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Phase-conjugate fiber-optic gyro

Pochi Yeh, Ian McMichael, and Monte Khoshnevisan Rockwell International Science Center, 1049 Camino Dos Rios, Thousand Oaks, California 91360. Received 23 December 1985. 0003-6935/86/071029-02$02.00/0. © 1986 Optica Society of America.
Several types of phase-conjugate gyro are proposed in the literature.1-4 In this Letter, we describe a new type of fiber­ optic gyro that uses the phase-reversal property of polariza­ tion-preserving phase conjugation. Although the insensitivity of phase-conjugate gyros to reciprocal phase shifts and their sensitivity to nonreciprocal phase shifts such as the Faraday effect have been reported,3,4 to date no one has demonstrated rotation sensing. In this Letter, we report the first demonstration of rotation sensing with a phase-conju­ gate gyro.
Polarization scrambling is a well-known source of signal fading and noise in fiber-optic gyros. Polarization-preserv­ ing fibers and couplers must be used to decouple the two states of polarization and hence improve the sensitivity.5 In the phase-conjugate fiber-optic gyro, a polarization-preserv­ ing phase conjugator is used to restore the severely scram­ bled waves to their original state of polarization.6-8 This eliminates the signal fading and noise due to polarization scrambling without the need for polarization-preserving fi­ ber.
Referring to Fig. 1, we consider a phase-conjugate Michelson interferometer9 in which a fiber loop is inserted in the arm that contains the phase-conjugate reflector φ*. We now examine the phase shift of light as it propagates along the fiber. From point A to point B, the light experiences a phase shift of
where k = (2πn)/λ is the wave number and L is the length of fiber, R is the radius of the fiber coil, Ω is the rotation rate, λ is the wavelength, and c is the velocity of light. The second term in Eq. (1) is due to rotation. In the return trip, the phase shift is
where we notice that the term due to rotation is reversed because of the change in propagation direction relative to the rotation. If there were no phase conjugation, the total round-trip phase shift due to regular mirror reflection would be 2kL. However, because of the phase reversal on phaseconjugate reflection, the round-trip phase shift becomes

This phase shift can be measured by using the interference with the reference beam from the other arm. Notice that as a result of the phase reversal on reflection, the reciprocal phase shift kL is canceled on completion of a round trip. The net phase shift left is due to anything nonreciprocal such as rotation.
This net phase shift is proportional to the rotation rate and can be used for rotation sensing. In addition, if the phaseconjugate reflector is polarization-preserving,6-8 it will pro­ duce a true time-reversed version of the incident wave and will undo all the reciprocal changes (e.g., polarization scram­ bling, modal aberration, temperature fluctuation) when the light completes the round trip in the fiber. Since the polar­ ization scrambling and modal aberration of multimode fibers can be corrected by polarization-preserving phase conjuga­ tion, multimode fibers can replace the polarization-preserv­ ing single-mode fiber in this new type of gyro.
Figure 2 shows a schematic diagram of the experimental setup used to demonstrate the phase-conjugate fiber-optic gyro. Since this experiment does not use a polarizationpreserving phase-conjugate mirror, it does not demonstrate the correction of polarization scrambling. However, the experiment does measure the phase shift described by Eq. (3). A highly reflective beam splitter BS1 isolates the argon laser from retroreflections of its output. The light reflected by BS2 is focused by lens L1 (60-cm focal length) into a crystal of barium titanate to provide the pumping waves for degenerate four-wave mixing (DFWM). The light transmit­ ted by BS2 is split into two arms of a Michelson interferome­ ter by BS5. One arm of the interferometer contains a 10-cm radius coil of ~ 7 m of optical fiber. Since the phase-conju­ gate mirror in this experiment is not polarization-preserving, we use single-mode polarization-preserving optical fiber. Light exiting the fiber provides the probe wave for DFWM. The c-axis of the barium titanate crystal is parallel to the long faces of the crystal and points in the direction of beam splitter BS3. The pumping waves from mirrors M2 and M3 have powers of 18 and 3 mW, respectively, and their angle of incidence is ~45°. The probe wave, exiting from the end of the fiber loop, makes a small angle (<10°) with the pumping wave from mirror M2 and has a power of 0.7 mW. Under these conditions we obtain a phase-conjugate reflectivity of 50% and a response time of 0.1 s. The reference arm of the interferometer is terminated by a mirror M4 mounted on a piezoelectric transducer so that the operating point of the interferometer can be set at quadrature. Light from both arms combines to form complementary fringe patterns at detectors D3 and D4. Detectors D1 and D2 measure the powers in the recombining waves.
The fiber coil is rotated with the rest of the setup remain­ ing fixed at various rotation rates [first clockwise (CW), then

Fig. 1. Schematic drawing of the phase-conjugate fiber-optic gyro. Fig. 2. Experimental setup of the phase-conjugate fiber-optic gyro. 1 April 1986 / Vol. 25, No. 7 / APPLIED OPTICS 1029

9. M. D. Ewbank, M. Khoshnevisan, and P. Yeh, "Phase-Conjugate Interferometry," Proc. Soc. Photo-Opt. Instrum. Eng. 464, 2 (1984).
Fig. 3. Measured phase shift as a function of applied rotation rate.
counterclockwise (CCW), etc.] in a square wave fashion for 10 cycles with an amplitude of 120°. The measured powers from all detectors are used to calculate the average phase shift between rotation in the CW and CCW directions of rotation. Figure 3 shows a plot of the measured phase shift as a function of the rotation rate. The solid line indicates the expected rotation-induced Sagnac phase shift. The large uncertainty in the data is due to rapid (faster than the response time of the DFWM) phase changes that are produced by the twisting of the fiber when the fiber loop is rotated and that act as a source of noise.
In conclusion, we have proposed a new type of fiber-optic gyro that uses polarization-preserving optical phase conjugation, and we have presented the first demonstration of rotation sensing by a phase-conjugate gyro.
This research is partially supported by the Office of Naval Research.
References 1. J.-C. Diels and I. C. McMichael, "Influence of Wave-Front-Con-
jugated Coupling on the Operation of a Laser Gyro." Opt. Lett. 6, 219 (1981). 2. P. Yeh, J. Tracy, and M. Khoshnevisan, "Phase-Conjugate Ring Gyroscopes," Proc. Soc. Photo-Opt. Instrum. Eng. 412, 240 (1983). 3. C.J. Bode, "Phase Conjugate Optics and Applications to Interferometry and to Laser Gyroscope," in Experimental Gravitation and Measurement Theory, P. Meystre and M. 0. Scully, Eds (Plenum, New York, 1983), pp. 269-291. 4. B. Fischer and Shmuel Sternklar, "New Optical Gyroscope Based on the Ring Passive Phase Conjugator," Appl. Phys. Lett. 47, 1 (1985). 5. W. K. Burns, R. P. Moeller, C. A. Villarruel, and M. Abebe, "Fiber Optic Gyroscopes with Polarization Holding Fiber," Opt. Lett. 8, 540 (1983). 6. P. Yeh, "Scalar Phase Conjugation for Polarization Correction," Opt. Commun. 51, 195 (1984). 7. I. McMichael and M. Khoshnevisan, "Scalar Phase Conjugation Using a Barium Titanate Crystal," in Technical Digest, Conference on Lasers and Electro-Optics (Optical Society of America, Washington, D.C., 1985), paper THN1. 8. I. McMichael, M. Khoshnevisan, and P. Yeh, "Polarization-Preserving Phase Conjugator," submitted to Opt. Lett.
1030 APPLIED OPTICS / Vol. 25, No. 7 / 1 April 1986