Carrier Density Dependent Index, Frequency Chirp and FM Modulation, and Frequency Linewidth in Semiconductor Lasers

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1 Smcnduc Olcncs (Fahan Rana Cnll Unvsy) Cha 4 Ca Dnsy Dndn ndx Fquncy Ch and F dulan and Fquncy Lnwdh n Smcnduc Lass 4. nducn 4.. Ca Dnsy Dndn Rfacv ndx n Smcnduc Lass: n Cha 6 h fllwn xssn was band f h dlcc cnsan f smcnducs al n na 3 q d s n Ps. nˆ fs f m 3 s FBZ s nq m q m h na h Th dlcc cnsan and h facv ndx dnd n h lcn and hl dnss. Ths dndnc s xlc n h naband cnbun h dlcc cnsan and mlc huh h ca dsbun funcns n h nband cnbun. Th abv xssns a ah cmlcad. n smcnduc las chans n h ca dnsy affc bh h an as wll as h facv ndx. n h wds chans n h ca dnsy affc bh h al and h manay as f h facv ndx. Th cmlx facv ndx s n n' n" n' c W dfn a quany as fllws ' dn 4 dn dn' dn dn" dn d dn Th abv xssn s usful snc can b usd xss chans n h al a f h facv ndx n ms f h maal dffnal an dn' d dn 4 dn Th valus f na h a an fquncy can an anywh fm 0 f ms cmmnly usd -V an maals wh valus n h 4 7 an bn ycal. Als n ha h facv ndx dcass wh an ncas n h ca dnsy. 4.. Cavy d Fquncy Shf wh a Ca Dnsy Chan: n Cha h fllwn xssn was dvd f h chan n h cavy md fquncy du a chan n h cavy facv ndx

2 Smcnduc Olcncs (Fahan Rana Cnll Unvsy) n' n' * n'. * n. d 3 d 3 f h ca dnsy n h acv n chans by n hn h chan n h acv n facv ndx s d n' n 4 dn Th csndn chan n h cavy md fquncy s * n' n'. d 3 v d dn a n * n' n. d 3 f h cavy s a Faby-P hn h abv xssn can als b wn n ms f h md u vlcy v v d ~ a dn n 7 F xaml n a 550 nm las f n 5 0 cm -3 5 a. 075 n 3. 6 d ~ dn 0 cm and 5 h chan n h cavy fquncy s 4 GHz whch s aund nm. Alcans ha qu a sabl fquncy cal suc dmand ha h ca dnsy n h las acv n b f f flucuans. 4. Dc Cun Fquncy dulan n Smcnduc Lass 4.. nducn: Cnsd a cun mdulad las as shwn blw. (f) Las A dc cun mdulad smcnduc las n Cha h fllwn xssns w dvd f h small snal chan n h ca dnsy and h hn dnsy n a sns a cun mdulan f R f n n n R n f n R n f f f f n f f H f n f qv R a a Sus h cavy md fquncy s als m dndn f R f Thn

3 Smcnduc Olcncs (Fahan Rana Cnll Unvsy) av d ~ dn av d ~ dn f f f n f H f qv R a Th abv quan dscbs h fquncy mdulan (F) sns f h las. Bcaus f h ca dnsy dndn facv ndx h fquncy f h lasn md s mdulad n sns a cun mdulan. W can als w av d ~ dn f n f av d ~ dn f n f R a n f f n n m dman n can w h abv xssn as dn d dp n d d P d Th nsananus fquncy shf s nal h a f chan f h hn dnsy h a f chan f h las uu w. Fquncy mdulan (F mdulan) s als usd ansf nfman n fb cal nws. n such schms dcn and nfman val a h cvn nd s m cmlcad cmad h schms ha us nnsy mdulan. 4.3 Las Phas s and Las Fquncy Lnwdh 4.3. nducn Phas s: Cnsd a snusdal snal whs has s chann wh m A A cs Th nsananus fquncy s vn as d d d d A m vayn has s hf quvaln a fquncy vaan. Th m has ns fs a m vayn has wh a z ava valu f h has dffnc 0 Hwv h hh d clan funcns f h has dffnc a n all z. F xaml 0 Th abv has clan funcn s clsly lad h fquncy lnwdh f h snusdal snal as dscussd blw. f h has ns has Gaussan sascs hn all hh d clan funcns f h has dffnc can b wn n ms f h scnd d clan funcn vn abv. F xaml n!! vn n n 0 n dd Th dubl facal sn sns h duc f all dd ns fm n Fquncy Scum f Snals wh Phas s: Th fquncy scum A s dfnd as fllws S f a snusdal snal

4 Smcnduc Olcncs (Fahan Rana Cnll Unvsy) A A A A A S d A Th anld bacs mly nsmbl avan. nsmbl avan can b lacd by m avan f h snal s dc. Sus A A cs hn A A A A A and A A A cs cs Th fs m n h squa bacs s z un avan. Th scnd m s cs f h s n has ns hn A A S d A A A A Th fquncy scum cnsss f w dla funcns a h fquncy f h snusdal snal. f h has ns s assumd by Gaussan sascs hn A cmmnly ncund cas s whn h has ns clan sns has dffusn wh h fllwn clan funcn Th fquncy scum n hs cas bcms S A A d A A A A n h snc f has ns h dla funcns hav badnd n Lnzans wh a full wdh a half maxmum (FWH) qual whch s als calld h lnwdh f h scum Las Phas Chnc: S fa u dscussn n lass has bn fcusd n h hn dnsy h al numb f hns nsd h las cavy. Lasn was dnfd wh h buldu f a la hn ulan nsd h las cavy abv hshld. f hs w all h was lass hn lass wuld n hav bn any m nsn han hh w ncandscn lh sucs. Las lh has has chnc. W dscuss hs has chnc n blw. W assum ha h fld f h cavy nmd s nmalzd such ha * 3 nn. d

5 Smcnduc Olcncs (Fahan Rana Cnll Unvsy) wh s h cavy md fquncy. Th fld nsd a las cavy abv hshld can b wn as R s h numb f hns nsd h cavy and H s h has f h fld. s n dffcul s vn u nmalzan f h cavy nmd ha h al ny nsd h cavy wll qual. ha h fld amlud s nal. n a smulad mssn css h fld f h md hn has h sam has as h has f h cavy fld ha smulad h ansn. Thf whn hns mully va smulad mssn h has s svd. Hwv h has f h fld f a snanusly md hn has n lansh wh h has f h fld nsd h cavy. vy snanusly md hn has a andm has wh sc h has f h fld nsd h cavy. Blw hshld h hns nsd h las cavy a msly a sul f snanus mssn and hf cavy fld has n wll-dfnd has. Abv hshld h hns nsd h las cavy a msly a sul f smulad mssn and h cavy fld hf has a wll-dfnd has. n addn h has f h cavy fld mans cnsan f ln duans and w call hs y has chnc. Phas chnc s n unqu las flds. Phas chn lcmanc snals n h KHz Hz and GHz fquncy ans hav bn aund f v a cnuy (.. ad wavs). Bu has chn sucs a h cal fquncs w mssn unl h las was nvnd Phas s Fquncy Scum f Ocal Flds and Chnc Tm: n Scn 3.3. h fquncy scum f snusdal snals was lad h has ns. Th sam hlds u f cal snals. Th nfmc schm shwn blw can b usd masu h fquncy scum f cal snals. Fxd m Ocal snal Dc Th nu lh s sl n w usn a 50/50 bam sl flcd ff ms and hn cmbnd aan wh h sam bam sl. Th suln nnsy s dcd wh a hdc. On f h ms s mvabl and s usd nduc a dlay n n f h sl snals wh sc h h n. Th ava hdc cun s nal h squa manud f h fld cmsd f h cal snal and s m-dlayd vsn... f h cal snal has n amlud ns.. f.. hn h fquncy scum f h cal snal can b wn n ms f h dc cun. S d d.. 0 vabl m

6 Smcnduc Olcncs (Fahan Rana Cnll Unvsy) Th quany 0 s calld h nfam. Th Fu ansfm f h nfam wh sc h dlay vs h fquncy scum f h cal snal. Sus ha n cs ˆ hn cs... Fs sus ha h s n has ns. n hs cas h nfam quals cs 0 and h fquncy scum quals S Th nfam s schd blw and shws h nfnc fns bwn h snal and s m dlayd vsn ha ss fv ndcan fc has chnc. w sus h snals has has ns and h has ns has Gaussan sascs and h has clan funcn s vn by Th nfam quals cs 0 Th nfam s schd blw. Th nvl f h nfam dcays xnnally wh a dcay cnsan qual. Th quany s calld h chnc m f h snal. s h m scal v whch h has f h snal wuld lly n chan. As h dlay s ncasd and h has f h snal dffuss and h hhs f h as n h nfam bcm small. Th fquncy scum quals

7 Smcnduc Olcncs (Fahan Rana Cnll Unvsy) S ha h FWH f h scal dnsy s qual h nvs f h chnc m. Th FWH f h scal dnsy s usd as a masu f h chnc m f an cal snal Las Phas Dynamcs and Las Lnwdh: Cnsd a las an abv hshld wh a sady sa hn numb n h cavy qual and w assum ha. Th lcc fld can b wn as R n d sudy h dynamcs f h has w nd fu u hw smulad and snanus mssn vns affc h las has. Cnsd a smulad mssn vn a m. Rh af h smulad mssn vn h fld bcms R ha h has f h fld has n chand bf and af h smulad mssn vn. Th cavy hn numb s nw n m han h sady sa hn numb. Th hn numb wll dcay va laxan scllans unl h hn numb aan achs h sady sa hn numb. w cnsd a snanus mssn vn a m. Th has f h fld f h addd hn s n h sam as ha f h cavy fld. Sus h has f h fld f h addd hn s wh sc h has f h cavy fld. Rh af h snanus mssn vn h fld s sn sn cs R sn cs R R R n ahcal snan h lcc fld has n h cmlx lan bf and af h snanus mssn vn a shwn n h Fu abv. Th anl s b cnsdd a andm vaabl wh a unfm bably dsbun n h nval 0. Thf sn cs 0 sn cs ha h ava hn numb af h snanus mssn vn s ( )

8 Smcnduc Olcncs (Fahan Rana Cnll Unvsy) cs sn as xcd. Th ncas n h amlud f h fld af snanus mssn wll dcay va laxan scllans unl h cavy fld s R Th hn numb has und h sady sa valu. Hwv h has has bn shfd by sn Th abv analyss shws ha ach snanus mssn vn cs h has f h cavy fld by an amun axmaly qual sn. n any m nval h al chan n h has f h cavy fld can b band by summn v h cnbuns fm all h snanus mssn vns ha han dun hs nval sn Snc h hass a cmlly andm and unclad sn 0 sn v n And f s allwd b nav hn sn av ns Fm h has clan funcn fllws ha h fquncy scum f h las fld s S wh h FWH las lnwdh s vn by a s v n Th abv xssn s h Schawlw-Twns sul f h las lnwdh. xsss h fac ha h las lnwdh s dmnd by h snanus mssn a snc snanus mssn vns caus h has f h cavy fld dffus n m. Unfunaly h Schawlw-Twns xssn alhuh accua f as lass undsmas h xmnally masud lnwdhs f smcnduc lass by m han an d f manud. a s Phas Dynamcs and Lnwdh f Smcnduc Lass: n smcnduc lass hn numb chans sul n ca dnsy chans whch lad facv ndx chans and whch n un lad shfs n h cavy md fquncy. All hs cmlcad dynamcs a caud by h quan dvd al n hs Cha d d W can hn f h m dndn fquncy n ms f a m dndn has d d d d

9 Smcnduc Olcncs (Fahan Rana Cnll Unvsy) Cnsd a snanus mssn vn a m. Rh af h snanus mssn vn h cavy fld s R cs sn sn Th chan n h cavy hn numb fm h sady sa valu mmdaly af h snanus mssn vn s cs cs Th cavy hn numb wll nw und laxan scllans n whch h ca dnsy and h hn numb sclla 90-ds u f has unl h hn numb achs h sady sa valu aan. Dun hs laxan scllans h cavy md fquncy and h has chans a vnd by h quan d d d d Onc h laxan scllans a v and h hn numb has und s sady sa valu h n chan n h has s cs Whn h laxan scllans a v h cavy fld s R Th al has chan causd by h snanus mssn vn s sn cs ( ) n any m nval h al chan n h has f h cavy fld can b band by summn v h cnbuns fm all h snanus mssn vns ha han dun hs nval sn cs Snc h hass a cmlly andm and unclad 0 sn cs v n a s

10 Smcnduc Olcncs (Fahan Rana Cnll Unvsy) And f s allwd b nav hn fllws ha h FWH f h las lnwdh s sn v n v n a s Snc valus f a n h 4 7 an h smcnduc las fquncy lnwdh s 7 50 ms la han h Schawlw-Twns lm. Th addnal lnwdh badnn s du has chans ha accmany laxan scllans bcaus f h ca dnsy dndn facv ndx n smcnducs. a s

Lecture 23. Multilayer Structures

Lecture 23. Multilayer Structures Lcu Mullay Sucus In hs lcu yu wll lan: Mullay sucus Dlcc an-flcn (AR) cangs Dlcc hgh-flcn (HR) cangs Phnc Band-Gap Sucus C Fall 5 Fahan Rana Cnll Unvsy Tansmssn Ln Juncns and Dscnnus - I Tansmssn ln dscnnus