Sampled, Super-structured Multi-channel FBG

Transcription

1 Faby-Po bad-pass fl Sampld Sup-sucud Mul-chal FBG λ δ L gap Bagg 4 Samplg podc supsucu of FBG gas mulpl cops chals of h fucy spos FBG pa 0 / cos/λφ spac doma Sc samplg abls a fla spcal spos FBG pa 0 / cos/λφ spac doma Sc samplg pa S spac doma c samplg pa S spac doma Sampld FBG S Wasd fb wh o gag ps Sc Sampld FBG S Sampld FBG spos fucy o walgh doma Wasd fb wh o gag ps Sampld FBG spos fucy o walgh doma Each pak pss a spos chal Ufom c lop of h fucy spos s a sul of h Fou Tasfom of h sc samplg fuco dmosad by Ibs al

2 Samplg of a Fb Bagg Gag Basd o Fou Aalyss Samplg by podc phas No Samplg Fou Tasfom Fucy Spac FBG pa 0 / cos/λφ spac doma Rfac Idx Chag Fb Sua Samplg Sc Samplg Sua Sc Sc Sua Spcal Fl Rspos φ Phas samplg pa S xp[φ] Phas sampld FBG S spac doma No wasd fb wh phas samplg Phas sampld FBG spos fucy o walgh doma Gag axs mm Walgh m Dsg of 7-5 chal FBGs Na fld dffaco of a phasshfd phas mask Yulog Shg Joshua E. Rohbg. Dpam of Physcs Physcs Egg ad Opcs C fo Opcs Phoocs ad Lass Usy Laal shg@phy.ulaal.ca Nohop Gumma Rdodo Bach CA 9078 USA

3 Na fld of h Phas mask fo wg FBG UV las Phas mask Opcal fb Ifc m- pa m Λ G Ifc Lhogaphy Rcodg fc fgs Subsa wh 60 μm spacg Moao. Modlg dffaco a fld of a Phas Mask. Impac o FBG pfomac 3. Nol phas masks Phas shfs phas mask ad FBGs Phas shfs h FBG allows complx-alud couplg coffcs suls mo fucoals ad b pfomac Applcaos Mul-chal DFB lass Phas-shfd FBG Phas-oly Mul-chal sampld FBG Tadoal Mhod: Fabca h sam phas shf h phas mask?? Pa Tasf fc lhogaphy R. Kashyap Fb Bagg gags Chap. 6 Acadmc 999 Phas-Oly Sampld Mulchal FBGs Na fld dffaco af a phas shf x aθ θ Agl of fs dffacd od x IEEE Phoocs Tchology L 00 Joual of Lghwa Tchology accpd 003 Rgoous coal aalyss Aalyg h fg Phas dsbuo sad of Isy dsbuo A phas shf s o plcad FBG bu s spl up o wo half-phas shf FBG 3

4 Spl of h phas shf Asymmy of Damma Samplg fuco by h spl of phas shf Mos auhos w sd sy dsbuo h a fld. W masu h pods of h fgs h a fld dffaco aagd pa a dff alog x Amog all h pod of 500 m h a wo pods of 600 m dcag h phas shf of 50 m s spl o wo phas shfs of 5 m. Th spaao of h half phas shfs s x aθ Phas shfs ad opcal pahs a accumulad As h sgal popagas alog h FBG Compud FT of h sampld fuco wh wo-spl half phas shfs of a spaao x Expmal spcum of a sampld FBG popooal o h phas mask-fb spacg 4

5 Rollg-off o mulchal FBG Expmal spcum of a sampld FBG Masud spcum Compud wh Phas shf spl modl Expmal spcum of a sampld FBG Expmal spcum of a sampld FBG 5

6 Expmal spcum of a sampld FBG Implmao of phas-oly Damma samplg fuco A phas shf of fo FBG h phas mask s mplmd by oducg a gap of 50 m h phas mask sulg a goo of 750 m A Damma samplg fuco coas a suc of phas shfs whch a mplmd by a suc of 750 m ach pod of mm. W chag h suc of L by h sam suc bu of L Phas shf of s mplmd by goo of 50 m Tha dos o chag h Damma fuco Wh h phas shfs spl up h Damma samplg fuco h FBG bcoms / / 0L Spcal asymmy s mod Th samplg fuco poducs chals of ual sgh Expmal Rsuls Samplg fuco wh compsao fo phas shf spls Rflco db Walgh dug m Fabcad 9 chal FBGs. Y. Shg al aoal pa PCT WO 03/ Y. Shg al IEEE Phoocs Tch. L ol. 6 No

7 Cocluso Ioduco Spa. Fl Fg Num. Rsul Mulpl Coclusos Phas shfs a phas mask usd fo wg FBGs a o plcad h fb co bu spl o wo halfmagud phas shfs wh a logudal spaao popooal o phas mask o fb spacg. Ths spl causs asymmy h chal spcum of a FBG W bul a phas-shf spl modl whch pdcs pcsly h spcal asymmy obsd a phasoly sampld FBG. Ths fudamal udsadg h a fld s aluabl fo all h phas-shfd phas masks fo a ay of FBGs A compsao chu s poposd whch poducs mul-chal sampld FBGs of hgh chal cou wh ual chal ampluds ad o asymmy. PHASE SHIFT DIFFRACTION x Na fld dsbuo of phas shfd FBG phas mask. y Dsac bw phas mask ad h fb co d / 6.5 μm Λ λ 0 4Λ Shfd FBGs Nomally Icd UV Bam Fb Co d 5μm Ioduco Spa. Fl Fg Num. Rsul Mulpl Coclusos Ioduco Spa. Fl Fg Num. Rsul Mulpl Coclusos ANALYZING RANGE DISCRETIZATION OF MAXWELL S EQUATIONS Igula gag Sufac Plasma Eascc Fld Full-Vcoal L Na fld o Fsl fld <λ d>>l Isg fld: d 6.5μm Na fld dffaco Fa fld o Fauhof fld Th bouday bw a ad fa fld s dfd by Raylgh dsac as: DL / λ fom h souc. Maxwll s Euaos B E J m Faaday D H J Amp D Gauss B 0 Gauss La Isoopc Nodsps Maals: D εe ; B μh Elcc ad Magc Cu Dss Losss: J H ; J σ E m Y Algohm d od cal dffcs m ad spac o saggd Casa gds. 7

8 8 Spac-m cha 0 E E E B { } B f H m H D { } D f E 3 y y x x b a b y a y b x a x E E E E m D H m D H H H m C E m C E H H m C E m C E Dscao fo D TE mod Spa. Fl Ioduco Fg Num. Rsul Mulpl Coclusos Explc ad smpl schm Aods solg smulaous uaos Fully coal whou fuh appoxmaos Tm oluao s compud dcly Tas s compud dcly Pods fo complxs of sucu shap ad maal composo Adaags Cosdabl compu mmoy Oly g umcal suls o physcal paos Dsadaags ADVANTAGES & DISADVANTAGES OF Spa. Fl Ioduco Fg Num. Rsul Mulpl Coclusos RESULT a. & b. : λ 0 50m S 0.5 dx.5m.5 Λ pm.0μm N 3 Λ pm b. : Phas Shf δ Λ pm / 4 50 m Fld sy dsbuo a. b. Podc bouday codo ca smula f lgh bu s o aalabl wh phas mask has phas shf Bouday codo PML Spa. Fl Ioduco Fg Num. Rsul Mulpl Coclusos EXTEND WIDTH 750m Lwdh θ θ 4 fo d 6.5μm L wdh 40μm Igal wh oh mhod Fo hs dmso mhod ds oo bg mmoy Af phas mask oly f spac popagao Popagao ca b compud by as mhod Spa. Fl Ioduco Fg Num. Rsul Mulpl Coclusos

9 Ioduco Spa. Fl Fg Num. Rsul Mulpl Coclusos Ioduco Spa. Fl Fg Num. Rsul Mulpl Coclusos DATA TRANSFORM INTEGRAL FFT Icd : Gauss Impuls wdbad lcomagc xcao f 3τ Souc xp s[ 3τ ] souc τ Tm Doma FT: Gauss spcum fucy doma [ f ] H xp d F TF 0 F souc TF [ U y ;0 ] : d5μm Spal fl: d0μm Idsy pa Amplud Spaal Fl: TF [ U y ; x ] d T y xp [ ] λ y TF U y ;0 λ Λ pm.0μm L wdh 6 μm λ 0 50m δ 50m dx.5m Ioduco Spa. Fl Fg Num. Rsul Mulpl Coclusos Ioduco Spa. Fl Fg Num. Rsul Mulpl Coclusos IDEAL CONDITION COMBINE DIFFRACTED FIELDS Ifc fg pa of phas mask ca b dscbd as: xp[ x x0 / Λ y cosθ / λ] xp[ x x0 / Λ y cosθ / λ] Pla wa cdc Cooal mask Λ/4 Phas shfg popagao Cooal mask δ cos x x0/ Λ/ Phas-shfd phas mask 9

10 Ioduco Spa. Fl Fg Num. Rsul Mulpl Coclusos Ioduco Spa. Fl Fg Num. Rsul Mulpl Coclusos COMBINE FRINGE SYSTEMS Fld A: cos x x0 / Λ / y cosθ / λ x x0 / Λ x x0 / Λ Fld B: 3 [ ] y cosθ / λ x0 x0 / Λ δ cos x / Λ Fld C: 34 cos x x0 / Λ / x 0 L δ x 0 L RESULT Phas shf phas mask spls o wo half-amplud phas shfs Two half-amplud phas shfs occu a h boudas of h h fg sysms Th spl of h phas shf s h wo fc bw wo dffacd bams fom h wo gag scos spaad by h phas sp δ. xx y x y aθ Λ pm.0μm L wdh0 μm λ 0 50m δ 50m dx.5m d 0 μm L 5 μm d 5 μm Ioduco Spa. Fl Fg Num. Rsul Mulpl Coclusos Ioduco Spa. Fl Fg Num. Rsul Mulpl Coclusos NUMERICAL RESULT MULTIPLE PHASE SHIFTS : d5μm Pod Aalyss Ifc pod Λ pm / 500m A h boudas phas shfs 3.5 pods oal phas shf of: / 5m δ/ wo half phas shfs a o y complly spld δ γ x L 0 x L 0 x 03 L 3 x Spaal Fl: d0μm Ifc pod Λ pm / 500m A h boudas phas shfs 7 pods oal phas shf of: m δ/ I h cal fc pods a o-flucd wo half phas shfs a spld y Λ pm.0μm L wdh6 μm λ 0 50m δ 50m dx.5m 0

11 Ioduco Spa. Fl Fg Num. Rsul Mulpl Coclusos x y aθ Ioduco Spa. Fl Fg Num. Rsul Mulpl Coclusos MULTIPLE PHASE SHIFTS CONCLUSION Mulpl phas shfs phas mask a spl ad popagad ddually wha h spacg bw h ghbog phas shfs. Th spl half-amplud phas shfs ca coss o dug h popagao whou chagg h alus. δ γ Th phas shf phas mask s o plcad FBG fb co Idally a phas shf a podc phas mask wll poduc h fc fg sysms h dffaco fld. Λ pm.0μm L wdh0μm d 0μm Th wdh h hd fg sysm x y aθ dpds o h popagao dsac y fom h phas mask o h fb co. λ 0 50m δ 50m γ 50m Two half-amplud phas shfs occu a h boudas of h h fg sysms. dx.5m δ δ γ γ δ Boadbad Fxd Dspso Compsao 80 km dspso compsao Co Tchology: hgh-chal-cou Fb Bagg Gags Rflco db GDR ps GDR spc Walgh m Fucy GH max IL ppl ch /- 0. db IL o-ufomy / db GDR_spc p-p 9.30 ps

12 Lmaos fo h samplg mhods Samplg appoachs a basd o h soa couplg hoy ca xpla h mchasm of h mulpl chal fomao bu cao pod accua soluo of h chal slf whch wll ably mak h a-chal spcum o-dal. Th podc samplg mhod s hly suabl o dsg a mul-chal FBG wh dcal chal-chal spos ad cosa chal spacg. I fals f h complx spcum of ach chal o h chal spacg ds o b cosdably dff. Is Scag Algohms fo h Syhss of Bagg Gags OUTLINE Ioduco Fs Bo appoxmao Ia soluo of h Gl Fad-La-Machko uao Lay-plg algohm Numcal xampls Coclusos Ioduco Complx fls add/dop ga flag dspso compsao c. a ud WDM fb commucao sysm Fabcao of complx gag sucu s possbl Dsg ad syhss Bagg gag bcoms y mpoa Is ScagIS mhods: Fs Bo appoxmao Igal mhod Dffal mhod -- lay-plg algohm Nola opmao mhod Gc algohm Slow sach spac s hug Dsg mo paccal gag pofl Fs Bo Appoxmao Fs Bo appoxmao accous oly h fs flco fom h mda Ipu oupu Ipu oupu O flco Th flcos Fou asfom lao xs bw h fl spcum spos δ ad h gag couplg fuco : / FT [ δ ] δ δ dδ

13 R0. Fs Bo Appoxmao R0.5 Mhod fo Syhss Fb Bagg Gag Lay plg algohm R0.75 R0.88. R. Fcd al. A ffc s scag Algohm fo h dsg of oufom fb Bagg gag IEEE J. Quaum Elo J. Skaa al. O h syhss of fb Bagg gag by lay plg IEEE J. Quaum Elo Rd cu: ag spcum Blu cu: cosucd spcum Fs Bo appoxmao s oly ald fo dsg low-flcy<0.5 gags Is scag poblm Scag ad popagao max fo complx FBGs Quaum mchacs s scag poblm: d h Y k V Y k EY k m d Sa fuco: Y k poal: V Elcomagc s scag poblm: μ 0 E E N E c m Scag wa: E Syhss of fb Bagg gag: Rflc spcal: H R plasma of lco dsy: N coupld coffc: Scag max: Popagao max: Complx FBGs cosh ah M S M lm P M T 0 0 M T M P M S M P ah 0 3

14 4 Skaa s Lay plg algohm Tasfom max: sh cosh sh sh sh cosh u u u ah d Causaly ad lay-plg 0 F b F H T m b 0. m b B 0 B H R b u u Pocdus of Skaa s LPA. ah d d u Tm doma Lay plg algohm u u u u h aca /

15 Exampls : Dsg of m Bad-pass Fl Exampls 3: Dsg of 0m Bad-pass Fl Cocluso Oul Fou kds of LPA a Ioducd Two Kds of Skaa s LPA a pod Th hos of Skaa s LPA d fuh pob. Ioduco Ia lay-plg Algohm Dsg WDM badpass fl Cocluso Fuu wok Syhss of olum gag by LPA Syhss of mul-chal gag by LPA 5

16 Rfac dx modulao of FBG Aalyss ad Syhss of FBG Rfac dx modulao: Couplg coffc : δ cos[ θ ] Λ θ Λ ω xp[ θ ] c Aalyss Λ Λ Syhss Couous Lay-plg algohm Couous Lay-plg algohm Coupld-mod uaos du u d d u d 0 Rflco spcum: u0 Syhss lao: Rcca uao d d Local flcy: u d Syhss d d 0 d d 0 0 Smpso s ul Rug-Kua mhod Smpso s ul Aalyss d d L 0 0 Rug-Kua mhod 6

17 7 Dsc lay-plg algohm Tasfom max: sh cosh sh sh sh cosh u u u ah d Dsc Lay-plg algohm 0 L 0 0 FFT 0 FFT Aalyss Syhss d d Mhods fo Dsg Fb Bagg gag Opmal mhod: Vaao Aalg algohm Gc algohm Ia lay plg algohm Ia lay-plg algohm

18 Th cogc of Ia LPA Modfd Fou Tasfom Mhod Th ola popy of LPA bcomg appoxma la Rcca uao d d If s al d d Podg a hgh umb of dg of fdom Small modfyg gag ad spcum ach ao ah d ah d d d ah d 0 H R 0 ah d ah I{ } L f d ah [ H ]xp Dsg xampl:00g WDM fl Th spcfcaos of WDM fl Fla flcy of 0.99 h sgal pass bad of 0.4 m aoud h c walgh of 550 m. Isolao of -30 db h ou-of-h-bad m ad m Maxmum dspso blow 00 ps/m wh h sgal pass bad. Th gag coas o phas ump 8

19 Mhods of mog h phas ump gag Nga pa of gag bcomg pos. Nga pa of gag bcomg pos. Rmog ga pas of gag 3. Dcasg h ga pa of gag sp by sp Rmog ga pas of gag Dcasg h ga pa of gag sp by sp 9

20 Mhods of shog h gag Smoohg gag Thshold Smoohg by Wlch wdows Rmog small lobs Smoohg wdows Wdows ad h Spcum 0

21 Exampl of smoohg gag Scalg gag Scalg Dsgd Rsuls Thshold Mhod Dsgd Rsuls Rmog small lobs M 0 so bw BWU ms maxdp Lob # Isolao db -0.5 db Badwdh m BWU GDR ps -0.5 passbad ps/m M40 Iso bw BWU ms0.639 maxdp

22 Dsgd Rsuls Rmog ga couplg coffc ad small lobs Gaussa ad ILPA Apodd FBG M 0 so bw BWU ms maxdp M 6 so bw BWU ms maxdp Apodao Isolao db -0.5dB BW m -30 db BW m - db BW m BWU Goup dlay ppl ps -0.5 db BW m/ps ILPA Gaussoa I Gaussa II Dsgd Rsuls Dcasg h ga pa of gag sp by sp Dsgd Rsuls Dcasg h ga pa of gag sp by sp Lob # Ia # Isolao db -0.5dB BW m -30 db B m - db BW m BWU Goup dlay ppl ps -0.5 db BW m/ps Th badwdh of fla-op cosas spcum m Lob # Ia # Isolao db -0.5dB BW m -30 db BW m - db BW m BWU Goup dlay ppl ps -0.5 db BW m/ps Th badwdh of fla-op cosas spcum m

23 Dsgd Rsuls Dcasg h ga pa of gag sp by sp Coclusos Ia lay-plg algohms w dlopd Cogc codo Fabcao cosas Dsg of WDM fl Fuu wok: Lob # Ia # Isolao db -0.5dB BW m -30 db BW m - db BW m BWU Goup dlay ppl ps -0.5 db BW m/ps Th badwdh of fla-op cosas spcum m Dsgd dspso compsao Rfcs H. L M. L Y. Shg ad J. E. Rohbg Adacs h Dsg ad Fabcao of Hgh-Chal-Cou Fb Bagg Gags Id Tuoal J. Lghwa Tch. ol. 5 No M. B D. Fauch R. Vallé A. Salma G. Ado Y. Shg ad S. L. Ch Bagg gags phooducd ZBLAN fbs by fmoscod pulss a 800 m Op. Ls Vol. 3 No G. Tmblay ad Y. Shg Effcs of h phas-shf spl o phas-shfd fb Bagg gags J. Op. Soc. Am. B ol.5 o H. L M. L K. Ogusu. Y. Shg ad J. E. Rohbg Opmao of a couous phas-oly samplg fo hgh chal cou fb Bagg gags Opcs Expss ol.4 No J. E. Rohbg H. L J. Poplk J. Zwback ad Y. Shg A ol phas-oly sampld 45-chal fb Bagg gag w wh dffaco-compsad phas mask Opcs L. ol.3 No G. Tmblay J. N. Gll Y. Shg M. B ad G. Paul-Hus Opmg fb Bagg gags usg a gc algohm wh fabcao-cosa codg J. Lghwa Tch. ol. 3 No Y. Ouyag Y. Shg M. B ad G. Paul-Hus Ia lay-plg algohm fo dsgg fb Bagg gags wh fabcao cosas J. Lghwa Tch. ol. 3 No Y. Shg ad L. Su "Na-fld dffaco of gula phas gags wh mulpl phas-shfs" Op. Expss H. L Y. Nakamua K. Ogusu Y. Shg ad J. E. Rohbg Ifluc of claddg-mod couplg losss o h spcum of a laly chpd mul-chal fb bagg gag Opcs Expss Vol. 3 No Y. Shg J. E Rohbg H. L Y. Wag ad J. Zwback Spl of phas-shf a phas mask fo fb Bagg gags IEEE Phoocs Tch. L ol. 6 No Y. Shg Y. Qu ad J. Wag Dffaco of phas mask wh schg os fabcao of fb Bagg gags Op. Eg. Spcal sco o Dffac Opcs Vol.43 No H. L T. Kumaga K. Ogusu ad Y. Shg Adacd dsg of mul-chal fb Bagg gag basd o a lay-plg mhod J. Op. Soc. Am. B ol H. L ad Y. Shg "Dc Dsg of Mul-chal Fb Bagg Gag wh Dsc Lay-plg Algohm" IEEE Phoocs Tch. L ol.5 No H. L Y. Shg Y. L ad J.E. Rohbg " Phasd-Oly Sampld Fb Bagg Gags fo Hgh Chal Cous Chomac Dspso Compsao" J. Lghwa Tch. Vol. No J.E. Rohbg H. L Y. L J. Poplk Y. Shg Y. Wag P.B. Wlcox ad J. Zwback Damma fb Bagg gags ad phasoly samplg fo hgh chal cous IEEE Phoocs Tch. Ls ol. 4 No Y. Shg J. E. Rohbg H. L W. Yg ad J. Zwback Phas mask dsg ad phas mask fo wg opcal fb Bagg gags Iaoal Pa PCT WO 03/