Mode-Locked Multi-Quantum-Well Lasers: Comparison between Different FD-TM Models

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1 Mode-Locked Mult-Quantum-Well Lasers: Comparson between Dfferent FD-TM Models A.Barletta P. Bardella I. Montrosset Dp. Elettronca and PhotonLab Poltecnco d Torno Italy Paolo.bardella@polto.t

2 Introducton Our goals: Revew the models for M actve sectons reported n the lterature and usually appled n combnaton wth a mean feld rate equaton Improve our Travelng Wave smulator to descrbe n a more realstc way the carrer denstes n M sectons Use the newly mplemented models to smulate Mode-Lockng M lasers

3 Examples of smulatons We studed a Mode Lockng laser consttuted by An actve M regon () A Saturable Absorber (AS) L ass L gan =50µm =020µm L barrer =8nm L well =7.5nm L SCH =32.5nm Dffusvty=cm 2 s - Inter-well capture tme =0ps I abs I actve r AS L r R

4 The M models wth to 3 populatons 3D Quas - 2D 2D to 3 carrer equatons The model consderng 2D and 3D carrers (transport effect n the SCH) s the most popular [agaragan et al. JQE 992] The model consderng also the quas 2D states ( gataway ) s not very popular [McDonald and O Dowd JQE 995] These models n ther orgnal formulaton all assume unform fllng of the wells In currently used FDTW models only the 2D carrer densty s consdered

5 The M model wth M2 carrers populatons I 3D [Lowery et al. JQE 998] SCH L e d ξ< leakage factor d e SCH R 2 M 2D d dffuson from SCH to the frst well capture tme from the adjacent wells e emsson from perpheral wells to SCH M equatons for the wells 2 equatons for the SCH

6 The M model wth 2M2 carrer populatons. I [.Ross et al. JQE 200] SCH L 3D d d b 2 Quas 2D b b 2 b b M b c d e e e M d dffuson from SCH to gateway and vce versa b dffuson above the barrers capture from gateways to the correspondng wells e emsson from wells to the correspondng gateways d SCH R 3D 2D M eq.s for the wells and the gateways and 2 eq.s for the SCH

7 The carrer equatons: mplementaton n FDTW smulator S S v dt d g e SCH c SCH n ) ( = ( ) S S v dt d g c c n ) ( 2 = The 2 populatons (2 equatons for carrers for photons): The M2 populatons model (M2 for carrers FDTW for photons): ( ) S S v dt d dt d g c e n b e c b n ) ( 2 = = The 2M2 popolazons model (M2 for carrers FDTW for photons):

8 The mplemented travelng wave model for the electrcal feld r L z z F z t = j F z t jk R z t S sp z t v g t z R z t = j R z t jk F z t S sp z t v g t z an Couplng term ( ) = ( ) ( ) ( ) ( δ ) ( ) ( ) ( ) * ( ) ( δ ) ( ) ( ) ( ) 2 2 S z t F z t R z t r R Spontaneous emsson The system has been solved usng a Splt Step technque [B.S. Km et al. JQE2000]

9 Selecton of parameters for the comparson The dfferent models requre dfferent parameter sets The parameters have been chosen n order to have comparable P-I and electro-optc modulaton characterstcs of a Fabry-Pérot laser 40 P-I IR 5 Output Power [mw] IM Response [A.U.] 2 populatons M2 populatons 2M2 populatons Current [ma] f [Hz] -5 0

10 Mode lockng maps: models comparson The Saturable Absorber s modeled as an actve regon operatng under threshold: wth ths model changng the bas current n the absorber we change the dfferental absorpton The workng condtons for a 5 wells laser are evaluated n the Saturable Absorber an secton currents plane 2 populatons M2 populatons (Lowery) 2M2 populatons (Ross et al.) [ma] I [ma] I [ma] I I [ma] A I [ma] A I [ma] A Q-swtchng 40Hz ML Hgher frequences ML

11 Mode lockng maps: nfluence of the number of wells Ths model easly allow to nvestgate the dependence of devce behavor on the dfferent parameters We report the maps evaluated changng the numbers of wells and keepng all the other parameters unchanged M2 populatons 3 M2 populatons [ma] I [ma] I I [ma] A I [ma] A Q-swtchng 40Hz ML Hgher frequences ML

12 Conclusons and Future Improvements Dfferent exstng models of M structures have been ntroduced n a TD TW smulator A comparson of these models has been performed A further mprovement s requred to model the Saturable Absorber n a more physcal way