S OPTICAL COMMUNICATIONS

Transcription

1 S-8.3 OPTICL COMMUNICTIONS oud : Optial fibrs 7..7 aswr. Mods of a optial fibr. Numbr of mods supportd by a fibr: V a M or laddg ( ) a, V or laddg Th ut-off wavlgth orrspods to Thrfor V ( ) a ( ),45 V,45 or laddg ( a) ( ) (, 45) or laddg M,45 µ (,4 m) M 8 (M is a roud umbr!) This mthod is a good approximatio oly wh th umbr of mods is quit big. or xampl if V (<,45) th formula givs: MV / v though th umbr of mods arrid by th fibr is rally o. or small umbr of mods o should always osidr th graph, whih is a rsult of tru simulatios. aswr. Mods ad rfrativ ds of a optial fibr. Th fibr must b gl-mod for all wavlgths btw,µm ad,6µm. W kow that if th fibr is gl-mod at,µm it will b gl-mod at,6µm. Thrfor, w look for th valu of th or rfrativ dx or suh that V,45 for,µm. a,45 laddg < or or,454 laddg or laddg,45 a,45454 aswr 3. Disprsio ad th agl of apta. Th tr-modal disprsio of a multimod fibr is giv by T D δ t r L, δ (fratioal rfrativ dx diffr) whr T/L puls broadg pr uit lgth spd of light rfrativ dx of th or rfrativ dx of th laddg

2 Th apta agl θ max is giv by Dt max r θ δ W kow that th rfrativ ds of th or ad th laddg ar of th sam ordr of magitud. Dt o max r θ 3,7 NOTE: D tr must b xprssd similar uits as D tr - s/m. Maximum bit-rat B is giv by BL < δ D B D max t r t r L,5 Mb. s

3 S-8.3 OPTICL COMMUNICTIONS oud : Nolar ffts fibrs 4..7 aswr. Efftiv lgth of a optial fibr. P L ff L P αz dz L ff α αz L α αl ibr : α db,8db/km, Lkm α db α,44 L ff 8,7 km 4,343 ibr : α db,8db/km, Lkm L ff 5,9 km aswr. Slf-phas modulatio(spm). L φmax ff 5km 3 γp W km W Maximum L ff wh α db,db/km is (L>> -αl <<) αl Lff, 7km α α Phas shift of is ot possibl! P mw: L km ff W km W 5 3 αl l( Lff α ) L L 5, α α ff 68 km aswr 3. Stimulatd rama sattrg(ss). L ff, 7km α 6 rit ff 6 5 m P g L 3 m 3 ff,7 m W adius halvd ff is oly ¼ of th origal rit rit Po, w P 9mW 4 37mW ftr amplifiatio powr lvls ovr SS thrshold a b ahivd but this is ot grally th situatio gl hal systms. I multi-hal systms SS is muh mor probabl.

4 S-8.3 OPTICL COMMUNICTIONS oud 3: ibr-opti Compots..7 aswr. ss of a abry-pérot filtr. ( ) 4 T, L L : width of passbad ss: S t rsoa frquy Z N N L, ( ) ( ) 4 L T T ( ) S L L 4 Trigoomtri formula: ( ) x y y x y x os os S S S S S >>, os os , N L S

5 aswr. abry-pérot filtr. Th fss of abry-prot filtr is giv by ( is th mirror rfltivity) ( ) ( ) ± ( ) >> ± 4 ± fltivity must b smallr tha, Th fr sptral rag S is qual to S L ssumg that th mdium btw th mirrors is air () w hav 4 S L m, mm L S Th width of th passbad is giv by S S 5GHz 4 aswr 3. Couplr. I optis w work with amplituds! ssumg is th amplitud of light omg at port, it divids btw th two paths ad aordg to Path ad Path (mmbr thr is a / phas shift aross a ouplr) Th fibr dus a phas shift L Th amplituds gog through paths ad th rombs at port aordg to Similarly P P

6 ( ) [ ] [ ] ( ) ( ) ( ) ( ) ( ) os os ) ( P

7 S-8.3 OPTICL COMMUNICTIONS oud 4: ibr-opti Compots 8..7 aswr. ss of a abry-pérot filtr. S roud 3. aswr. Erbium Dopd ibr mplifir(ed). Th output saturatio powr P s of th amplifir is otd to th ga G by: P l ( G) g( ) ( G ) g L Ps whr g is th small-sigal ga offit ad L is th amplifir lgth. g() lshap ad is tak to b. Th small-sigal ga ga G small-sigal is giv by thrfor, G l g L small sigal g L l ( G ) smallsigal P ( G) g( ) ( G ) l( G ) P P { g( ) ( G ) s P s P P l s G G G l smallsigal G smallsigal G smallsigal rprsts th ga P log log mw ( G) 8dB ( G ) db small sigal G 63, G small sigal P s 34,86mW, 3dBm whih souds rasoabl it orrspods to a put powr of 3,3dBm (,3dBm-8dB) wh w kp md that at dbm th output was ot yt saturatd (saturatio mas that th ga has droppd 3dB). aswr 3. dd/drop rsoator. Th rfltio of a rg-rsoator is giv by ( α ) L, α α os whr α is th splittg ratio os th ouplrs ad is th phas shift dud by th rsoator. wavlgth is droppd if.

8 k, k N L k L k k [ µ m], k N

9 S-8.3 OPTICL COMMUNICTIONS oud 5: Trasmittrs ad ivrs 5..7 aswr. Quatum ffiy of LED. Most of th spotaously mittd photos ar rfltd bak from th smiodutor / air trfa. I additio som fratio of photos is rfltd from th surfa du to th mismath of rfrativ dis. So th mittd photos oly gt through a o limitd by th agl of total tral rfltio. Th fratio of trasmittd photos a b approximatd by dividg th ara of th o op d by th total ara of sphr with radius of. or total tral rfltio w must hav (Sll): o α 9 smiodutor α air air smiodutor smiodutor o r ( α ) smiodutor sphr o sphr 4 4 smiodutor 4smiodu tor Th trasmittd tsity through th surfa is T ( ) I o m g so th total quatum ffiy is ( smiodutor ) ( ) 4 η xt 4 4 ( ) ( ) ( ),4%

10 aswr. Photodttor. bit o powr rivd bit photos rivd,55µm, rat 9 bits/s, P av,µw Numbr of photos pr bit Th avrag powr P av a b writt as h P av N rat (h is Plak ostat) whr (h)/ is th rgy of o photo ad th trm ½ disribs th probability that bit ours. Pav N 56 photos h rat aswr 3. Quatum Effiy ad sposivity. Extral quatum ffiy η xt, or ust quatum ffiy η, of a photodttor is dfd as th umbr of ltros that otribut to th photourrt dividd by th umbr of idt photos. of ltros I hf η ηxt. of idt photos q P Itral quatum ffiy η t dsribs th ability of a photodttor to ovrt absorbd photos to ltro-hol pairs. It is dfd as th umbr of ltros that otribut to th photourrt dividd by th umbr of absorbd photos. η i of of ltros absorbd photos If w kow th tral quatum ffiy w a alulat th xtral quatum ffiy from th followg formula W ηxt ηt ( Θ )( α ), whr Θ is th rfltivity, α is th absorbtio offit ad W is th thikss of th absorptio rgio of th dttor. Thrby th trm (-Θ ) rprsts rfltios ad (- -αw ) dsribs th absorbtio.

11 sposivity: sposivity is th ratio of output photourrt () to th idt optial powr (W). If w rmmbr that th photourrt is th produt of ratd ltros/tim uit ad ltro rgy, w d up with th followg formula. s it a b s, rsposivity is (idally) larly proportioal to wavlgth. I p P η xt, I p q η P hf xt q h W QE: η η ( Θ )( α ) xt 3,5 fltio: Θ, 386 3,5,3µ m,3µm: η t, 9966,35µ m η xt,9966, ,6 C,3 m,665, ,63 Js 3 m i mm,mm ( )( ), 665,55µ m,55µm: η t, 9468,35µ m η xt,9468, ,6 C,55 m,646, ,63 Js 3 m W mm,mm ( )( ), 646 W

12 S-8.3 OPTICL COMMUNICTIONS oud 6: ibr opti masurmts..7 aswr. bit rror rat (BE). Tim T btw two rrorous bits (BE - ) T 64, s rat BE 55 bits 5 6 s Ndd masurmt tim 64,5s h m 3s or BE -4, T 6456s Ndd masurmt tim 6456s 746,7days yars aswr. abry-prot avity mods. soat frquis ar bor wh wavs travllg opposit dirtios (gr ad blu) sid th avity trat with ah othr ad form a rsoat (sum) wav (rd). rquis ad amplituds of origal wavs must b qual ad thy must add -phas. This is illustratd ig.. igur : Two wavs trat ad form a rsoat wav.

13 soat frquis rprst stadg EM-wavs th avity ad th followg must hold. k L, k N (oditio for stadg wavs) rquy ad wavlgth ar otd to ah othr through spd. f f k k L f f L Wh k w gt th fudamtal frquy (L/), oft dotd by f. f L Irag k givs harmoi frquis f L, ( k ) st harmoi (L) 3 f L, ( k 3) d harmoi (L(3/) ) M M ig. : udamtal frquy ad thr harmois This a b formulatd as f f f, N whr f, f mod spag L L (latio btw diffrt frquy shifts ad diffrt wavlgth shifts a b drivd from th abov mtiod quatio f.) Th amout of wavlgths 3,m avity rsoa is L 3, m L k k 4 6,55 m wavlgths! or khz soud wavs th avity lgth should b m v 344 s s L k k 4 s f Hz s 3 688m

14 aswr 3. Itgratg sphr(isp) diod sphr mm,7854mm 5mm mm 5mm out 9,63mm out f,4999 sphr Pout diod ρ,7854,98 P ρ f 7854,98,4999 sphr ( ) ( ),394% If th diamtr is hagd from 5mm to 4,9mm If rfltivity hags Pout P 4,9mm out 8,86mm out f,483 sphr Pout diod ρ,7854,98 P ρ f 7854,98,483 sphr diod sphr ρ ρ ( ) ( ), ,96 ( f ),96 (,4999),397%,4% Wh alulatg th ffts o output powr w us th origal as as a rfr,394 log db,394 Th fft of th hag diamtr,397 log,3db,394 Th fft of th hag rfltivity,4 log,65db,394