8/3/2019 S. Huang et al- Optical Kerr-Effect in Fiber-optic Brillouin Ring Laser Gyroscopes

1/3

IEEE PHOTONICSTECHNOLOGY LEITERS, VOL. 5 , NO. 3, MARCH 1993 365

Optical Kerr-Effect in Fiber-optic BrillouinRing Laser GyroscopesS. Huang, L. Thkvenaz, K. Toyama, B. Y. Kim, and H. J. Shaw

Abstruct-The optical Kerr-effect in a reciprocal fiber-opticBrillouin ring laser gyroscope is investigated. It is found that theKerr effect, as the major error source of the rotation ratemeasurement in this gyroscope, causes a bias of beat frequencywith nonlinear dependence on rotation rate.A differential Stokespower of 1 mW inside the ring resonator is measured to producea beat frequency bias of 69 Hz , which agrees well with theoreti-cal expectation.

INTRODUCTIONIS letter investigates the optical Kerr-effect in a

stimulated Brillouin scattering as the gain mechanism[1]-[31. The advantage of the BFOG over other types offiber-optic gyroscopes is its direct re adou t of rotation rate,measured as a beat frequency between counter-propagat-ing lasing waves inside a fiber ring resonator. In BFOGsystems previously reported, the frequency separation oftwo resonator modes was used as a constant beat fre-quency offset [l], [2] and t he fluctuation of this offset d ueto, for example, temperature could be a major errorsource in the ro tat ion rate measurement. On the o therhand, the optical Kerr-effect (present in all BFOGs) isthe main error source for the reciprocal BFOG systemreported here, which uses the same resonator mode forboth counte r-propag ating lasing waves [3]. Th e Kerr-effecthas been investigated previously in interferometricfiber-optic gyroscopes (IFOGs) [4] and resonant fiber-optic gyroscopes (RFOGs) [5], [6]. This effect causes anon-reciprocity between the two counter-propagatinglightwaves in the fiber coil, resulting in a spu rious rotatio nsignal. Various methods for reducing the Kerr-effect havebeen discussed also in the context of IFOGs [71, [SI andRFOGs [5], [9]. However, this letter represents the firstdetailed study of the Kerr-effect in a BFOG system. Inthe following, an all-fiber reciprocal BFOG is describedfirst. Theoretical analysis of the beat frequency offset dueto the Kerr-effect is presented next. Finally, measure-ments of the beat frequency of an experimental systemare described and shown to agree with the theoreticalanalysis.

RECIPROCAL FO G SYSTEMFig. 1 shows the schematic of the reciprocal BFOGsystem [3]. The system is made with nonpolarization-

Trillouin fiber-optic gyroscope (BF OG ) which utilizes

Manuscript received November 3, 1992; revised December 24, 1992.This work was supported by Litton Systems, Inc.The authors are with the Edward L. Ginzton Laboratory, StanfordUniversity, Stanford, CA 94305.IEEE L o g Number 9207615.

maintaining single-mode fibers, spliced together at pointsS. Pum p light from a laser-diode-pumped 1.32 p mNd:YAG ring laser is split into waves P p and PF by the3 dB coupler C,. P; and PF are coupled to the fiber ringresonator through the coupler C,, resulting in counter-propagating pump waves P , and P , in the ring. The statesof polarization of pumps P; and P? at the coupler C,are a djusted by the polarization controllers PC1 and PC2such that both P , and P, have the same eigen state ofpolarization in the ring.The resonance of the resonator is locked to the pumpfrequency by a FM sideband technique, where the pumpis modulated by a phase modulator PM 2 and the through-put of the pump Pi is tapped by the coupler C, anddetected by the detector D,. he detected signal is usedby the stabilization circuits for adjusting the voltage ap-plied to phase modulator PM1 in order to maintain theresonator at resonance for the pump P,. This, in turn,ensures that the pump P, is also at resonance when thegyroscope is at rest, because P , and P , see the sameresonant frequencies.With resonance maintained, th e power levels of P , andP , are enhanced greatly in the resonator and two Bril-louin lasing waves B, and B, are excited in oppositedirections to their respective pumps P , and P,, when thepower levels of P , and P , are above the Brillouin thresh-old. The Brillouin waves resonate, which selects theirfrequency and increases the efficiency of conversion ofpump power to Brillouin power. The circulating Brillouinwaves B, and B, are trapped by the coupler C , andcombined by the coupler C , to produce a beat frequencyoutput from detector D,. When the gyroscope rotates, theresonant frequency seen by P, differs from that seen byP , due to the Sagnac effect. This p um p walk-off effector resonator detuning from resonance for P, reduces thepower levels of P , and B, in the resonator. This limitsthe maximum measurable rotation rate because B, even-tually vanishes once the power of P2 becomes lower thanthe Brillouin threshold. At this point, the beat frequencyis also lost.

BEATFREQUENCYFFSET INDUCED BYKERR-EFFECTWhen the BFOG system is operating properly, thereare four circulating waves inside the ring: two pump wavesP , and P,, and two Brillouin waves B, and B,, with theirpowers also represented by the same symbols P,, P,, B,,and B , , respectively. The nonlinear index seen by B,

1041-1135/93$03.00 0 993 IEEE

Authorized licensed use limited to: EPFL LAUSANNE. Downloaded on January 27, 2010 at 00:14 from IEEE Xplore. Restrictions apply.

8/3/2019 S. Huang et al- Optical Kerr-Effect in Fiber-optic Brillouin Ring Laser Gyroscopes

2/3

366 IEEE PHOTONICS TECHNOLOGY LET TERS, VOL. 5, NO . 3, MARCH 1993

Beat Frequency

Fig. 1. Schematic diagram of a Brillouin fiber-optic gyroscope. PI an dP,: pump waves; B , an d B,: Brillouin waves; D: detector, C : coupler,PC: polarization controller, PM : phase modulator, and S: splice.

through the Kerr-effect is given byan,, = a n , ( B , + 2 B , + 2 P , + 2P2) /Aef f ( 1 )

where 11, is th e nonli near index coefficient, A,, is theeffective fiber-core area, and a accounts for polarizationeffects, ranging from 1 for linear polarization to 2/3 forcircular polarization [101. Because the eigen st ate of polar-ization in a non-polarization-maintaining fiber resonatoris elliptical in general, a should be between 1 and 2 /3 forthe current system. There is a factor of two difference inthe coefficients between the first term and th e remainingthree terms in (1) because the first term is the self phasemodulation and the ot hers are th e cross phase modulationterms for B , . No te tha t only the first two terms exist in theIFOG [7] and RF OG [5] .The nonlinear index seen by B ,is similarly given bya n g , = an2(2B,+ B , + 2 P , + 2P,) /Aeff (2 )

where the self phase modulation term is now the secondone. The differential nonlinear index change AnB = anB ,- anB, between B , and B , results in a beat frequencyoffset. Including both the Sagnac effect and the Kerr-effect, the beat frequency between B , an d B , can bewritten as

AfB = f B 2 -fBl = SO + T A B . (3 )The first term in (3) represents the Sagnac effect withscale factor S and rotation rate fl, the positive sign ofwhich corresponds to the clockwise rotation in Fig. 1, andthe second term represents the beat frequency offset dueto the index difference caused by the Kerr-effect withpower imbalance A B = B , - B , and coefficient T =( f a n 2 ) / ( n A e f f > ,where f is the average frequency of theBrillouin waves and n is the effective refractive index ofthe fiber. The second term T A B causes a spurious rota-tion rate m easurement. Th e calculated value of T for thecurrent system ranges from 51 Hz/mW for a circularpolarization to 76 Hz/m W for a linear polarization, wheren2 = 3.2 x cm2/W [ l l l and A ,, = n- X 4.6' p m 2are used. Note that in (3) the pump waves are canceledout and the beat frequency offset is only proportional tothe power imbalance A B = B , - B , .

Rotat ion Rate RFig. 2. Theoretically expected dependence of the beat frequency onrotation rate under Kerr-effect. P;"/Pi" is the ratio of the input pumppowers.

The power imbalance A B could be caused by twofactors. The first is initial power imbalance between theinput pumps Pp an d P;" at the coupler C,, possibly dueto an imperfect splitting ratio of the coupler C, and/orunequal losses in the fiber arms from the coupler C, tothe coupler C , . The sign of the power imbalance AB =B , - B , is equal to t he sign of P?/Py - 1. The second isthe pump walk-off effect, where the levels of Pz and B ,are reduced at high rotation rate, making A B negative athigh rotation rate.Th e effects of these two factors are schematically shownin Fig. 2. The ideal gyroscope response due only to theSagnac effect is the dotted straight line passing throughthe origin. When the Kerr-effect is included, the gyro-scope response is either shifted upward for Pp/Pf" > 1or downward for PF/Pp < 1 and it is also bent down-ward at high rotation rate because of the pump walk-offeffect. The response is also truncated in the figure, indi-cating the disappearance of the beat signal due to thepump walk-off effect at high rotation rate.

EXPERIMENTThe beat frequency of the BFOG system of Fig. 1wasmeasured as a function of rotation rate. The length, freespectrum range, finesse, and linewidth (FWHM) of theresonator are 27 m, 7.5 MHz, 75, and 100 kHz, respec-tively. The balance of the input pumps PF/P,i" wasadjusted by introducing bending losses at points A , andA , in Fig. 1.The input pump powers Pp an d PF weremeasured using a non-invasive clamp-on microbendingcoupler (courtesy of Raynet Corp.). In order to magnifythe beat frequency offset, which is much sm aller than thebeat frequency itself, the bea t frequency due to rotation issubtracted from the total measured beat frequency AfB inplotting the experim ental results. In Fig. 3 the vertical axis

is A fB - SR, where the scale factor S = 0.966(kHz/deg/sec) is determined from the linear fit to thedata at low rotation rate. Thus, Fig. 3 shows the differencebetween the curved response and the dotted straight linein Fig. 2.Thre e sets of da ta are shown in Fig. 3, corresponding tothree input pump ratios P;"/Py = 1.89, 1.43, and 0.79.

Authorized licensed use limited to: EPFL LAUSANNE. Downloaded on January 27, 2010 at 00:14 from IEEE Xplore. Restrictions apply.

8/3/2019 S. Huang et al- Optical Kerr-Effect in Fiber-optic Brillouin Ring Laser Gyroscopes

3/3

HUANG et a l . : K E R R - E F F E C T I N F I B E R -O P T I C B R I L L O U I N R I N G L A S E R G Y R O S C O P E S 367

h2 600v2 4006. 200Y

g oxs -200%2 -400L

- 6 0 0 1 A .- A CCW R otation I CW Rotation A-100 -50 0 50 100

Rotation Rate R (degsec)Fig. 3. Measu red beat frequency bias as a function of ,rotation rate.Three data sets are shown at input pump power ratios Pp/P; = 1.89,1.43. and 0.79.

The beat frequency is lost at about 9W/s because of thepump walk-off effect. Although the data points are scat-tered somewhat, presumably due to fluctuating power ofthe circulating Brillouin waves, which modulates the beatfrequency offset through the Kerr-effect, the followingobservations can be made. First the data sets shift down-ward as the input pump ratio Pp/Py changes from 1.89to 0.79. Second, the data sets bend downward at highrotation rate. These two observations agree with the ex-pectations based on the Kerr-effect, as schematicallyshown in Fig. 2.Fig. 4 shows the beat frequency offset A f B - SR a tR = 0 as a function of the power imbalance AB . T hepower imbalance A B = B , - B , is determined by calcu-lating the circulating Brillouin power B j in the ring fromthe measured input pump power using a formula basedon Brillouin fiber ring laser theory [12]: B, =P t , , { d R l}, j = 1,2), where Pth nd Pi{ are thecirculating pump power threshold and the input pumppower threshold which are 0.37 an d 21 mW, respectively,in the current system. The vertical error bars in Fig. 4show the fluctuation of the experimental beat frequenciesas previously mentioned. Th e slope of the best linear fit tothe data points is 69 Hz/mW, which lies between thetheoretical limits of 51 an d 76 Hz/mW. This agreementfurther verifies that the beat frequency offset is caused bythe Kerr-effect.

CONCLUSIONSThe large Kerr coefficient implies a requirement on thepower balance between the two internal Brillouin wavesto an accuracy of a few milliwatts for low grade to a fewnanowatts for high grade gyroscopes. For balancing thetwo input pump powers, a feed-back control scheme de-

veloped for the RFOG [9] can be adopted. To avoid the

h 500 I I I I IL 0 Data PointsF; m -

$ 300 -BU0i5 200 -P

loo-U

Differential Circulating Brillouin Power AB (mW)Fig. 4. Mea sured depende nce of the beat frequency bias on the differ-ential Brillouin power inside the resonator. The straight line is the bestlinear fit with slope of 69 Hz/mW.

Brillouin power unbalance caused by the pump walk-offeffect, we propose a symmetrical resonance stabilization,which taps both input pumps Pp an d PF and places thepump frequency at midway between the two resonantfrequencies seen by P , and P,, so that the Brillouinpowers B , an d B , are balanced even at high rotationrates. This approach is presently being studied.

REFERENCES[l] F. Zarinetchi, S. P. Smith, and S. Ezekiel, Stimulated Brillouinfiber-optic laser gyroscope, Opt. Lett., vol. 16, pp. 229-231, 1991.[2] R. K. Kadiwar and I. P. Giles, Optical fiber Brillouin ring lasergyroscope, Electron. Lett., vol. 25, pp. 1729-1731, 1989.[3] S. Huang , K. Toyama, P.-A. Nicati, L. Thtvenaz, B. Y. Kim, and H.

J. Shaw, Brillouin fiber op tic gyro with push-pull phase modulatorand synthetic heterodyne detection, in Proc. SPIE, Fiber Opticand Laser Sensors X , vol. 1795, Boston, MA, Sept. 8-11, 1992.S. Ezekiel, J. L. Davis, and R. Hellwarth, Intensity dependentnonreciprocal phase shift in a fiberoptic gyroscope, in Proc. FirstIntemat. Conf. Fiber-optic Rotation Sensors and Related Technolo-gies, Springer-Verlag, New Yo rk, 1982, pp. 332-336.K. Iwatsuki, K. Hotate, and M. Higashiguchi, Kerr effect in anoptical passive ring-resonator gyro, J . Lightwave Technol., vol.

[6] K. Takiguchi and K. Hotate, Partially digital-feedback schemeand evaluation of optical Kerr-effect induced bias in optical pas-sive ring-resonator gyro, IEEE Photon. Technol. Lett., vol. 3, pp.R. A. Bergh, H. C. Lefevre, and H. J. Shaw, Compensation of theoptical Ke rr effect in fiber-optic gyroscopes, Opt. Lett., vol. 7, pp.R. A. Bergh, B. Culshaw, C. C. Cutler, H. C. Lefkvre, and H. J.Shaw, Source statistics and the Kerr effect in fiber-optic gyro-scopes, Opt. Lett., vol. 7, pp. 563-565, 1982.K. Takiguchi and K. Hotate, Method to reduce the opticalKerr-effect-induced bias in an optical passive ring-reson ator gyro,IEEE Photon. Technol. Lett., vol. 4, pp. 203-206, 1992.[lo] R. A. Bergh, Ph.D. d issertation, Stanford University, Stanford, CA,1983, ch. 4.[l l] G. P. Agrawal, Nonlinear Fiber Optics. New York: Academic,1989, p. 183.[12] P. Bayvel and I. P. Giles, Evaluation of performance parametersof single-mode all-fiber Brillouin ring lasers, Opt. Lett., vol. 14,

[4]

[SILT-4, pp. 645-651, 198 6.

679-681, 1991.[7]

282-284, 1982.[8]

[9]

pp. 581-583, 1989.

Authorized licensed use limited to: EPFL LAUSANNE. Downloaded on January 27, 2010 at 00:14 from IEEE Xplore. Restrictions apply.