Mc lc

MC LCDANH MC HNH V........................................................................................................................................................1 THUT NG VIT TT....................................................................................................................................................1 LI NI U.......................................................................................................................................................................3 CHNG 1............................................................................................................................................................................5 GII THIU CHUNG.........................................................................................................................................................5 1. 1. LCH S PHT TRIN CA CCH T BRAGG QUANG .......................................................................................................5 1. 2. S LC CNG NGH CH TO FBG..........................................................................................................................6 1.3. S LC V CC NG DNG CA FBG........................................................................................................................9 CHNG 2.........................................................................................................................................................................11 CH TO FBG...................................................................................................................................................................11 2.1 NHY TRONG SI QUANG.....................................................................................................................................11 2. 1. 1 M hnh trung tm mu..............................................................................................................................11 2. 1. 2 M hnh thay i mt ............................................................................................................................12 2. 2 CC PHNG PHP TNG NHY............................................................................................................................13 2. 2. 1 X l bng Hydro.......................................................................................................................................13 2. 2. 2. X l bng nhit........................................................................................................................................13 2. 2. 3 X l bng c hc.......................................................................................................................................14 2. 3 MT S PHNG PHP CH TO CCH T...................................................................................................................16 2. 3. 1 Chiu x tia cc tm im-im.................................................................................................................16 2. 3. 2 Chiu x bng xung laser CO2..................................................................................................................17 2. 3. 3 Phng php dy vi thu knh...................................................................................................................18 2. 3. 4 Phng php cy ion.................................................................................................................................19 2. 3. 5 Phng php mt n bin tia UV..........................................................................................................19 2. 4 TM TT...............................................................................................................................................................20 CHNG 3.........................................................................................................................................................................21 C IM CU TRC V TNH CHT CA FBG.................................................................................................21 3. 1 GII THIU............................................................................................................................................................21 3. 2 IU KIN KT HP PHA...........................................................................................................................................24 3. 3 CC PHNG TRNH GHP MODE................................................................................................................................25 3. 4 L THUYT M HNH HO FBG................................................................................................................................27 3. 5 CU TRC V TNH CHT CA CC DNG CCH T......................................................................................................30 3. 5. 1 Cch t Bragg u (Uniform FBG)...........................................................................................................303. 5. 1. 1 Cu trc.................................................................................................................................................................... 30 3. 5. 1. 2 M t ton hc.......................................................................................................................................................... 31 3. 5. 1. 3 Thi gian tr v tn sc............................................................................................................................................ 34

3. 5. 2 Cch t Bragg quang chu k thay i ........................................................................................................353. 5. 2. 1 Cu trc.................................................................................................................................................................... 35 3. 5. 2. 2 M t ton hc ca CFBG........................................................................................................................................ 36

3. 5. 3 Cch t iu bin chit sut ......................................................................................................................393. 5. 3. 1 Nguyn l................................................................................................................................................................ 39 3. 5. 3. 2 M t ton hc ca AFBG....................................................................................................................................... 40

CHNG 4.........................................................................................................................................................................43 CC NG DNG CA CCH T BRAGG SI QUANG.........................................................................................43 4. 1 NG DNG CA CCH T BRAGG QUANG TRONG B TN SC .......................................................................................43 4. 1. 1 Gii thiu...................................................................................................................................................43 4. 1. 2 Hin tng tn sc trong si cp quang....................................................................................................43 4. 1. 3 B tn sc bng quang si cch t Bragg chu k bin i tuyn tnh........................................................45

Hong Trng Giang Lp D2001 - VT

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Mc lc4. 2 NG DNG CA FBG TRONG B TCH GHP KNH OADM.........................................................................................48 4. 2. 1 Tng quan v WDM...................................................................................................................................48 4.2.2. K thut tch ghp knh quang....................................................................................................................50 4. 2. 3 Cc cu hnh OADM .................................................................................................................................514. 2. 3. 1 OADM da trn FBG v coupler 3 dB.................................................................................................................... 51 4. 2. 3. 2 OADM da trn FBG v cu hnh giao thoa March-Zehnder................................................................................53 4. 2. 3. 3 Cu hnh OADM s dng FBG v Circulator......................................................................................................... 54 4. 2. 3. 4 OADM da trn cch t t gia Coupler............................................................................................................... 55 4. 2. 3. 5 Cc tham s ca cc cu hnh OADM..................................................................................................................... 56

4. 3 NG DNG CA FBG TRONG CN BNG KHUYCH I CA THIT B KHUYCH I QUANG SI EDFA..............................58 4. 3. 1 Tng quan v EDFA...................................................................................................................................584. 3. 1. 1 Cu to v nguyn l hot ng ca EDFA:...........................................................................................................58 4. 3. 1. 2 Tng cn bng cho khuych i EDFA.............................................................................................................. 59

4. 3. 2 ng dng ca FBG trong b cn bng khuych i EDFA.......................................................................62 4. 4 MT S NG DNG KHC CA FBG.........................................................................................................................68 4. 4. 1 NG DNG TRONG CM BIN................................................................................................................................68 4. 4. 2 ng dng trong cng ngh Laser ..............................................................................................................69 TI LIU THAM KHO..................................................................................................................................................72

Hong Trng Giang Lp D2001 - VT

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Danh mc hnh v

DANH MC HNH VHnh 2. 1. C ch nhy trong m hnh trung tm mu................................................................................................. 12 Hnh 2. 2. Phn ng ph v cu trc Si-O-Ge do nhit..................................................................................................... 13 Hnh 2. 3. Ch s chit sut khc x thay i theo sc cng.............................................................................................15 Hnh 2.4: X l bng tia cn cc tm................................................................................................................................ 15 Hnh 2. 5. S phng php ch to im - im.......................................................................................................... 17 Hnh 2. 6. Cu trc dy vi thu knh.................................................................................................................................. 18 Hnh 2. 7. S b tr mt n v si trong phng php cy ion....................................................................................19 Hnh 2.8: Phng php mt n bin s dng tia UV................................................................................................... 20 Hnh 3. 1 Cu to v chit sut ca FBG.......................................................................................................................... 21 Hnh 3. 2: M t c tnh ca FBG................................................................................................................................... 23 Hnh 3. 3: Ph phn x ca cch t Bragg dng cch t u, di cch t 1cm, B=1550 nm, =0. 8 nm.................23 Hnh 3. 5: Cch t Bragg chu k u UFBG..................................................................................................................... 31 Hnh 3. 6: S nguyn l ca ma trn truyn t dnh cho UFBG v non - UFBG......................................................33 Hnh 3. 7:M hnh cch t Bragg chu k thay i CFBG.................................................................................................. 35 Hnh 3.8: A Ph phn x ca cc cch t c gi tr Chirp dB/dz =1 v -1; B: thi gian tr theo bc sng ca CFBG; ph phn x ca cc cch t c gi tr chirp -1;-2;-4 (nm/cm)............................................................................39 Hnh 3.9: th iu bin chit sut si quang AFBG.................................................................................................... 41 Hnh 3.10: Ph phn x ca AFBG vi L=10 mm ,neff =1.447, D =1550 nm ..............................................................42 Hnh 4.1 S thay i ca vn tc nhm theo bc sng trong quang si n mode thng thng.................................44 Hnh 4.2 Hu qu ca tn sc i vi tc truyn ca mng a) xung ti u pht b) xung thu c ti u thu v thit b thu khng th phn bit c hai xung k tip..........45 Hnh 4.3 Nguyn l b tn sc ca quang si cch t Bagg chu k bin i...................................................................46 Hnh 4. 4. M hnh c bn ca thit b b tn sc dng cch t Bagg chu k thay i tuyn tnh...................................47 Hnh 4. 5: H thng ghp bc sng mt hng.............................................................................................................. 49 Hnh 4. 6: H thng ghp bc sng hai hng............................................................................................................... 49 Hnh 4. 7: M hnh c bn ca OADM............................................................................................................................. 50 Hnh 4. 8 : M hnh OADM da trn FBG v coupler 3 dB.............................................................................................52 Hnh 4. 9: OADM da trn cu hnh giao thoa Mach-Zehnder........................................................................................53 Hnh 4. 10: OADM da trn FBG v Circulator............................................................................................................... 54 Hnh 4. 11: Cu hnh OADM dng cch t nm gia Coupler.........................................................................................55 Hnh 4. 12: M hnh cch ly knh OADM.................................................................................................................... 56 Hnh 4. 13: Suy hao xen trong OADM.............................................................................................................................. 57 Hnh 4. 14: M hnh v tham s ca phn x ngc trong OADM.................................................................................. 58 Hnh 4. 15: m hnh mc nng lng ca si quang pha tp Erbium............................................................................... 58 Hnh 4. 16: Cu trc modul EDFA thc t........................................................................................................................ 59 Hnh 4. 17: Cu hnh b lc t ngoi EDFA................................................................................................................61 Hnh 4. 18: Cu hnh b lc t gia EDFA..................................................................................................................... 61 Hnh 4. 19: EDFA khng s dng v c s dng FBG..................................................................................................... 62 Hnh 4. 20: c tuyn thc nghim khuych i ca EDFA ph thuc cng sut tn hiu u vo ti bc sng 1550 nm............................................................................................................................................................................. 65 Hnh 4.21: h s khuych i ph thuc bc sng trong trng hp khng s dng v s dng cch t Bragg CFBG cho khuych i EDFA...................................................................................................................................................... 67 Hnh 4. 22 M hnh h thng cm bin s dng FBG v nguyn l hot ng................................................................69

Hong Trng Giang Lp D2001 - VT

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Danh mc hnh v

Hong Trng Giang Lp D2001 - VT

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Thut ng vit tt

THUT NG VIT TTADM AFBG AWG BFBG CFBG Add / Drop Multiplexing Apodisation Fibre Bragg Grating Array Waveguide Gratings Blazed Fibre Bragg Grating B tch ghp knh Cch t iu bin chit sut Dy cch t dn sng Cch t chiu x Bragg

Chirped Fibre Bragg Grating Cch t Bragg si quang chu k bin i Ghp knh mt cao phn chia theo bc sng B khuych i quang si pha tp Erbium Cch t Bragg si quang Li si khng c lin kt Si - Ge Cng dn sng Planar Cch t Bragg si quang chu k bin i tuyn tnh Cch t Bragg si quang chu k ln B ghp knh B tch ghp knh quang B khuych i quang si Phn cc ph thuc suy hao Cch t Bragg si quang chu k u

DWDM Dense Wavelength Division Multiplex EDFA FBG GODC GPW Erbium Doped Fibre Amplifier Fibre Bragg Grating Germanium Oxygen Deficient Center Gate Planar Waveguide

LCFBG Linear Chirped Fibre Bragg Grating LPG MUX OADM OFA PDL UFBG Long Period Grating Multiplexing Optical Add / Drop Mutiplexing Optical Fibre Amplifier Polarisation Depent Loss Uniform Chirped Fibre Bragg Grating

Thut ng vit tt UV WDM WGR Ultra Violet Wavelength Division Multiplex Waveguide Gratings Router Tia cc tm Ghp knh phn chia theo bc sng B nh tuyn cch t

Li ni u

LI NI UCuc cch mng khoa hc v k thut v ang din ra mt cch mnh m trn ton cu. Cuc cch mng ny a nhn loi tin sang mt k nguyn mi , k nguyn ca nn vn minh da trn c s nn cng nghip tr tu. Khoa hc k thut gp phn thc y kinh t pht trin v tin sang mt giai on mi l nn kinh t tri thc. Trong vin thng l ngnh cng nghip ca tng lai v ng vai tr v cng quan trng trong mi mt ca i sng x hi. Mng truyn dn quang ra i p ng c cc nhu cu ca ngi s dng dch v vin thng v bng thng ln , cht lng tn hiu m bo. iu ny dn n s pht trin tt yu ca mng truyn dn quang. N nhanh chng pht trin tr thnh mng ng trc tc ln vi nhiu cng ngh mi ra i phc v cho mng nh WDM hay EDFA . Cng vi s pht trin ca mng truyn dn quang th cc cng ngh ch to thit b quang cng ngy cng pht trin. Cc thit b mi ra i nhm tng tc v cht lng truyn dn cho mng cng nh khc phc cc nhc im c hu ca mng quang nh l tn sc , suy hao , khuych i cng sut K t khi ra i vo nm 1978 , cch t Bragg si quang c nhng bc pht trin v cng mnh m v hin nay tr nn ph bin. N khng ch c s dng cho cc ng dng trong mng truyn dn quang m cn c s dng cho cc ng dng khc nh laser v cm bin quang. Vi cc u im ca mnh nh s a dng trong ng dng , n nh cao v gi thnh h, cch t Bragg si quang v s pht trin hn na trong thi gian ti. Di s hng dn tn tnh ca thy Trn c Nhn cng nh s gip ca cc thy c trong b mn thng tin quang ca Hc Vin , em tin hnh nghin cu v nguyn l v cc ng dng ca cch t Bragg si quang. n nay em hon thnh bn n vi ti Cch t Bragg si . Bn n c 4 chng: Chng I : Gii thiu chung - gii thiu v lch s v cng ngh ch to cng nh ng dng ca cch t Bragg si quang. Chng II : Cc cng ngh ch to cch t Bragg si quang - chng ny tin hnh tm hiu v cc cng ngh ch to v c im ca tng loi cng ngh . Chng III : Tnh cht v c im ca cch t Bragg si quang - chng ny chi tit cch t Bragg si quang v c im cu to v cc m t ton hc ca cc tnh cht ca cc dng cch t. Chng IV : ng dng ca cch t Bragg si quang - chng ny m t v cc ng dng ni bt ca cch t trong cc h thng hin nay.

Li ni u Do ti c ni dung rng v tng i mi m, iu kin thi gian v kin thc cn hn ch nn ti khng trnh khi nhng thiu st , em mong nhn c s gp chn thnh ca cc thy c gio v cc bn ti c hon thin hn. Em xin chn thnh cm n n cc thy c trong khoa vin thng , b mn thng tin quang nhng ngi gip em trong thi gian qua. Em xin cm n thy Nguyn c Nhn ngi tn tnh gip em trong qu trnh nghin cu v hon thnh n. Cm n n bn b v ngi thn to iu kin v ng vin bn n ny hon thnh tt p. H Ni ngy 18 thng 10 nm 2005 Sinh vin Hong Trng Giang

Chng 1: Gii thiu chung

CHNG 1 GII THIU CHUNG 1. 1. Lch s pht trin ca cch t Bragg quangM hnh cch t Bragg quang c a ra v chng minh cc tnh cht ca n ln u tin vo nm 1978 bi Hill et al. n nm 1989, n c m t mt cch r rng hn bi Meltz et al, cch t Bragg quang c to ra bng cch s dng php chiu giao thoa hai lung tia cc tm UV-exposure. Vi s pht trin ca mnh, FBG c lin quan trc tip v cht ch vi s pht trin ca si quang, n c kh nng s dng trong vic xy dng cc b lc dng tch ghp knh trong h thng truyn ti d liu a knh. Ni bt nht trong nhng ng dng ny l FBG c dng cho h thng DWDM, FBG l c s cho cc thit b la chn th ng cho cc bc sng n, ghp bc sng v chn bc sng bng hp. N lm vic tt trong iu kin cc yu t v nhit v sc cng c m bo bi v cc iu kin ny c th nh hng n tin cy ca FBG. S pht trin nhanh chng ca FBG v cc ng dng trong mng vin thng quang v cc h thng cm bin thc y l nng cao tc t ph trong nghin cu, nhng kt qu ny lm ci thin v pht trin cht lng cng nh cc tnh nng ca cc thit b quang. Trong tng lai, cc tnh nng ca cc thit b ny c th vt qua cc gii hn hin ti bng vic s dng k thut photonic. Tnh nng nhy cm vi mi trng l mt im khng tt ca FBG, tuy nhin hin nay n li c s dng rt nhiu trong cc h thng cm bin. Mt trong cc ng dng l cu ch sillica, n lin quan n tnh cht khng b nh hng bi in t trng ca FBG. FBG c chu k ln c a ra v chng minh bi Vengkarsar v nhm nghin cu ca ng, n lp tc c ng dng rng ri trong cc b lc thng bng v c s dng trong cc h thng mng DWDM, l cc b cn bng khuych i EDFA, trong cc h thng laser nh cc thit b cn bng laser pht. Hn na, FBG ang tr nn rt ph bin vi t cch l mt thit b quang n gin, linh hot v c v s cc ng dng trong cc thit b v h thng quang.

Chng 1: Gii thiu chung Cc dng cch t Bragg hin ang c s dng ph bin trong cc ng dng hin nay bao gm cc loi : FBG chu k u (Normal FBG), FBG chu k tuyn tnh (linear chirped FBG) v Apodisation FBG.

1. 2. S lc cng ngh ch to FBGK thut to ra cch t Bragg quang u tin l k thut mt n bin pht minh do Vengsarkar et al, phng php ny s dng si quang Si-Ge giu Hidro t trong mi trng chiu x laser KrF ( = 248 nm) thng qua mt n bin lm bng silica m Crom. Mi cch t c to ra trn si quang c di chng 1 inch v chu k ca cch t vo khong 60 m cho n 1 mm. Ph truyn nh sng ca cch t c gim st ngay trong qu trnh to nn cch t, thi gian to ra mt cch t nm trong khong 5 10 pht. Phng php mt n bin ny l phng php c s dng rng ri nht hin nay do tin cy trong ton b qu trnh s dng n. Vi vic cho php cc mt n bin c th c ti s dng v cc yu cu trong lc ch to c gim thiu lm gim gi thnh ca sn phm. Nhc im ca phng php ny l vic to ra cc cch t c chu k khc nhau chng ta ch co duy nht mt cch l thay i bng cc mt n c chu k khc nhau v iu ny lm tng gi thnh sn phm. Zhang et al ch to cch t Bragg quang bng cch s dng phng php chiu x trc tip tia UV ln si quang theo im - im. Qu trnh chiu x im im ph thuc vo cc yu cu v chu k v p ng ph. Qu trnh ny c iu khin bi mt my tnh s dng chng trnh iu khin ng ngt chiu x v v vy n c u im rt ln l c kh nng iu khin mt cch mm do chu k ca cch t sn phm bng vic thay i cc thng s chiu x thng qua phn mm iu khin. Nhc im chnh ca phng php ny l vic n tiu tn nhiu thi gian trong vic chiu x, hn na yu cu k thut ca phng php ny rt nghim ngt. Mt k thut mi dng ch to FBG s dng chiu x tp trung xung laser hng ngoi femto giy. Phng php ny c thuyt trnh bi Kondo et al. Trong k thut ny, si quang c chn l si quang n mode tiu chun cho truyn ti (NA=0. 11, ng knh trng mode 9. 3 0. 5 m, ng knh v 125 2 m,

Chng 1: Gii thiu chung bc sng ct 1260 40 m). Li v v ca si quang ln lt l Silica nguyn cht v Silica pha Ge. Cc xung laser c s dng gy nh hng to ra s thay i chit sut ca si. rng xung laser khong 120 fs, bc sng 800 nm v tn s lp khong 200 khz. Chm laser c a ti v tp trung trong phm vi khong 20 li ca si quang. Cc tnh nng ca FBG sn phm c gim st bi camera CCD t trn microscope. Si quang c t vo mt my tnh iu khin v s c chiu x laser hng ngoi bi phng php im - im. Vic phn tch p ng ph v ph truyn dn ca FBG c phn tch v gim st cng lc to ra cc sn phm c tnh nng theo yu cu. Cc FBG sn xut theo cng ngh ny c tui th rt cao. Hin nay hu ht cc FBG u c ch to theo phng php chiu x tia UV ln si quang nhng Davis et al v Karpov et al a ra kh nng s dng xung laser CO2. Thc nghim ca h da trn cu hnh bao gm mt my tnh iu khin dng iu chnh v tr si quang. Di s iu khin ca my tnh, cc xung laser n (~ 0. 5W, 300ms) c tp trung vo phn ng knh ca si quang ti cc v tr xc nh trc dc theo chiu trc si. Mt h thng gim st c lp ngay pha trn si dng gim st v tr ca si v m bo rng cc li vt l khng xy ra trong qu trnh ch to. Mt ngun quang bng rng c bc sng nm trong khong 1. 4 - 1. 6 m c chiu vo si quang v mt my phn tch ph cng c s dng phn tch nhm gim st ph truyn dn ca FBG ang c ch to. u im chnh ca phng php ny l vic k thut s dng laser CO2 khng qu t, cc yu t k thut ca FBG c gim st cht ch v khng xy ra cc li vt l lm cho mo, bin dng FBGs. Mt k thut ch to FBG khc c Lin v Wang a ra, trong cu trc chit xut theo np gp ca si quang c to ra bng cch khc axit trn si quang. Loi FBG ny c ch to theo cch sau : mt si quang dch tn sc tiu chun vi ng knh v ban u l 125m c s dng. Mt lp v kim loi mng vi dy 120nm c ph ln si quang vi mt lp cht bo v chng li s n mn ca axit ti cc v tr nh trc, sau n c nhng vo dung dch axit flohidric. Khi cc phn khng c bo v s b n mn bi axit vo trong

Chng 1: Gii thiu chung ng knh li khong 42m. Phn mt n s c thit lp sao cho cu trc np gp c chu k l 400m trong di tng cng ca FBG l 20nm. Vic mt nh sng truyn dn ti a nm ti hai u ca FBG do hin tng phn x, bi v lc chnh lch v chit sut gia hai mi trng truyn nh sng l ln nht (chit sut khng kh l 1). Mt trong cc tnh nng ca FBG ch to theo phng php ny l quan h gia bc sng v mt nng lng truyn dn c th iu chnh bn ngoi bng cch thay i cc iu kin tc ng c hc khi ch to, bi v ch s chit sut iu ch truyn dn to nn bi nhiu cu trc np gp khc nhau. Mt k thut ch to FBG khc cng c a ra bi Fujimaki et al. Trong k thut ny, cc ion Helium c a su vo trong li si quang thng qua mt mt n kim loi, khong cch cch t c to ra l 60m. Vic cy cc ion ny gy nh hng n chit sut ca si quang v to nn cch t. Loi cch t ny c th c s dng trong b lc chn bc sng trong truyn dn quang. Vic ch to FBG hin nay l tng i n gin, cc phng php s dng thng ph thuc vo lnh vc v mc ch s dng chng hn nh s dng trong cc h thng truyn dn hay l cc h thng cm bin Phng php s dng ch to FBG hin nay ph hp vi tnh cng nghip c a ra v chng minh bi Liu l s dng tia UV tc ng ln si quang to nn mt dy cc vi thu knh. Dy vi thu knh ny c to nn bng vic s dng laser bc sng 248nm chu k xung 20ns. Vi phng php ny, thi gian dng cho vic ch to s nhanh gp 4 ln so vi phng php s dng mt n kim loi. Tm li, cc phng php s dng ch to FBG c lit k vo 2 dng : l phng php s dng chiu x tia UV v phng php khng s dng chiu x tia UV. Trong phng php s dng chiu x tia UV, chia lm hai k thut chnh l k thut chiu x tia UV im - im v k thut mt n bin . K thut chiu x im im l k thut c tnh mm do v ph hp cho vic ch to cc FBG c cc c tnh ph khc nhau nhng li khng ph hp cho vic ch to hng lot, trong khi phng php mt n bin khng ph hp vi vic thay i c tnh ph ca cch t, nhng li ph hp vi vic ch to hng lot v gi thnh cho vic ch to ny tng i r, c 3 loi mt n bin c s dng l mt n Crom, mt n

Chng 1: Gii thiu chung in mi v mt n kim loi. Trong phng php khng s dng chiu x tia UV, k thut s dng laser CO2 c gi thnh r, cn cc phng php cy ion v phng php khc axit vn ang cn trong qu trnh thc nghim.

1.3. S lc v cc ng dng ca FBGCc c im v cm quang v kh nng tng thch vn c vi si quang cho php ch to rt nhiu loi FBG khc nhau, c bit l cc LPG. Hin ti, cc FBG c rt nhiu ng dng trong cc h thng cm bin v truyn dn quang. B lc chn bc sng rt hp dng cho b khuych i quang EDFA l mt v d in hnh v ng dng ca loi thit b ny. Hin nay mc d cc cch t quang dng ny c tp trung pht trin cho cc ng dng lin quan n truyn dn quang v cc h thng cm bin nhng vn c nhiu ng dng tim nng khc c th pht trin nh l chuyn mch quang, x l tn hiu quang v.v... Cc ng dng ca n c th tp trung vo 3 ng dng chnh nh sau: + ng dng trong cc h thng cm bin: - Cm bin nhit - Cm bin sc cng - Cm bin p sut. + ng dng trong laser quang: - Laser cch t quang bn dn - Khoang n nh ngoi cho laser bn dn - Khuych i kch thch Erbium cho laser + ng dng trong truyn dn quang: - B tn sc - Cc h thng ghp knh phn chia theo bc sng WDM - B lc cn bng cho khuych i Erbium - B tch ghp knh

Chng 1: Gii thiu chung - B phn x nhiu - Khuych i Raman Nh vy cch t Bragg hin v ang tr thnh mt trong nhng pht minh v thit b quang c cc ng dng a dng trong thc t. Trong cc chng sau chng ta s m t cc thuc tnh v ng dng c th ca tng loi cch t Bragg si quang lm r hn vn ny.

Chng 2: Ch to FBG CHNG 2

CH TO FBG 2.1 nhy trong si quangKhi nim nhy trong si quang c a ra u tin bi Hill. nhy trong si quang c nh ngha nh l mt tnh cht ca vt liu dn quang c th hin kh nng lu gi qu trnh iu bin vi sai nhm phn b cng pht x quang theo mun. Tnh cht ny c ng dng nhiu trong ch to cc thit b quang, chng hn nh cch t. Cch t chit sut khc x l mt thit b quang c nhim v iu bin tn hiu theo chu k hoc pha ca sng ti. Vic ch to cc cch t dng ny thng dng cc vt liu c tnh cht nhy cm nh sng, chng hn nh Li, Ga-As, Ba-Ti, m t nhy nh sng trong si quang, chng hn si Ge, ngi ta a ra mt s m hnh. Nhng m hnh ny da vo s thay i nh hp th ca vt liu v mi quan h Kramer-Kronig phn tch s bin thin ca chit sut khc x. 2. 1. 1 M hnh trung tm mu C ch to ra nhy trong si quang l da trn s nh hng ca s thay i chit sut khc x vo s pht x nh sng ca cu trc GeO khng hon ho v nh hp th vt liu ti bc sng 252nm. Cu trc khng hon ho ny c gi l m hnh trung tm mu. Cu trc ny c to ra do qu trnh ion ho c pht x. Hnh 2. 1 minh ho qu trnh to trung tm mu Ge. Trung tm mu c to ra do s ph v lin kt Ge-Ge/Si gii phng 1e t do. Qu trnh ny cng vi qu trnh chiu x bng tia cc tm s to ra nh hp th mi bc sng 195, 213 v 281nm. Qu trnh ny l lin tc do tnh cht cu trc ca vt liu SiO2. Theo m hnh ny, ngi ta chng minh c rng chit sut khc x ti mt im ch ph thuc vo mt v vc t nh hng ca cc ion c to ra do ph v lin kt. N c th hin bng ph hp th electron ca cc ion ny. C th

Chng 2: Ch to FBG nhn thy rng bng hp th ny tng ng vi trung tm GeE. Dng biu thc Kramer-Kronig ngi ta c th nh gi c s thay i ca bng hp th ny.

Ge/Si

E

Ge/Si

hv

Ge

im khng hon ho

Ge

Hnh 2. 1. C ch nhy trong m hnh trung tm mu

2. 1. 2 M hnh thay i mt M hnh thay i mt da vo tnh cht mt ph thuc vo qu trnh ion ho pht x ca GeO. S ion ho ny chnh l s b gy cc vng ring nh (2 hoc 3 phn t) trong cu trc vt liu si. Ngi ta chng minh c rng mi quan h gia thay i mt v ch s chit sut khc x l xp x tuyn tnh. Mc d m hnh thay i mt c a ra nm 1991, nhng mi n nm 1998 ngi ta mi xc nhn cc kt qu ny bng cch dng knh hin vi in t. Tuy nhin cc kt qu a ra vn cha y . L thuyt v m hnh ny hin nay ang tip tc c nghin cu. Ngoi cc m hnh chng ta nu trn cn c mt s m hnh m chng ta khng nu ra y, chng hn nh m hnh dch chuyn electron, Vic ng dng cc m hnh ny vo qu trnh ch to cch t chnh l vic s dng cc tnh cht lm tng nhy.

Chng 2: Ch to FBG

2. 2 Cc phng php tng nhy tng hiu qu ca cch t, nhy ca cch t phi t c gi tr ph hp, v vy yu cu tng nhy. Phn ny trnh by tm tt cc phng php tng nhy p ng ca si quang. Cc phng php c s dng bao gm: X l bng Hydro, x l bng nhit v x l bng c hc. 2. 2. 1 X l bng Hydro Khi dch chuyn si quang trong mi trng Hydro p sut cao ti nhit phng, cc phn t Hydro s khuch tn vo trong si. Cc phn t ny s ph v lin kt Si-O-Ge to ra Si-OH v GeO cc tnh m nh hnh 2. 2.

O O Si O O

O Ge O O + H2 O

O Si O OH +O O

O Ge O O

Hnh 2. 2. Phn ng ph v cu trc Si-O-Ge do nhit

Cu trc Si-OH c nh hp th ti bc song 1390nm nm trong vng ph s dng. Tuy nhin iu ny khng nh hng nhiu v thc t mt -OH trong si nh hn nhiu mt GeO2 (lng OH ch chim 1-2%). Ngoi ra c th khc phc hin tng ny bng cch thay cht ti H2 (Hydro) bi D2 (tri) v khi ph ca nh hp th nm ngoi ca s ph s dng. S thay i chit sut khc x mc cao, n 6.10 3 , c tc dng lm tng nhy khi c tc dng ca tia cc tm. 2. 2. 2. X l bng nhit Chi nhit l phng php n gin trong vic dng nh hng ca nhit lm thay i chit sut khc x. Vng si quang cn lm tng nhy c qut bng ngun nhit to thnh t oxi v hydro giu vi nhit khong 1700oC trong vng 20 pht. nhit ny hydro khuch tn vo li si rt nhanh v to phn

Chng 2: Ch to FBG ng b gy cu trc GeO. Qu trnh ny to ra nh hp th bc sng 250nm trong li si v lm tng nhy. Khi tia cc tm s c nh hng ln n s thay i ch s chit sut khc x. Phng php ny c th lm tng nhy vi h s ln hn 10. Phng php tng nhy bng nhit c rt nhiu u im. R rng nht l nhy to ra rt n nh khi so vi phng php x l bng hydro v trong phng php x l bng hydro, khi hydro thm thu ra khi si th nhy ca si s gim. Ngoi ra vt liu dng ch to cch t cng khng yu cu c nhy cao. Nhc im chnh ca phng php ny l do x l nhit cao nn bn si khng cao. 2. 2. 3 X l bng c hc Bng thc nghim ngi ta chng minh c rng khi thay i sc cng b mt ca cch t kt hp vi chiu x bng tia cc tm, ch s chit sut khc x cng thay i. Hnh 2. 3 biu din s thay i tng ng gia chng. Ngoi ra, khi chiu x bng tia cc tm, cch t lm bng si Ge s to nn sc cng. L do l khi chiu x bng tia cc tm, cc phn t b b gy (hay l cu trc khng hon ho) ca lin kt Si-Ge-O s sp xp li theo cu trc cht ch hn lm tng mt . iu cng c ngha l nhy s tng. Trong mt s trng hp, h s tng nhy ca phng php ny c th ln hn 10.

Chng 2: Ch to FBG2 1.8 1.6 1.4 thay i chit sut khc x 1.2 1 0.8 0.6 0.4 0.2 0 0 0.2 0.4 0.6 Khng sc cng 0.8 1 1.2 Sc cng 3%

nh hng ( .10e6/cm2)

Hnh 2. 3. Ch s chit sut khc x thay i theo sc cng

2. 2. 4 X l bng tia cn cc tm Phng th nghim Starobudov a ra phng php lm thay i ch s chit sut bng cch s dng cc tia cn cc tm cho si Ge Si ti bc sng 330 nm. M hnh m t qu trnh lm vic ca h thng ny cho bi hnh 2. 4 sau:Conduction band Conduction band

S1 T1 240 nm T1 DID 330 nm DID

GOCD

GOCD

Hnh 2.4: X l bng tia cn cc tm

Chng 2: Ch to FBG Trong hnh v trn, mt h thng tia UV c bc sng khong 240 nm c dng kch thch si Si Ge t trng thi S0 n nh ln trng thi kch thch S1 m si c xu hng b ion ho, do t pht hoc do cc ion 240 nm khc kch thch t bn ngoi. Qu trnh ion ho ny s nh hng n ch s chit sut ca si v ngi ta c th iu khin qu trnh ny t c cc ch s chit sut khc nhau ti cc v tr khc nhau. Vic ny s dn n s thay i v sp xp li cu trc ca li si quang v gy nn s thay i chit sut. u im chnh ca cng ngh ny l sn phm do n to ra c n nh nhit rt cao nhng n li khng yu cu vic luyn li bng nhit.

2. 3 Mt s phng php ch to cch tHin nay c rt nhiu phng php ch to cch t. mc ny chng ta s a ra cc phng php c dng ph bin hin nay. 2. 3. 1 Chiu x tia cc tm im-im S ca phng php ny c biu din hnh 2. 5. Trong s , cc thnh phn c tc dng nh knh thin vn v knh hin vi c tc dng lm gim kch thc ca lung chiu x tia cc tm. My tnh c kh nng iu khin b dch v tm chn sng. Ngun tia cc tm c to ra t laser KrF chiu qua mt khe hp. Ton b qu trnh ch to si u c thc hin mt cch t ng v do my tnh iu khin bng phn mm. Phng php ny c u im chi ph thp, d dng thc hin v c kh nng to ra cch t c chu k v di khc nhau.

Chng 2: Ch to FBGTm chn sng Dng UV Knh thin vn Knh hin vi B dch Gng 248nm

My phn tch ph Si

LED

Hnh 2. 5. S phng php ch to im - im

2. 3. 2 Chiu x bng xung laser CO2 Nm 1998, ngi ta a ra mt phng php ch to cch t chu k di. Trong phng php ny, mt my tnh iu kin c cu c hc gn c nh vo si vi chnh xc 0.1m c th iu chnh tiu im Gaussian 145m ca dng laser CO2. Trong khi si c dch bng b dch, my tnh iu khin b chn sng cho php dng laser chiu vo si. c th quan st d dng c th t cc thit b nh my phn tch ph, camera. Ngoi ra phng php ny, khi th vi si mang ti H 2 v khng mang ti H2 ngi ta nhn thy rng cht lng ca cch t chu k di ch to t si khng mang ti chiu x CO2 km hn. Ngoi ra, nhit yu cu i vi si khng mang ti H2 khi chiu x trong qu trnh chiu x l 1700 trong khi i vi si mang ti H2 l t 800oC n 1200oC. iu c ngha l mc cng sut yu cu cho si mang ti H2 ch bng khong so vi si khng mang ti H2. Phng php chiu x CO to ra cch t rt n nh. c tnh bng tn b loi b khng thay i ngay c khi nhit tng ln n 1200oC trong khi cch t dng phng php chiu x bng tia cc tm b nh hng bi nhit . Nh vy cch t dng phng php chiu x c c u im bn v chu c nhit cao do n thng c s dng trong thc t.

Chng 2: Ch to FBG 2. 3. 3 Phng php dy vi thu knh Phng php dy vi thu knh c u im l gi thnh thp, n c th sn xut vi s lng ln cch t. Hnh 2. 6 ch ra cu trc ca dy vi thu knh. ch to dy vi thu knh, ngi ta dng si silica nng chy di khong 1. 3m vi suy hao thp trong vng 180nm n 1100nm. ng knh ca li v lp m tng ng l 400 m v 440 m . Sau khi x l loi b lp m, si c ct thnh cc ming nh 2cm. Tip theo cc mu ny c xp lin k t vo khun nhm. Sau chiu x bng tia cc tm nh dng cho dy thu knh. Ch rng chu k ca dy vi thu knh tng ng vi bc sng 440 m (bng vi ng knh lp m ca si).Khun Al 248nm

248nm

Dy vi thu knh

Hnh 2. 6. Cu trc dy vi thu knh

Mc d phng php ny c u im v gi thnh nhng n cng c rt nhiu nhc im. Mt nhc im d nhn thy l kh khn trong vic thc hin cc thao tc ch to mng bi v qu trnh ny i hi chnh xc cao. Hn na khi s dng vic tp trung nh sng vo mt vng no c th lm nh hng n cu trc mng. khc phc nhc im ny, chng ta c th s dng mng vi mt mt li.

Chng 2: Ch to FBG 2. 3. 4 Phng php cy ion Bng thc nghim ngi ta bit rng phng php cy ion lm tng ch s chit sut mc cao i vi hu nh tt c cc vt liu ch to si quang, v vy y l phng php rt ph bin trong thc tin. thc hin ngi ta dng si Ge c li ng knh 9 m vithnh phn 97SiO2:3GeO2, v lm bng Si nguyn cht vi ng knh 125m . Cch b tr mt n v si nh hnh 5. 6. Si c cy bng ion He2+ ti nhit phng thng qua mt mt n kim loi bng cch dng my gia tc 1. 7 MV (nng lng ca ion khong 51MeV). Khi ion c cy vo li, phn v s c khc axit ng knh cn khong 53m .

ion Mt n

Si quang

Hnh 2. 7. S b tr mt n v si trong phng php cy ion

quan st ngi ta dng mt my phn tch ph. T i n kt lun ti vng cy ion, chit sut khc x tng ln ng k. Nh vy c th thy rng phng php ny c hiu qu i vi hu ht cc loi vt liu. y chnh l u im ni tri ca phng php ny. 2. 3. 5 Phng php mt n bin tia UV y l dng phng php ph bin nht dng ch to FBG. Hnh 2. 5 m t chi tit phng php ny.

Chng 2: Ch to FBGLaser kch thch 248 nm Mt n bin

LEDiu khin phn cc

Phn tch ph quang

Hnh 2.8: Phng php mt n bin s dng tia UV

i vi thit b ny, mt n bin cho php cc xung laser t ngng truyn qua theo ng vung gc, ngng ca xung trong h thng ny quy nh 100 mJ/ cm2 / 1 xung. Trong cc mt n c mt s c chu k khc vi cc mt n cn li v do vy nh hng ca sng laser cng khc so vi cc phn cn li, do nh hng ca laser m chit sut ca cc v tr khc nhau trong li si c th khc nhau. Ph ca cch t c gim st bng nh sng ca mt LED bng rng chiu qua cch t v a n mt my phn tch quang ph. Khi sng phn x tr li t cch t tho mn cc yu cu v ph th ngun laser s ngng pht v sn phm c hon thnh.

2. 4 Tm ttTrn y chng ta trnh by mt cch khi qut v cch t FBG, cc tnh cht ca cch t c xy dng da trn cc m hnh khc nhau v cc phng php ch to cch t ph bin hin nay. Mi phng php ny u c u nhc im ring. la chn phng php ti u chng ta phi da vo cc tiu ch khc nh gi. Thc t hin nay cc phng php ny ngy cng c hon thin v mt s phng php mi ang c xut th nghim. la chn mt phng php ch to thch hp ngi s dng cn cn c vo cc tnh cht cng nh ng dng v yu cu cht lng ca FBG s dng cc cng ngh ch to ph hp.

Chng 2: Ch to FBG

CHNG 3 C IM CU TRC V TNH CHT CA FBG 3. 1 Gii thiu B ti B truyn

B phn x

Khong cch

=B/neff

Chit sut

z

Hnh 3. 1 Cu to v chit sut ca FBG

Cch t Bragg quang thc cht l s xo trn cu trc ch s chit sut theo dng chu k dc theo hng truyn sng ca si quang v c m t trong hnh trn. Ch s chit sut ca FBG c tnh theo phng trnh sau :

Chng 2: Ch to FBG

n( x, y, z ) =Trong n(x, y ,z )

2 n( x, y z )( + n x cos( , , , ) y z

)

z(3. 1)

l ch s chit sut trung bnh ca li si quang v

n ( x , y , z )l ch s iu ch v l chu k ca FBG.

Mt lng nh nh sng c phn x ti mi im ni ch s chit sut ca FBG thay i. S phn x hon ton trong FBG xy ra ti cc bc sng ring khi xut hin mode ghp mnh nht. y gi l iu kin Bragg c m t trong phng trnh (3. 2), bc sng m ti c s phn x hon ton c gi l bc sng Bragg B. Ch c nhng bc sng tho mn iu kin Bragg l chu nh hng ca cch t v phn x mt cch mnh m. FBG trong sut i vi cc bc sng nm ngoi vng bc sng Bragg. Bc sng Bragg c tnh nh sau:

B = 2 neff

(3. 2)

Trong neff l ch s khc x nh hng v l chu k ca FBG. y chnh l iu kin xy ra phn x Bragg. T phng trnh (3. 2) chng ta c th thy rng bc sng Bragg hon ton ph thuc vo ch s khc x v chu k ca cch t. Cc cch t di vi ch s khc x thay i khng ng k c nh phn x rt nhn v bng tn phn x rt nh nh m t trong hnh (3. 2):

Chng 2: Ch to FBG

Ph nng lng

Hng phn x

B Ph nng lngHng ra

Ph nng lng

Hng ti

Ngun vo

Hnh 3. 2: M t c tnh ca FBG

i vi cch t Bragg u, cc tham s ch s khc x nh hng n eff v chu k cch t l c nh. Dng ph phn x ca loi cch t ny c m t trong hnh (3. 3):

Hnh 3. 3: Ph phn x ca cch t Bragg dng cch t u, di cch t 1cm, B=1550 nm, =0. 8 nm

Chng 2: Ch to FBG

3. 2 iu kin kt hp phaFBG cho php truyn nng lng gia cc mode trong mt si quang. iu ny c th t c bng vic thay i pha ca mt mode sao cho n kt hp c vi pha ca mt mode khc. Cc FBG thng c lm trn si quang trn sau khi bc i lp v acrylat c ngha l si quang c xem nh c cu trc 3 lp vi cc chit sut khc nhau, trong lp trong cng l lp li c chit sut l n1, tip n l lp v c chit sut l n2 v ngoi cng l khng kh vi n3 = 1. Vi si quang n mode vi cc tham s nh trn thi mode trung tm c hng s truyn t BCO cho bi:2 2 2 n2 < BCO = nCO < n1 (3. 3)

V cc mode ngoi c ch ra bi cu trc v - khng kh c hng s truyn nh sau:2 2 n3 < Bu < n2

(3. 4)

Kt qu, cc mode pht x c th hng s truyn trong gii hn:0 < Brad < 2 n3

(3. 5)

tm hiu s bin i ch s chit sut theo chu k dc theo chiu di si quang, vic kt hp pha u tin c thc hin gia mode c bn v mode chm (mode v) xut hin khi:1 2 =2

(3. 6)

Trong trng hp ghp cn mode gia hai mode ny, 2 = 1 v phng trnh c vit li:1 =

(3. 7)

Chng 2: Ch to FBG Trong cc biu thc (3. 6) v (3. 7) l chu k ca s thay i ch s iu ch v 1 v 2 tng ng l hng s truyn ca mode c bn v mode c ghp i cng vi n. Cch t thc hin ghp mode chm c xem nh l m b phn x hay l cch t Bragg. c trng ca cc thit b ny da trn c s ghp mode gia mode c bn ti v i. i vi cc cch t chu k ln (c 1 v 2 u ln). iu kin kt hp cho ghp hng ti cha mode c bn v mode truyn ca v cho bi:1 2 =2

(3. 8)

3. 3 Cc phng trnh ghp modeNguyn l ghp cp mode c s dng thnh cng m t cc thuc tnh ph ca cc cch t Bragg. S bin i ch s phn x theo chu k dc theo chiu di ca si quang c m t nh sau:n( z ) = n0 + n( z )cos[ 2 + ( z )]

(3. 9)

Cc hm n( z ) v ( z ) l cc hm bin i chm hn so vi chu k cch t ; n0 l chit sut ca li, n( z ) l hiu s chit sut li - v. Tham s ( z ) l pha ca ch s iu ch; n c s dng miu t s dch chuyn pha hay l chirp cch t. Dc theo cch t sng ti 1 v sng phn x 2 lin quan vi nhau bi phng trnh mode:dv1 = iv1 + iq ( z )v2 dt dv 2 = iv2 iq ( z )v1 dt

(3. 10)

Ni bin ca vng 1 v 2 quan h vi bin ca trng in t, ta c:A( z ) = v1.e i z B ( z ) = v2 .e + i z

(3. 11)

a(z) l ch s ghp mode, cho bi:

Chng 2: Ch to FBGa( z ) =

n( z ) 2n0

(3. 12)

V l ch s mt iu hng ca bc sng phn x t FBG Bragg = 2 _ n0 = 2n0

c nh ngha:= 2 n0

(3. 12)

Trong trng hp cch t Bragg c nhiu gi tr n dc theo chiu di cch t, cc phn tch ph c th t c bng cch gii quyt cc phng trnh ghp mode khc nhau. Trng hp cc cch t ng dng cng c gii quyt tng2 t. H s phn x v1 ( ) / v2 ( ) v R = ti im bt u ca cch t l (t-v):

() =

q sinh( L) f sinh( L) + i cosh( L)

(3. 13)

s inh 2 ( L) R () = 2 cosh 2 ( L)-

q

2

; 2 = q 2 2 (3. 14)

Mt vi ng dng quan trng t kt qu ny: l c th chng minh h s phn x Rmax xut hin khi quan st iu kin phn x ti = 0:Rmax = tanh 2 (qL)

(3. 15)

Tip theo bng tn Vzero c xem l im zero th 2 trong tnh ton phn x: Vzero n = 1 + Bragg n0 nL

(3. 16)

Vi cch t c nL >> Bragg , cng thc c n gin ho nh sau:Vzero n = n0

(3. 17)

Chng 2: Ch to FBG Phng trnh (3. 16) cung cp thng tin v vic gy ra hiu ng ch s thay i n gin bng cch tnh ton ph bng tn ca cch t. Tng t cho cch t cng loi, vic thay i ch s cng sut cng c th dng phng trnh (3. 14) tnh ton, vi Rmax ti = Bragg . hiu mt cch y v cc thuc tnh ca cch t Bragg quang, khi nim tr nhm hay tr thi gian phi c tnh ton. Vi cch cch t loi ny thi gian tr c th c quyt nh bi pha ca h s phn x cho trn. Nu = phase ( ) v thi gian tr cho nh sng phn x ngc tr li t cch t cho bi: =d dw =

2 d . 2 c d

(3. 18)

V di hiu qu Leff m nh sng ti cc bc sng ring s i qua trong cch t trc khi quay ngc tr li c tnh bng Leff = cn0 . Trong cc cch t

loi ny thi gian tr nh nht xut hin ti = Bragg . i vi cc bc sng gn cnh cc bng tn ca cch t c tn sc ln nht vi thi gian t bin ng ln ti cc bc sng. V vy, chnh lch thi gian t rng ln l c tnh ca dng ny, n ph thuc vo bc sng trc khi ra khi cch t. Hnh 3. 3 cho thy ph phn x v thi gian tr ca dng cch t ny vi thi gian tr tnh t (3. 15), tng ng vi thi gian tr nh nht. Vi bc sng gn z zeros , thi gian tr l max.

3. 4 L thuyt m hnh ho FBGTrong hu ht cc cch t si quang, cc ch s thay i trn nhng khong tng i u nhau theo b ngang ca li si, v hu nh khng c mt mode nh sng no truyn bn ngoi li. Chng ta gi nh rng s khng c mode v v b qua dng mode ny, nh vy th c tnh trng in t ca cch t c th c n gin ho v ch cn s chng mode gia mode hng i v hng v ca cc mode trong li. Trng in dc theo li ca si c th c biu din theo phng trnh sau: E(x, y, z) = A+(z)exp(-iz) + A-(z)exp(iz)e(x, y) (3. 19)

Chng 2: Ch to FBG Trong A+(z) v A-(z) l cc bin bin i chm ca sng nh sng hng i v v dc theo li si. E(x, y, z) c th c thay th bng phng trnh ghp mode. Phng trnh ghp mode c th n gin ho bng vic gim s mode xung cn hai mode v c m t nh sau:dR( z) = i ( z ) R ( z ) ik ( z ) S ( z ) + dz

d S( z) = ( z ) R ( z ) ik ( ) R ( z ) (3. 20) i z dzTrong R(z) = A+(z)exp[ i( /2)] v S(z) = A-(z)exp[- i( + /2)], R(z) l mode hng ti v S(z) l mode ca hng phn x ngc tr li, c hai l cc hm th hin cc mode bao thay i chm. l mt h s t ghp mode chung DC hay cn gi l s mt iu hng ni. k(z) l h s ghp mode AC hay cn c gi l mnh ghp mode bn trong ca cch t. Cc phng trnh ghp mode (3. 20) c s dng trong vic tnh ton ph p ng phn x ca FBG. H s ghp mode k(z) v ch s iu hng ni (z) l hai tham s rt quan trng ca phng trnh ghp mode. Chng l cc tham s c bn trong vic tnh ton ph p ng phn x ca FBG. H s t ghp mode c tnh nh sau: =+Trong 1d 2 dz

(3. 21)

1d l m t ca kh nng chirp c th ca chu k cch t v l 2 dz

pha ca FBG. H s mt iu hng c tnh nh sau: =

= - D 1 1 = 2n eff ( ) D

(3. 22)

Chng 2: Ch to FBG Trong D = 2neff l bc sng thit k cho s phn x Bragg khi khong cch cch t rt nh neff 0.= 2 neff

(3. 23)

Trong neff l s thay i ch s khc x c bn. H s ghp k(z) c th c tnh theo phng trnh sau: k ( z )n( ) ( z ) g z v (3. 24) =

Trong g(z) l hm ca iu bin chit sut v v l vn c th quan st c. H s ghp k(z) tng ng vi su iu ch ch s khc x: n(z) = n(z)g(z).Pha tri: R(-L/2)=1 nh sng ti R(-L/2) nh sng pht R(+L/2)

S(+ L/2) Chiu di cch t L S(-L/2) nh sng phn x -L/2 0 +L/2 Pha phi: S(+L/2)=0

Hnh 3. 4 : iu kin u v s tnh ton p ng ca cch t i vi nh sng ti Khng c tn hiu vo nu nh sng ti (pha phi ca FBG) c S(L/2) = 0 v s c tn hiu ti nu phn bn phi ca FBG tho mn R(-L/2) = 1. Da vo hai iu kin bin ny, iu kin ban u ca FBG c th c vit theo cc phng trnh (3. 20). H s phn x v truyn nh sng ca FBG do c th nhn c t cc iu kin u v phng trnh ghp mode:

Chng 2: Ch to FBG Pha tri : S(-L/2)=? R(-L/2)=1 (3. 25)

Pha phi: S(+L/2)=0 R(+L/2)=? (3. 26) ln ca h s phn x c tnh nh sau:= S ( L / 2) R ( L / 2)

(3. 28)

H s phn x nng lng r (h s phn x) c tnh theo cng thc: r = | 2| 3. 5. 1 Cch t Bragg u (Uniform FBG) 3. 5. 1. 1 Cu trc Cch t Bragg quang chu k u UFBG l dng cch t n gin nht trong h cc FBGs. N c ch to bng li si quang v dng phng php t nh hng gy ra bi giao thoa UV t cm ng. Trong cch t dng ny chu k cch t khng i v chit sut ca cch t dc theo phng truyn sng bin i mt cch tun hon. (3. 29)

3. 5 Cu trc v tnh cht ca cc dng cch t

Chng 2: Ch to FBGFBG core

cladding

Ngun sng

phn x

Chit sut thay i

Hnh 3. 5: Cch t Bragg chu k u UFBG

3. 5. 1. 2 M t ton hc Cc h s kt hp pha v h s ghp mode ca UFBG l hng s. Cc phng trnh (3. 20) s dng trong trng hp tng qut c thay th bng cc h s l hng s. Chng ta c mt s phng php s dng phn tch tnh ton trong cc phng trnh (3. 20). Cc phng php dng phn tch ca phng trnh ghp mode c th tm c da trn cc phng trnh iu kin bin (3. 25) v (3. 26). Nu x dch d / dz l 0, h s mt iu hng ni tng ng vi h s mt iu hng . Phng trnh gii quyt s lin h gia s phn x v s cho php truyn nh sng c biu din bi:A ( z ) = ik sinh[ B (z-L/2)] i sinh( B L) + B cosh(B L)

(3. 30) (3. 31)

A+ ( z ) =

B cosh[ B (z-L/2)] -isinh[B (z-L/2)] i sinh( B L) + B cosh(B L)

Trong B c m t nh sau:B = k 2 2 B = i 2 k 2

(k2>2) (k2