A novel hybrid single-polarization (SP) fiber ring resonator is demonstrated by using a polarization-maintaining coupler formed by splicing a section of SP fiber into the resonator. The SP fiber selectively eliminates the unwanted resonance by introducing high loss for the unwanted eigenstates of polarization in the resonator. The calculated result shows that this hybrid SP resonator is a good candidate for a tactical-grade performance gyro with a high environmental temperature stability. The experiment shows that the desired resonance in the resonator can keep an excellent stability in a wide temperature range, thus the temperature-dependent polarization-fluctuation drift in the resonant fiber optic gyro is sufficiently suppressed. As a result, a random walk coefficient of 0.08°/√h and a typical bias stability below 0.3°/h for an integration time of 300 s have been carried out.
© 2015 Optical Society of America
Since the first configuration of a resonant fiber optic gyro (RFOG) was proposed by Meyer and Ezekiel early in the 1983 , the RFOG has been considered to be a candidate for the next generation of the inertial rotation sensor because of its high accuracy and low cost. However, the performance achieved to date is still below expectation due to the noises resulted from the various effects. Among those, the temperature-related polarization fluctuation has been regarded as the main reason for the long-term instability of the RFOG .
In a polarization-maintaining fiber (PMF) resonator, two eigenstates of polarization (ESOPs) reproduce their polarization states after one roundtrip [3,4]. The unwanted ESOP appearing as the second peak or dip in the resonant curve , leads to the asymmetries of the resonant curve and causes both the intensity and interference bias errors. What’s more, the birefringence in the PMF resonator is temperature-dependent. Therefore, the polarization induced error is generally related to the environmental temperature changes and it affects the long-term stability of the resonant optic gyros [6–8].
To eliminate the polarization-fluctuation induced drift completely, a single-polarization (SP) fiber ring resonator is needed to ensure a single ESOP excitation [9,10]. Unfortunately, there is no commercial SP fiber coupler to date. Many groups have proposed different schemes of resonators to overcome the polarization-fluctuation based on PMF couplers [3–13]. Previously, combining the polarization-axis rotating splicing technique with the in-line polarizers has turned out a much wider operating temperature range [11,12]. A bias stability below 2°/h for an integration time of 100 s is successfully demonstrated in an RFOG with a ring length of 14.25 m. However, the in-line polarizers cannot meet the requirements of the polarization extinction ratio (PER) for full-temperature range application. Besides, the polarizers increase the complex of the resonator structure which may be an obstacle for the future miniaturization of the RFOG.
In this paper, a scheme for decreasing the polarization error by using SP fibers in a resonator has been proposed and demonstrated. Unlike the polarizers mentioned before, the SP fiber can satisfy the different requirements of PERs by selecting an appropriate length. The longer the SP fiber used in the resonator, the higher the PER becomes. The twin 90° polarization-axis rotated splices technique  is used to suppress the drift induced by the fiber pigtails of the PMF couplers. The simulation results suggest that the polarization-fluctuation induced error over a temperature range of 100°C can be reduced below the shot noise limited sensitivity. What’s more, replacing the polarizers with the SP fiber is advantageous for the miniaturization of the RFOG. Experiment results show that the bias stability is below 0.3°/h for an integration time of 300 s.
2. Principle and analysis
A spliceless ring resonator made completely from SP fibers only allows one ESOP to propagate in the resonator. Being lack of commercial couplers from SP fibers, the SP fibers were closed using two conventional PMF couplers with short leads spliced to the SP fibers, as shown in Fig. 1. Our measurements indicate that the polarization-fluctuation induced error is still large because of the existence of the PMF coupler in the resonator. A transmitter type resonator is indispensable. L1 and L2, and L3 and L4, are the pigtails of C1 and C2, respectively. Two sections of the SP fiber are spliced to the pigtails L1 and L2 to block the fast-axis lightwaves. The pigtails L3 and L4 of C2 are 90° polarization-axis rotated spliced to SP fiber (1) and SP fiber (2), respectively. The diameter of the resonator is 0.12 m. Normally, in a resonator without polarization-dependent loss, the length difference between the fiber segments of the two 90° polarization- axis rotated splicing points is controlled to one half of the beat length of the PMF . With the high PER of SP fibers in the resonator, the length difference between (L1 + L2) and (L3 + L4) shown in Fig. 1 should be adjusted to zero to effectively reduce the drift induced by the temperature fluctuation .
Compared to the scheme mentioned previously [12,13], SP fibers are adopted to replace the in-line polarizers. The key for SP operation is to selectively eliminate one state of polarization of the fiber’s fundamental mode while propagating the orthogonal state. The SP fibers can provide an 8 dB/m attenuation for the undesired ESOP while have a 0.05 dB/m propagation loss for the main ESOP.
The ultimate sensitivity of the RFOG is determined by the shot noise of the photodetector (PD). The minimum rotation rate Ωmin is given by 14]Fig. 2. The deterioration of the resonator finesse due to the loss from SP fibers is also depicted in Fig. 2. For the purpose of maintaining the reciprocity of the resonator, the SP fiber (1) and SP fiber (2) are of the same length. As can be seen in Fig. 2, the longer the SP fibers used in the resonator, the lower the finesse will be, because of the attenuation of SP fibers. What’s more, the shot noise limited sensitivity worsens due to the attenuation induced by the SP fibers. From technique views of a high-finesse resonator and a high-sensitivity RFOG, the appearance of the SP fibers in the resonator is unsatisfactory.
The RFOG output is proportional to the resonant frequency shift between the clockwise (CW) and counterclockwise (CCW) lightwaves propagating in the resonator. The error in the resonant frequency shift due to the existence of the unwanted ESOP in the resonator is given by Eq. (5) is inevitably deteriorated.
Figure 3 shows the relationship between the polarization-fluctuation induced error in the full temperature range and the PER of the SP fibers. As seen in Fig. 3, when the resonator equips with 10 m long SP fibers, the maximum PER is 80 dB and the polarization-fluctuation induced error can be reduced down to 1.4°/h. Compared to the theoretical shot noise limited sensitivity of 0.3°/h, it seems that much longer SP fibers are needed. However, for the practical applications, the RFOGs usually operate over a finite range of temperature, thus much lower polarization error can be achieved.
Figure 4 shows the polarization-fluctuation induced errors calculated as a function of the temperature change. Two different resonators are compared. The PMF resonator is integrated with two in-line polarizers with a PER of 30 dB for each . The hybrid SP/PMF resonator is spliced to two sections of the SP fibers with a PER of 40 dB for each. The length difference between L1 + L2 and L3 + L4 is about 2 cm which means that the phase separation between the two ESOPs varies from zero to π over a temperature range of 150°C . The maximum polarization-fluctuation induced error in the full temperature range is as large as 1.42°/h as indicated in Fig. 3; however, the polarization error over a temperature range of 100°C can be reduced down to 0.29°/h as shown in Fig. 4, which is below the shot noise limited sensitivity. Compared to the resonator with two in-line polarizers inserted, the polarization error is improved by a factor of 29.3. The simulation result suggests that the new hybrid SP/PMF resonator has a better ability to suppress the polarization-fluctuation induced error.
3. Measurements of the closed-loop RFOG
Two sections of a 5m SP fiber (single-polarization fiber for 1550nm from Verrillon, Inc.) are spliced to the resonator and the PER for each section of SP fiber is nearly 40dB. The attenuation of the SP fiber is about 0.044 dB per meter. Each fusion point between the SP fiber and the PMF causes a loss of 0.27 dB. The total loss of the resonator is 1.57dB. The measured finesse is about 14.7. According to Eq. (1), the shot noise limited sensitivity is calculated to be 0.3°/h with a light intensity of 18μW arrived at the PD . Figure 5 shows the measured resonant curves over a temperature range varying from 10°C to 40°C. Measured results show that only one resonance is excited, which keeps an excellent stability at different temperatures.
Figure 6 shows the experimental setup of the RFOG equipped with the hybrid SP/PMF resonator . All the fibers in the system are polarization maintaining except for the two sections of the SP fiber. A lightwave from a 5-kHz linewidth fiber laser is divided into two equivalent beams by coupler C3. The LiNbO3 phase modulators PM1 and PM2 are driven by sinusoidal waves with modulation frequencies f1 and f2, respectively. The CW and the CCW lightwaves from the resonator are detected by the InGaAs PIN photodetectors, PD1 and PD2. The output of the PD2 is fed back through the lock-in amplifier LIA2 to the servo controller PI1 to reduce the reciprocal noises in the RFOG. To make the CW lightwave work in resonance, the demodulated signal of the CW lightwave from LIA1 is fed back to the LiNbO3 phase modulator PM3 via the servo controller PI2 and the frequency shifting driver (FSD) for gyro signal detection. The frequency control word (FCW) is used as the gyro output via a low-pass filter (LPF). With the closed-loop operation, the excellent linearity and large dynamic range of the gyro output are achieved .
The sinusoidal rotation measurement results of the closed-loop RFOG are shown in Fig. 7. The rotation amplitudes of the sinusoidal swing are ± 0.05°/s, ± 0.01°/s, ± 0.005°/s, and ± 0.001°/s, respectively. Compared to the RFOG equipped with a PMF resonator integrated with two in-line polarizers , the achieved minimum rotation amplitude is improved by a factor of 5.
Figure 8(a) shows the typical outputs of the stationary RFOG in 1200 seconds for an integration time of 1 second. Figure 8(b) further illustrates the nature of the gyro stability where the uncertainty of the rotation rate is plotted versus integration time for a typical data run of 1200 seconds. As seen in Fig. 8(b), the rate uncertainty versus integration time has a slope of −1/2 up to an integration time of about 300 seconds. As a result, a random walk coefficient of 0.08°/√h is carried out. As previously discussed, the effects of polarization fluctuation can be greatly reduced by employing the SP fibers. The bias stability of Allan variance is about 0.3°/h for an integration time of 300 seconds. However, the bias stability deteriorates while increasing the integration time up to more than 300 seconds. Other sources contributing to the drifts are expected to be further reduced to improve the long-term bias stability, such as the optical Kerr effect .
In conclusion, a hybrid SP resonator is successfully demonstrated for an RFOG. Experimentally, the desired resonance in the resonator keeps stable in a wide temperature range without the appearance of an unwanted one. As a result, the gyro bias stability below 0.3°/h is successfully demonstrated for the integration time of 300 seconds. The calculated result shows that this hybrid SP resonator is a good candidate for a tactical-grade performance gyro with high environmental temperature stability. Benefiting from the replacement of the polarizers by the SP fibers, the RFOG equipped with this hybrid SP resonator can achieve a more compact size.
The authors would like to acknowledge financial support from the National Natural Science Foundation of China (No. 61377101).
References and links
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