ROTATION MEASUREMENT WITH THE USE OF A PULSED ER-DOPED FIBER LASER WITH INTEGRATED OPTIC CIRCUIT: PROPOSAL, SIMPLE THEORY, AND EXPERIMENT

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1 ROTATION MEASUREMENT WITH THE USE OF A PULSED ER-DOPED FIBER LASER WITH INTEGRATED OPTIC CIRCUIT: PROPOSAL, SIMPLE THEORY, AND EXPERIMENT Chao-Xiang Shi Dpartmnt of Elctrical Enginring and Computr Scinc Univrity of Michigan Bal Av Ann Arbor, Michigan Rci d 25 Fbruary 1997 ABSTRACT: W propo a no l puld fibr lar rotation nor with a LiNbO3 intgratd optic circuit, Sagnac fibr loop, Er-dopd fibr, and miconductor pumping lar. A impl analyi i compltd and th output quation i dri d. Th arianc of th output pul whn rotation occur i alo analyzd. In addition, w alo conductd a rlatd xprimnt for rotation maurmnt. Whn th gain of th fibr amplifir i o r th round-trip lo and th pha modulation frquncy atifi th total round-trip tim, thi optical ytm produc th lar miion in a pul tat. Th rotation rat i maurd from th hift of th pak poition of th output pul. It i hown that th rolution of rotation maurmnt incra if w u a mallr pha modulation dpth. But th harpn of th optical pul mut b maintaind by rducing th lo ( or incraing th gain of optical amplifir) in th whol optical ytm John Wily & Son, Inc. Microwav Opt Tchnol Ltt 15: , Ky word: Er-dopd fibr; fibr lar; intgratd optic circuit 1. INTRODUCTION Fibr-optic rotation nor Ž or fibr-optic gyrocop. with th Sagnac ffct for rotation maurmnt hav bn widly invtigatd for many yar 1. Baically, thr ar thr kind of fibr-optic gyrocop. On i th intrfromtric fibr-optic gyrocop Ž I-FOG., which utiliz an optical intrfrnc btwn th CW Ž clockwi. and CCW Žcountr- clockwi. wav that pa through a Sagnac loop 2. A low-cohrnc light ourc Ž SLD or multimod LD. i ud in th I-FOG, and th cot of whol gyro ytm i low. I-FOG ha found many practical u, uch a in car navigation and many othr indutrial application 3. Th cond typ of fibr gyrocop i th ronant fibr-optic gyrocop Ž R-FOG., which dtct th chang in ronant frquncy that i du to th Sagnac ffct in th high-fin ring ronator 4. Th R-FOG u a hort fibr to conform th Sagnac loop and can obtain high rolution in rotation maurmnt. Howvr, th R-FOG rquir a highly cohrnt light ourc, which i xpniv. Many wor phnomna, uch a th Krr ffct and Backcattring ffct mut b conidrd 5. Th third typ of FOG i an activ fibr-optic gyrocop mploying a timulatd Brillouin-cattring lar compod of a fibr-ring ronator Ž B-FOG.. It tranlat th Sagnac pha hift into a bat frquncy btwn th countrpropagation lar mod 6. In thi rarch w propo a novl fibr-optic rotation nor with an intgratd optic circuit, a Sagnac fibr loop, and an Er-dopd fibr amplifir. Thi optical ytm produc a lar miion in th pul tat if th gain of fibr amplifir i gratr than th whol round-trip tranmiion lo, and if th frquncy of pha modulator and th total loop lngth atify a crtain mod-lock condition. Th maurmnt of rotation rat i bad on th pak hift of output pul inducd by th Sagnac ffct. 2. BASIC CONFIGURATION AND EXPERIMENT SETUP Th baic configuration and xprimntal tup ar illutratd in Figur 1. Th ning part i compod of a Sagnac loop of lliptical-cor polarization-maintaining fibr Žabout 164 m., with an intgratd optic circuit Žfrom Ramr Inc. with inrtion lo of about 10 db at 1.55 m., which contain a LiNbO3 Y-branch wavguid with mtal lctrod for pha modulation. In addition, a polarizr i intgratd within th optical IC. Thrfor, thi intgratd optic circuit includ all th function of fibr polarizr, fibr couplr, and pha modulator in convntional all-fibr I-FOG. In thi work thr i alo a fdback loop Ž about 63 m. upplying an optical amplification Ž about 30 db at th mall ignal. with th Figur 1 Configuration of our propod fibr lar rotation nor and xprimntal tup MICROWAVE AND OPTICAL TECHNOLOGY LETTERS / Vol. 15, No. 5, Augut

2 Er-dopd fibr. A pic of Er-dopd fibr of 40 m i oppoitly pumpd by two m LD through m WDM couplr. An iolator i inrtd within th fdback loop to nur th on-dirction Ž clockwi. tranmiion in th whol ytm, and improv th prformanc of fibr amplifir by uppring th Rayligh cattring. An optical filtr with a 3-nm paband width and a cntral wavlngth of about 1.55 m i placd in th fdback loop. In thi xprimnt a in-wav lctronic ignal i applid to th pha modulator of th intgratd-optic circuit. Th frquncy of thi lctronic pha modulation ignal i f 913 kh Žqual to th fundamntal cavity frquncy., which atifi th mod-lock condition with th total lngth Ž about 227 m. of th fibr loop Žth avrag rfractiv indx of fibr i n In addition, th polarization tat i controlld to obtain a maximal ytm tranmiion. Th output i availabl from a 3-dB fibr couplr, which alo fd back optical powr to th ning loop through th intgratd optic circuit. In th xprimnt, th nd of output fibr to th fat photodtctor i carfully cut in a lant plan, o that it will not produc any rflction back to th loop cavity. 3. EXPERIMENT, SIMPLE ANALYSES, AND DISCUSSION Th opration of thi puld fibr lar gyrocop i dcribd a follow. At firt, th optical wav gnratd from th ASE of Er-dopd fibr i injctd into th ning loop through th fibr couplr and intgratd optic circuit. Th lightwav i thn paratd into two part by th LiNbO 3 intgratd optic circuit, in th man tim th oppoit ign pha modulation i producd for th two light wav. Th paratd light wav thn propagat ovr th ning loop with CW Ž clockwi. wav and CCW Ž countrclockwi. wav. Finally, an intrfring ignal btwn th CW and CCW wav i producd. Thi produc th intnity modulation du to th tim diffrnc and th oppoit ign of pha modulation btwn th CW and CCW wav. Thi intrfring ignal ha th am form a th gyro ignal of convntional I-FOG, which i thn amplifid by th fibr amplifir and fd back to th Sagnac loop through th fibr couplr and intgratd optic circuit. In th mantim, om optical powr alo arriv at th fat photodtctor. Th fdback light will thn continu th procdur mntiond abov. Thrfor, th total output ignal at th fat photodtctor i a ummation of th intrfring ignal for ach round trip. If th gain of th fibr amplifir i ufficint to compnat for th round-trip lo in th whol ytm, th lar miion can b producd. W firt look at th ca of a CW lar; that i, thr i no lctrical modulation ignal at th pha modulator. Bcau th optical gain i gratr than th round-trip lo, th initial light ignal of ASE will gt a nt amplification ach tim it travl through th fibr loop. Thi procdur continu until a trong light ignal aturat th gain of fibr amplifir, a balanc i rachd, and a tady CW lar miion i thn t up. Figur 2 how th CW lar pctrum, that i, th lar pctrum whn th pha modulation ignal i not applid Ž no drivn currnt to th pha modulator.. On th othr hand, if an lctrical ignal i placd on th pha modulator and th frquncy of pha modulation ignal and th lngth of th whol fibr loop L Žincluding both th ning loop and fdback loop of Er dopd fibr amplifir. atifi th rlation of 2i, i 1, 2,... Ž i th tranmiion tim of th total round trip, including th tim Figur 2 Optical pctrum of thi fibr lar whn th modulation ignal i not applid Ž i.., CW lar opration. on both th Sagnac loop and Er dopd fibr loop., mod lock i gnratd and th lar miion xhibit a pul output. Figur 3 i th lar pctrum whn th pha modulation ignal Ž V 9.67 V. i applid and mod locking occur. Th modulation frquncy of th pha modulator i f 913 kh, which i jut qual to th fundamntal cavity frquncy. Whn mod locking occur, th lar pctrum apparntly bcom broadr compard with Figur 2. Corrponding to Figur 3, Figur 4 illutrat th maurd output pul of thi mod-lockd fibr lar. It i n that th output i of a priodic pul. Th mot ditinct pul ar obtaind whn th drivn frquncy i 913 kh, producing two output pul pr modulation priod 7. Th doubl pul rptition compard with that of th drivn ignal can b undrtood from Eq. Ž. 1 th tranfr function of th pha-modulatd Sagnac intrfromtr i a coin function; thrfor, if th lctronic pha modulation ignal i of a in function, th output of th Sagnac intrfromtr ha two tranmiion pak in on priod of drivn ignal. It hould alo b notd that th pul duration of our fibr lar i quit long. Thi i bcau th modulation frquncy of our fibr lar i vry mall Žqual to th cavity frquncy of th long fibr ronator., whra in th homognouly broadnd lar th pul duration of th activly mod-lockd lar dpnd not only on th atomic linwidth but alo on th modulation frquncy 8. Th larg modulation frquncy with th harmonic mod lock would rult in th hort pul duration 8, but th harmonic mod lock i not our focu in thi articl. In addition to th abov dicuion, w hould point out that whn th rotation movmnt i input into thi modlockd fibr lar ytm, th output pul of thi fibr lar chang bcau of th Sagnac ffct. Th rotation rat can b thn maurd by dtcting th pak hift of th output pul. W nxt u a impl mthod to analyz how th rotation maurmnt can b prformd by thi Er-fibr lar gyro ytm. Bad on th abov dicuion, th firt-tim intrfring ignal Ži.., on that ha had only on round-trip tranmiion. arriving at th fat PD ha a wavform output 312 MICROWAVE AND OPTICAL TECHNOLOGY LETTERS / Vol. 15, No. 5, Augut

3 i th rfractiv indx of th fibr. i th Sagnac pha hift inducd by th rotation movmnt, xprd a 4 RL c, 3 whr i th rotation rat, R th radiu of Sagnac loop, c th vlocity of light propagation in fr pac, and th wavlngth of light ourc. Th abov firt-tim intrfrnc optical ignal i obtaind from th fibr couplr and amplifid by th Er-dopd fibr amplifir, thn fd back into th Sagnac loop through th fibr couplr and intgratd optic circuit. Thrfor, thi intrfring ignal will thn furthr th propagation dcribd a abov. Conidring th ffct of optical fdback with amplification, th cond-tim intrfrnc ignal Ži.., on that ha had two round-trip tranmiion. ha bn drivd a Figur 3 Optical pctrum of th mod-lockd fibr lar whn th amplitud voltag of modulation ignal i V 9.67 V and th modulation frquncy i jut qual to th fundamntal cavity frquncy f 913 kh Ž. 2 2 Ž. 4 P t AK 1 co co t 2 1 co což t. 4, Ž 4. and th third-tim intrfrnc ignal Ži.., on that ha had thr round-trip tranmiion. that occur aftr fdback ha bn twic drivd i Ž. 3 3 Ž. 4 P t AK 1 co co t co což t. 4 1 co což t. 4. Ž 5. Th total output at th fat photodtctor i th ummation of th numbr of th abov-mntiond intrfring ignal, which i xprd a Ž. P t P t P t P t, 6 tot Figur 4 Maurd output pul of th fibr gyro whn thr i no rotation input Ž corrponding to Figur 3. with intnity modulation Žth am a th output of Sagnac intrfromtr. xprd a Ž. Ž. 4 Ž. P t KA 1 co co t, 1 1 whr i a paramtr of th fring contrat, K i a contant rflcting th quivalnt round-trip lo Žincluding tranmiion lo, plicing lo, lo of ach optical dvic, and th plitting lo of fibr couplr., A i th gain of th Er-dopd fibr amplifir, and it hould b alo notd that th gain of optical amplifir i alway gratr than th round-trip lo in thi optical ytm. In addition, i th modulation frquncy of pha modulation ignal Ž 2 f., i th ffctiv pha-mod- ulation dpth, xprd a 2 in f. 2 m i th wav-propagation tim through th Sagnac loop and i xprd a nl c, l i th lngth of th Sagnac loop, n From Eq. Ž. 6, if w lt 2n, n 1, 2, 3,... Žthi condition can b ralizd by propr adjutmnt of th pha modulation frquncy to match th whol round-trip tim., in thi ca th mod lock i gnratd and th total output ignal from th fat photodtctor i of a pul, which can b xprd a K KA1 co což t. 4 P Ž t., Ž 7. tot 1 KA1 co což t. 4 whr K i th photodtcting cofficint. W nxt invtigat how th rotation can b maurd by thi fibr gyro ytm. From th abov dicuion and Eq. Ž. 7 w that th output i a ri of pul. W can thn dtrmin th poition of output pak through th following quation: W hav P t 0. 8 tot což t. 2n, n 0,1,2.... Ž 9. Ž. Equation 9 i a condition rquird to find th pak poition of th output pul. From thi quation, w that th pak poition dpnd on th Sagnac pha hift, that i th optical pul will hift if th rotation occur. Thi prop- MICROWAVE AND OPTICAL TECHNOLOGY LETTERS / Vol. 15, No. 5, Augut

4 Figur 5 Maurd output pul of th fibr gyro whn th input rotation i 40 dg Ž CW rotation. by a mchanical rotation tabl. Th applid voltag of amplitud for th pha modulation ignal i V 3.24 V, and th modulation frquncy i f 913 kh Figur 6 Maurd output pul of th fibr gyro whn thr i no rotation input. Th applid voltag of th amplitud for th pha modulation ignal i V 3.24 V, and th modulation frquncy i f 913 kh rty can b utilizd for th rotation maurmnt. W firt look at th ca whn thr i no rotation input; that i, 0. In Eq. Ž. 9, if th ffctiv pha modulation dpth i lctd to b btwn 0 2, Eq. Ž. 9 i atifid only whn n 0. In thi ca, th pak poition of th output pul ar dtrmind through th following quation: t 2j 1 2, j 0,1,2,..., 10 0j whr t0 j rprnt th pak poition whn thr i no rotation input and j dnot th pak numbr of th output pul in tim axi. Whn th rotation occur, th pak of output pul will hift, which ar dtrmind by th following quation. t arc co 2j, j 0,1,2,..., Ž 11. ij ž / whr tij rprnt th pak poition whn th rotation i input. W thn driv th rotation rat from th Eq. Ž 10. and Ž 11. a Figur 7 Maurd output pul of th fibr gyro whn th input rotation i 40 dg Ž CCW rotation. by a mchanical rotation tabl. Th applid voltag of amplitud for th pha-modulation ignal i V 3.24 V, and th modulation frquncy i f 913 kh c in t 4 RL whr t i th tim hift of th output pak du to th rotation, xprd a t tij t 0j, which i a maurabl valu. W can thu maur th rotation rat by dtcting th tim hift of th output pak. Figur 5 dmontrat th output pul whn th clockwi Ž CW. rotation input Ž 40 dg. i upplid through a mchanical rotation tabl. For a mod-lock opration, th voltag amplitud of modulation ignal i V 3.24 V, and th modulation frquncy i qual to th fundamntal cavity frquncy f 913 kh. W can that th pak poition of th output pul ar hiftd Ž th paration i changd. whn th rotation occur. In addition, for comparion, in Figur 6 w rcordd th output pul whn thr i no rotation input Ž i.., 0.. Figur 7 i th maurd output whn th countrclockwi Ž CCW. rotation i input Ž 40 dg.. Figur 8 how th calculatd rult of th tim hift of th output pak a a function of th rotation rat with diffrnt ffctiv pha-modulation dpth. Th paramtr Figur 8 Calculatd rult of th tim hift of th output pak a a function of rotation rat with diffrnt amplitud of pha modulation ignal ud ar dirctly lctd corrponding to th practical valu of xprimnt; that i, L 227 m, f 913 kh, 1.55 m, R 5 cm, and th avrag rfractiv indx i 314 MICROWAVE AND OPTICAL TECHNOLOGY LETTERS / Vol. 15, No. 5, Augut

5 Figur 9 Maurd rult of th tim hift of th output pak a a function of rotation rat with diffrnt amplitud of pha modulation ignal n From Figur 2, w that th rotation rat can b drivd from th tim hift of th output pak. Figur 9 i th maurd rult of th tim hift of th output pak a a function of rotation rat. Th rotation rat in th tranvral axi corrpond to th practical valu input by th mchanical rotation tabl. From th Figur 8 and 9 it can b n that th xprimnt i conitnt with th thortical rult. W alo that th lop of th plot i incrad whn w u a mall amplitud voltag of lctronic modulation ignal Ž i.., th pha modulation dpth i mall., which indicat that th rolution of rotation maurmnt i incrad. Howvr, th mall-amplitud modulation ignal will broadn th output pul, and th optical pul will vn diappar 8. For xprimntal confirmation, w incrad th amplitud of th applid voltag of th lctronic pha modulation ignal to V 9.67 V, and kpt th am modulation frquncy. Thi can b n in Figur 4. In addition, Figur 10 alo how th limit ca whn th amplitud voltag of th pha-modulation ignal i mall a V 2.67 V. Comparing Figur 6, 4, and 10, it i apparnt that th optical pul i broadnd Ž thi i not favorabl. if th amplitud of th pha modulation ignal Ž i.., pha modulation dpth. i rducd. If th amplitud of th pha modulation ignal i rducd blow V 2.67 V, th output pak i vn diappar. Bad on th abov dicuion, w can now obtain th Figur 10 Maurd output pul of th fibr gyro whn thr i no rotation input. Th applid voltag of amplitud for th pha modulation ignal i dcrad to V 2.67 V concluion that in ordr to obtain th high rolution of rotation maurmnt th ky point i to u a mall pha modulation amplitud of lctronic ignal and not lo th harpn of th optical pul. Thi can only b ralizd by rducing th lo Ž or incraing th optical gain. in th whol optical ytm. Th lo includ th inrtion lo of ach componnt and th plicing lo. In th prnt rarch, th lo of th whol optical ytm i aumd to b larg bcau of imprfct dvic and rror opration. W bliv that th rolution can b gratly improvd if w furthr rduc th optical lo. Bcau thi optical rotation nor ytm work bad on th puld lar opration, and th rotation maurmnt can b ttd by th pak hift of output pul. Thi dtction mthod might b impl in lctronic compard with th pha-dtction tchnology of th traditional I-FOG. Th whol ytm i alo impl compard with th ronator fibr-optic gyro. Alo, th ida in thi articl might prov uful for th cintit working on optical-fibr gyro or lar. 4. CONCLUSION W hav propod a novl puld fibr-optic gyro with th u of an intgratd-optic circuit, a Sagnac fibr loop, and an Er-dopd fibr amplifir. In thi optical ytm, a lar miion in th pul tat wa producd bcau th gain of th fibr amplifir i gratr than th round-trip lo and th frquncy of pha modulator matchd th total loop lngth Žincluding both th Sagnac loop and th fdback EDFA loop.. A impl analyi ha bn prntd and th xprion of th output pul ha bn drivd. Whn th rotation occur, th pak of th output pul will hift. Thi proprty ha bn ud for th rotation maurmnt. It ha bn xprimntally hown that th rolution of rotation maurmnt i incrad if w u a mall pha modulation dpth; howvr, th u of a mall pha modulation dpth will rult in th broadning of th output pul. In ordr to kp th harpn of th optical pul, w hould rduc th optical lo Ž or incra th optical gain. of th whol ytm. REFERENCES 1. H. C. Lfrv, Commnt about Fibr-Optic Gyrocop, Proc. SPIE Fibr Opt. Lar Snor, 1987, pp R. D. Mollr, Opn Loop Output and Scal Factor Stability in a Fibr Optic Gyrocop, IEEE J. Lightwa Tchnol., Vol. 7, pp , T. Kumagai, H. Kajioka, S. Oho, and H. Snob, Dvlopmnt Opn-Loop Fibr Optic Gyrocop for Indutry and Conumr U, Proc. SPIE 1785 Fibr Optic and Lar Sning, Boton, 1992, pp G. A. Sandr, M. G. Prnti, and S. Ezkil, Paiv Ring Ronator Mthod for Snitiv Intrtial Rotation Maurmnt Gophyical and Rlativity, Opt. Ltt., Vol. 6, pp , K. Hotat, Noi Sourc and Countrmaur in Optical Ring- Ronator Gyro, Proc. OFS 90, Sydny, Autralia, 1990, pp S. P. Smith, F. Zarintchi, and S. Ezkil, Stimulatd Brillouin Fibr Optic Lar Gyrocop, Opt. Ltt., Vol. 16, 1991, pp D. Otling, P. G. Sinha, and H. Engan, Spctral Stability and Smoothn of a Pha-Modulatd Fibr Lar, Opt. Ltt., Vol. 20, 1995, pp A. E. Sigman, Lar, Univrity Scinc Book, Mill Vally, CA, John Wily & Son, Inc. CCC MICROWAVE AND OPTICAL TECHNOLOGY LETTERS / Vol. 15, No. 5, Augut