hs extene the rnge in whih stle SLM opertion hs een rehe. Results show tht single moe stility is hieve when 0 pφ < 0.9 for φ=π/3 or π/4 n when pφ 0.9 for φ=π/6. Figure 9 shows the influene of the rrier injetion on the moe seletivity for the moifie DFB lser strutures uner stuy. When onsiering DFB strutures with non-uniform oupling oeffiients the moe seletivity inreses (ompre urves n with n ). On the other hn the introution of multiphse isontinuities ereses F, mking γl less influene y the rrier injetion (ompre urves n with n ). Moe seletivity normlise urrent I/Ith Fig. 9 Moe seletivity versus normlize urrent ensity. ) QWS DFB ; ) 3PS (φ, φ, φ) DFB with φ=π/3 n =0.7 ) QWS DCC DFB with = n r=1/3; ) 3PS (φ, φ, φ) DCC DFB with =, =0.7, φ=π/3 n r=1/3. Tle II Comprison nlysis of moifie DFB lser strutures. L = 300 µm; t = 0.3 µm Struturl Prmeters Threshol w = µm DFB struture QWS 3 PS QWS DCC 3 PS DCC φ π/2 π/3 π/2 π/3 r 1/3 1/3 γl F I th (ma) I=3I th γl P φ (mw) SMSR (B) I th < I < 3I th Tuning rnge (nm) Tle II summrizes the results otine for the moifie DFB strutures oth for the threshol n ove-threshol regimes. For the ner threshol regime, the QWS, while presenting goo gin mrgins, oesn't verify the seletion riteri for stle SLM, one it is generlly ssoite with lrge vlues of F. The lrgest vlues for the gin mrgin re otine using QWS strutures, either uniform or in DCC grtings. However, these strutures re lso ssoite with the highest vlues for F, preiting poor performnes in the high power regime, s it n e onfirme in Tle II. IV. CONCLUSIONS The esign of DFB lsers is omplex tsk. On one hn, ue to the gret mount of struturl prmeters involve. On the other hn, euse the improvement of lser figure of merit oes not neessrily mens enefit for ll the others. In this ontext, the TMM pproh seems to e powerful tool. Although quntifition of this nlysis is never exhustive, some remrks my e emphsize. The single QWS DFB lser lifts the moe egenery of the DFB with uniform grting, n it presents high moe seletivity, zero frequeny etuning n smll urrent ensities t threshol. However, they re lso relte to very poor single moe stility when the ising urrent inreses. The introution of more phse-shifts is seen to fltten the fiel istriution, lowering F n improving the lser performne in the ove threshol regime. The multiphse shifte DFB struture is not seriously ffete y the SHB effet, presenting the smllest hnges in the lsing wvelengths with respet to the injetion urrent. On the other hn, the onsiertion of non-uniform grting epths my improve the moe seletivity fe to the onventionl QWS DFB lsers, if the oupling hnges re onveniently hosen. We my therefore onlue tht, suitle omintion of the effets of inluing multiphse isontinuities in istriute oupling oeffiient struture my e vntgeously use to gurntee the stility of the SLM opertion with the urrent injetion. Referenes [1] H. Hus n C. Shnk, "Asymmetri tpers of istriute feek lsers", IEEE J. Qunt. Elet., QE-12, pp , [2] H. Ghfouri-Shirz, B.S.K. Lo, Distriute Feek Lsers Dioes - Priniples n Physil Moeling, Wiley, Chps. 5, 6, 7, [3] H. Kogelnik n C. V. Shnk, "Couple-wve theory of istriute feek lsers", J. Appl. Phys., 43, No.5, pp , [4] M. Ym n K. Skur, "Anlysis of lmost perioi istriute feek sl wveguies vi funmentl pproh", Appl. Opt., 26, No.16, pp , [5] C. Ferreir Fernnes, "Moe Spetrum n Threshol Gin Clultions in DFB Lsers", Mirowve n Optil Tehn. Letters, 12, No.6, pp , [6] C. Ferreir Fernnes, "Hole-Burning Corretions in the Sttionry Anlysis of DFB Lser Dioes", Mterils Siene & Engineering B - Soli Stte Mterils for Avne Tehnology, Elsevier, B74, No.1-3, pp , 2000.