644 OPTICS LETTERS / Vol. 8, No. 12 / December 1983

Passive fiber-optic ring resonator for rotation sensing

R. E. Meyer and S. Ezekiel

Research Laboratory of Electronics, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139

D. W. Stowe and V. J. Tekippe

Gould Electronics Laboratories, Rolling Meadows, Illinois 60008

Received August 22, 1983

A passive fiber-optic resonator technique for rotation sensing has been investigated. Preliminary data show anoise-equivalent rotation-rate sensitivity of 0.50/h (T = 1 sec), which is an order of magnitude above the photon-shot-noise limit. The major sources of error and ways of reducing such errors are discussed.

Various forms of optical inertial rotation sensors,based on the Sagnac effect, have been under develop-ment since the advent of the laser in 1960. These in-clude active techniques, such as the ring laser gyro,' andpassive techniques employing ring resonators2 or in-terferometers.3 In the past few years, low-loss single-mode optical fibers have been incorporated into inter-ferometers4 and, more recently, resonators.5 ,6 In thisLetter, we describe the use of a fiber-optic resonator forthe detection of inertial rotation; we present preliminarynoise-performance data, and we discuss several sourcesof error as well as possible methods for reducing theseerrors.

The technique of using a fiber resonator to detectinertial rotation, proposed in Ref. 2, is similar to thatalready discussed in previous papers on the passivediscrete-component ring resonator.7 '8 In the presenceof an inertial rotation rate Q (rad/sec) normal to theplane of the ring resonator, the clockwise and counter-clockwise resonances of the cavity are separated by afrequency Af given byl

Af = 4A QA

objectives, and the output beams are directed ontophotodectors PD1 and PD2 by beam splitters SI andS2, respectively.

To observe cavity resonances, we vary the length ofthe fiber resonator by stretching the fiber with a pi-ezoelectric transducer (PZT 1). When only one beamis coupled into the resonator, the output intensity as afunction of resonator length is as shown in Fig. 2(a). Ascan be seen, the intensity is high off resonance and dropsalmost to zero on resonance because the cavity is ob-served in reflection. The separation between the res-onances is the free spectral range, 66 MHz, and the fi-nesse shown in Fig. 2(a) is approximately 140. Theseresults indicate that the coupler exhibits a loss of lessthan 3% and equivalent reflectivity of 96%.

To achieve the high-finesse, single-frequency be-havior demonstrated by Fig. 2(a), the polarization of thelight must be controlled, both inside and outside theresonator. This is necessary because the resonator,even though it is made of single-mode fiber, can supporttwo eigenmodes of different polarization states. Out-

(1)

where A is the area enclosed by the resonator, P is theoptical perimeter, and X is the wavelength of the light.In order to measure Af, we introduce two counterprop-agating beams into the resonator and adjust the fre-quency of each beam to coincide with the correspondingcavity resonance. In this way, the frequency differencebetween the beams corresponds to the rotation rate asgiven by Eq. (1).

Figure 1 shows the experimental setup. The fiberresonator consists of 3.1 m of single-mode fiber (corediameter - 4.0 gzm) formed into a ring and closed by afused evanescent-wave coupler.9 Light from a 1-mWHe-Ne 6328-A laser, operating at a single frequency fo,is split by a beam splitter into two beams, which areshifted in frequency to fo + f l and fo + f2 by acousto-optic modulators A/O 1 and A/O 2, respectively, andcoupled into the fiber by microscope objectives. Lightis also coupled out of the fiber through these microscope

PZT I

Fig. 1. Schematic diagram of fiber-optic resonator gyro-scope.

0146-9592/83/120644-03$1.00/0 © 1983, Optical Society of America

December 1983 / Vol. 8, No. 12 / OPTICS LETTERS 645

1 0 sac

I IL:U~ J__ -T 80(Hz

(a)

3 -30 Hz

T

(b)

10 sec

-y -- - T-- H ! - - _JI ~-± I -1I= _60/

(C)

Fig. 2. (a), (b) Output of PD 1 as a function of cavity length,with and without proper polarization alignment, respectively.Free spectral range, 66 MHz; finesse, 140. (c) PSD 1 outputcorresponding to (a).

side the resonator, bulk optical components consistingof polarizers, half-wave plates, and quarter-wave platesare placed between the beam splitters and the micro-scope objectives in order to set the state of polarizationof the input beams so that only one eigenmode of theresonator is excited. Inside the resonator, a fiber-opticpolarization controller'0 (PC) is used to compensate forbirefringence in the fiber ring in order to achieve thehigh finesse shown. To illustrate the behavior when thepolarization is not properly aligned, Fig. 2(b) shows theintensity as a function of cavity length under the sameconditions as for Fig. 2(a), except that the state of po-larization of the input beam has been slightly changed,resulting in the appearance of a second resonance.

In order for inertial rotation to be detected, twocounterpropagating beams must be introduced into theresonator to measure the frequency difference betweenthe clockwise and counterclockwise resonances of thecavity. However, when both beams are simultaneouslyintroduced into the cavity we obtain the situation il-lustrated by Fig. 3(a). This figure, which is a simulta-neous record of the intensity measured by each photo-detector as a function of cavity length, shows the cavityresonances superimposed upon a noisy background.This background noise consists primarily of an oscilla-tion at the difference frequency (fi - /2) between thecounterpropagating beams, indicating that light fromeach beam has been backscattered within the fiber. Aswas discussed previously,8 the effects of backscatteringcan be greatly reduced by phase modulating one of theinput beams. In our setup, this may be implementedby applying a sinusoidal voltage to PZT 2, around whichone input fiber is wrapped (as shown in Fig. 1). If thisPZT is driven at a frequency fj with a sufficient ampli-tude to suppress the carrier frequency, then the fre-quency of the background oscillation will be shifted byintegral multiples of 4fj, which can then be removed byappropriate filtering techniques. Figure 3(b) shows thesimultaneous outputs of both photodetectors (afterfrequency components around /f have been filtered out)as a function of resonator length with optimal phase

modulation. As can be seen, the background oscillationhas been substantially attenuated.

To perform the measurement of Af (and thus of thecorresponding rotation rate Q), we employ modulationand feedback schemes described in detail elsewhere.7' 8

For this purpose, the cavity length is modulated at areference frequency fm = 15 kHz by PZT 1, and theoutput of PD 1 is demodulated at /r by a phase-sensi-tive detector (PSD 1), producing a voltage proportionalto the fm component in the PD 1 output. Figure 2(c)shows this PSD output as a function of cavity length,which is approximately a derivative of the resonance.Because the PSD output changes from positive to neg-ative across the resonance (and is zero at the center ofthe resonance), it can be used as an error signal by theservo electronics to lock the counterclockwise cavityresonance to the frequency of the output beam (fo + fi).When the cavity is locked in this way, the output of PSD1 [Fig. 4(a)] shows residual noise of approximately 2.5Hz (rms) when observed with a 0.3-sec time constant.

With the counterclockwise cavity resonance main-tained locked to the laser frequency (fo + fi), theclockwise beam (frequency fo + f2) is then introducedinto the ring and detected by PD 2. The output of PD2 is also demodulated at fm by PSD 2, and, in theopen-loop scheme, the PSD 2 output, which is a measureof Af (or Q), is shown in Fig. 4(b). (For our setup,rotation at Earth rate 2 E = 150/h produces a frequencyshift Af = 75 Hz). The left-hand side of Fig. 4(b) wasrecorded without phase modulation, and it shows large

(a) (b)

Fig. 3. Simultaneous outputs of PD 1 (above) and PD 2 asa function of cavity length: (a) without phase modulation,(b) with phase modulation.

0- -(a) (b)

(C)

Fig. 4. (a) Output of PSD I on lock; X = 0.3 sec. (b) Outputof PSD 2 corresponding to (a), secondary loop open, withoutphase modulation (left trace) and with phase modulation(right trace). (c) Same as (b) right trace, on a more-sensitivescale, r = 1 sec.

646 OPTICS LETTERS / Vol. 8, No. 12 / December 1983

oscillations at the beat frequency f2 - l. As the phasemodulation is applied and adjusted in amplitude, theseoscillations become small, as shown on the right-handside of Fig. 4(b). With the backscattering thus sup-pressed, Fig. 4(c) shows the open-loop PSD 2 output ona more-sensitive scale. As can be seen, the PSD 2 out-put exhibits rms frequency noise of about 2.5 Hz, or anequivalent rotation-rate uncertainty of 0.50 /h, for anintegration time of 1 sec. In addition, there is a bias inthe PSD 2 output of approximately 600 Hz, or 120'/h.(It should be noted that the outputs of PD 1 and PD 2are subtracted in PSD 2, as shown in Fig. 1, thus can-celing noise common to both beams.)

In practice, the fiber-optic rotation sensor wouldoperate under closed-loop conditions,8 as illustrated inFig. 1. In this scheme, the PSD 2 output is used,through a servo amplifier and a voltage-controlled os-cillator, to lock the clockwise beam frequency fo + f2 tothe clockwise cavity resonance. In this way, Af, theseparation of the cavity resonances that is due to rota-tion, is simply obtained by substracting f, from f2 withan up-down counter.

We now compare the noise in Fig. 4(c) with thatpredicted by the photon shot noise. For shot-noise-limited detection using the optimum modulation am-plitude in our present resonator, the uncertainty in themeasurement of rotation oQ would be8

(4A L(Nph7D-T)T1/2j(2)

where Nph is the average number of photons per secondarriving at the detector, 17D is the detector's quantumefficiency, -r is the integration time, and r is the fullwidth of the cavity resonance at half-intensity. Sub-stituting our experimental parameters into Eq. (2), wecalculate that the photon shot noise contributes anuncertainty iQ - 0.05'/h for an integration time of 1 sec.Thus the 0.5 0/h rms noise shown in Fig. 4(c) must comefrom sources other than shot noise.

There are several sources of noise and bias that cancontribute to the errors shown in Fig. 4(c). We havealready mentioned the backscattering problem, whichwe have substantially reduced by using phase-modu-lation techniques. Another important source of erroris the stability of polarization alignment. Variationsin environmental temperature or pressure inducechanges in the birefringence of the fiber, which resultin nonreciprocal phase shifts. Thus it is necessary toisolate the fiber resonator from temperature and pres-sure variations or to stabilize the polarization alignmentby a servo system." The optimal solution, however, isto use a single-polarization fiber, which has recentlybeen developed.12 Another source of nonreciprocalphase shift is the optical Kerr effect'3 that is due tounequal intensities in the counterpropagating beams.One way of reducing this source of error is the equali-zation of the two intensities by servo control.

The sensitivity of the fiber resonator gyro may beimproved by decreasing P/A and also F in Eq. (2). Theratio P/A may be decreased by using a larger-diameter

ring, and r may be decreased by using a longer fiber, i.e.,a multiple-turn resonator, as long as the additional fiberloss is small compared with the coupler loss. In addi-tion, an increase in the shot-noise-limited signal-to-noise ratio, i.e., (Nph7?Dr)'1 2 , would also improve thesensitivity, as shown in Eq. (2). Finally, an attractivepossibility for achieving a compact version of thisrotation sensor'4 is to replace the fiber with a thin-filmwaveguide in an appropriate substrate and to use inte-grated-optics techniques and a semiconductor laser toperform the necessary measurements.

This research was supported by the U.S. Air ForceOffice of Scientific Research and by the Joint ServicesElectronics Program at the Massachusetts Institute ofTechnology.

References

1. A. H. Rosenthal, "Regenerative circulatory multiple-beaminterferometry for the study of light-propagation effects,"J. Opt. Soc. Am. 52, 1143 (1962).

2. S. Ezekiel and S. R. Balsamo, "Passive ring resonator lasergyroscope," Appl. Phys. Lett. 30,478 (1977).

3. W. R. Carrington and R. Fredricks, Lear Siegler, Inc.,Grand Rapids, Michigan 49508, "Development of an op-tical rate sensor," Final Rep. to U.S. Office of Naval Re-search N00014-73-C-0377, November 1973.

4. V. Vali and R. W. Shorthill, "Fiber ring interferometer,"Appl. Opt. 15, 1099 (1976).

5. L. F. Stokes, M. Chodorow, and H. J. Shaw, "All-single-mode fiber resonator," Opt. Lett. 7, 288 (1982); "Sensitiveall-single-mode-fiber resonant ring interferometer," IEEEJ. Lightwave Technol. LT-1, 110 (1983).

6. R. E. Meyer and S. Ezekiel, "Fiberoptic resonator gyro-scope," presented at First International Conference onOptical Fibre Sensors, IEE, London, April 26-28, 1983.

7. S. Ezekiel, J. A. Cole, J. Harrison, and G. Sanders, "Pas-sive cavity optical rotation sensor," Proc. Soc. Photo-Opt.Instrum. Eng. 157, 68 (1978).

8. G. A. Sanders, M. G. Prentiss, and S. Ezekiel, "Passivering resonator method for sensitive inertial rotationmeasurements in geophysics and relativity," Opt. Lett.7, 569 (1981).

9. This coupler was provided by Gould Research Labora-tories.

10. H. C. Lefbvre, "Single-mode fiber fractional wave devicesand polarization controllers," Electron. Lett. 16, 778(1980).

11. R. Ulrich, "Polarization stabilization on single-modefiber," Appl. Phys. Lett. 35, 840 (1979).

12. D. N. Payne, "Review of birefringent fibers: preparingcharacteristic properties," in Digest of Topical Meetingon Optical Fiber Communication (Optical Society ofAmerica, Washington, D.C., 1983); J. R. Simpson, F. M.Sears, J. B. MacChesney, R. H. Stolen, W. Pleibel, and R.E. Howard, "Single polarization fiber," IEEE J. Light-wave Technol. LT-1, 370 (1983).

13. S. Ezekiel, J. L. Davis, and R. Hellwarth, "Intensity de-pendent nonreciprocal phase shift in a fiberoptic gyro-scope," in Fiberoptic Rotation Sensors, S. Ezekiel andH. J. Arditty, eds. (Springer-Verlag, Berlin, 1982), p.332.

14. J. Haavisto, "Thin film waveguides for inertial sensors,"Proc. Soc. Photo-Opt. Instrum. Eng. 412, 221 (1983).