Open Access
Add to BibSonomyAbstract
In a resonator integrated optic gyro (RIOG) employing a planar optical waveguide ring, the interference between backreflected light and signal light will not only cause nonreciprocal drift of cw and ccw resonance frequencies, but also deteriorate the original signal waveform of the resonator output. If contra-phase triangular phase modulation (CPM) were applied, a cosine-like ripple, whose initial phase varies randomly, would superpose upon the quasi-square waveform of the resonator output, resulting in increment of noise and the gyro’s angle random walk (ARW). Therefore, in-phase triangular phase modulation (IPM) technique is proposed and used to eliminate the ripple and improve the waveform quality of the resonator output, and the gyro’s ARW is obviously reduced from 3 to 0.8 deg/h1/2 compared to that of CPM. This enlightens a new way to design the scheme of backreflection/backscattering suppression.
© 2016 Optical Society of America
1. Introduction
Resonator integrated optic gyro (RIOG) based on the Sagnac effect is of great potential in realizing system-on-chip for optic gyros. It has attracted much attention from the fields of inertial navigation, attitude stabilization and etc., because it has high reliability and zero-wear-rate due to movable-component free [1,2]. A lot of gratifying achievements of RIOG have been reported [3–8]. Bias stabilities of 0.09deg/s with an integration time of 10s [4], and 0.05deg/s with an integration time of 400s [5] have been demonstrated for buried silica waveguide based RIOG recently. Stimulated Brillouin laser gyro employing ultrahigh-Q microresonator has achieved a sensitivity of 15 (deg/h)/(rt-Hz), but it is suggested that the microresonator size should precisely match the Brillouin shift frequency in silica to lower the lasing threshold [9–11].
Many factors, such as backreflection [12], backscattering [13], polarization fluctuation [14,15], Kerr effect [16], residual intensity modulation [17], Faraday effect [18] and etc [19], become the barrier that hinder the improvement of RIOG performance. It is known that even at rest, the interferometric effect between backreflected light and signal light in a RIOG does cause the detected resonance peak deviate away from the true resonance frequency of the resonator, then the nonreciprocal change between the detected CW and CCW resonance frequencies leads to gyro bias drift inevitably; therefore, backreflection is one of the most important nonreciprocal factors in RIOG [19]. Usually, phase modulation technology is not only used to set the bias operation point in order to increase detection sensitivity, but also use to suppress the backreflection and backscattering induced errors [13,20,21]. Nevertheless, if phase modulation were applied, the backreflection would cause deformation of the resonator’s original output signal [12]. The deformation, to some extent, does not influence too much on the gyro’s long-term bias stabilitity, because the gyro signal bandwidth is below one kilohertz in general, while the frequency of the resonator’s original output signal is beyond hundreds of kilohertz; after being processed by over-sampling, mean filtering and sliding mean filtering, the high-frequency noises generated by the deformation can be greatly suppressed and hardly contribute to the gyro bias drift. However, to further improve the gyro performance, the gyro noise and gyro drift must be suppressed simultaneously, especially for low-noise and wide-bandwidth applications.
Angle random walk (ARW) is usually used to evaluate the gyro noise. In interferometric fiber optic gyro, the factors that influence the ARW include electrical noise, photon shot noise, relative intensity noise, thermal phase noise, D/A noise and etc., all of which apply to RIOG. In addition, the laser frequency noise, frequency-lock noise and other noises have bad influences on RIOG’s ARW. In the study of contra-phase triangular phase modulation (CPM) technique, we found that though the backreflection induced gyro drift could be suppressed, the gyro ARW was not correspondingly reduced. The main reason is that a cosine-like ripple, whose initial phase varies randomly, would superpose upon the quasi-square waveform of the resonator output if CPM technique were applied. In this paper, in-phase triangular phase modulation (IPM) technique is proposed to eliminate the cosine-like ripple of the original signal; therefore, the signal quality is improved and the gyro ARW is obviously reduced. This lays a solid foundation to reach higher accuracy for RIOG.
2. Principle and simulation
The sketch map of backreflections in a transmissive resonator based RIOG is shown in Fig. 1. A narrow linewidth laser is locked to the CCW resonance frequency of a silica waveguide ring resonator, and the CW demodulated signal is approximately proportional to the rotation rate within a certain range. The modulation signals applied on the Y-branch phase modulator consist of four triangular waveforms f1 ~f4. IPM refers to f1 = f2 and their phase difference is zero; CPM refers to f1 = f2 and their phase difference is π. The triangular waveforms f3 and f4 are used to improve the carrier suppression ratio of the CW and CCW loops [21]. Some reasonable assumption is proposed to simplify discussion, which are: a) the backreflections are too small to cause non-ignorable forward attenuation; b) the backreflection coefficients of C and D are equal and much bigger than those of A and B, hence the backreflections of A and B can be neglected; c) the evanescent wave couplers C1 and C2 possess totally same and reciprocal features in CW and CCW directions; d) all losses are not taken into consideration except for the resonator’s inner loss.
Fig. 1 Sketch map of backreflections in RIOG. C1, C2: evanescent wave coupler; ISO: isolator; PM: Y-branch phase modulator; PD: photodetector; color arrows: signal light and its backreflected light for CCW (blue) and CW (red).
If there are no backreflection and other noise factors, the photon shot noise limited ARW can be expressed as [3]:
Where, F, A and N are the finesse, effective area and number of loops of the resonator, respectively; e is the electron charge; I is the peak photocurrent of photodetector; c and λ are the light velocity and wavelength in vacuum. The electric field of light at the resonator output port consists of the following components when backreflection is taken into consideration: Where, Y is the Fourier coefficients of the triangular phase modulation signals of CW/CCW directions, and fm are the corresponding harmonic frequencies; r is the backreflection coefficient; n and L are the effective refractive index and length of waveguide, respectively; θ is the phase difference between CW and CCW directions caused by optical path difference, refractive index difference and other factors; φ is the extra phase induced by phase modulation; hT and hR refer to the transmissive and reflective transfer functions of the resonator; αC and kC are the extra loss and coupling ratio of the resonator coupler; αL/2 refers to the propagation loss of half loop of the resonator; τ is the resonator’s round-trip time. Then the total electric field and the corresponding light intensity can be calculated by:The simulation results of resonator output are shown in Fig. 2. It can be seen that the DC component of the original output waveform, quasi-square waveform, would no longer agree with that of no backreflection if IPM were applied; and if CPM were applied, the backreflection would superpose a cosine-like ripple upon the quasi-square waveform. The number of ripple period in half of modulation period is related to the ratio of modulation voltage and modulator’s half-wave voltage, though the ripple period is not such complete on account of the resonator’s optical delay. The amplitude of the quasi-square waveform ΔI is approximately proportional to the rotation rate Ω, as shown in Fig. 2(b).
Fig. 2 Resonator’s original output signal under triangular phase modulation. The resonator’s diameter is 5cm. The unit propagation loss of waveguide is 0.5dB/m@1550nm. Other parameters used in simulations are: f1 = 1MHz, f2 = 1MHz, Vpp/Vπ = 2, kc = 0.01, αc = 0.01dB. a) at rest; b) rotating.
The change of phase difference between the light propagated along CW and CCW direction will cause the bias of quasi-square waveform change in case of IPM is applied, or cause the initial phase of cosine-like ripple change in case of CPM is applied, as shown in Fig. 3(a) and 3(b) respectively. The range of bias varies within under IPM is just equal to the amplitude of cosine-like ripple under CPM. As the cosine-like ripple is incomplete, and the number of ripple periods is only two or three while the sampling rate of signal processing module is finite, the integer period sampling condition cannot be well satisfied [12]. On the other hand, the original output quasi-square waveform under IPM always keeps a good shape and is backreflection-induced-ripple-free no matter how its bias changes; therefore, in the sampling region T1 and T2, there are always more high-frequency noise components in Fig. 3(b) than in Fig. 3(a). Though the actual ARW induced by CPM or IPM in a RIOG is not easy to be precisely and numerically predicted, the ARW under IPM is bound to be lower than that of CPM. It should be noticed that there is still residual ripple in fact but it is caused by the resonator’s optical delay rather than the backreflection.
Fig. 3 Simulation of relation between resonator’s original output signal and the initial phase of CW incident light. If CW initial phase changes while the CCW’s remains unchanged, their phase difference changes. a) IPM; b) CPM. T1, T2: sampling regions in time domain.
3. Experiments and discussion
A RIOG apparatus is built up according to Fig. 1. A fiber laser with PZT-tuning module is used, whose central wavelength is 1550nm and the linewidth is <1kHz. The transmissive resonator, which is made of Ge-doped, buried-type planar silica waveguide, has a diameter of 6cm and a finesse of 82, and the loaded Q-factor is 14.4 million. The photon shot noise limited ARW is calculated to be 0.014deg/h1/2 providing that the detected peak photocurrent of photodetector is 1mA according to Eq. (1). The Y-branch modulator is made of proton exchanged lithium niobate, whose two arms can be applied voltage independently, and their half-wave voltages are both 5.74V. The phase modulation signals can be divided into two groups, one consists of two in-phase or contra-phase high-frequency triangular waves whose peak-to-peak voltage and frequencies are both 20V and 1MHz, respectively; another one consists of two low-frequency triangular waves whose peak-to-peak voltages equal to the full-wave voltage of modulator, and frequencies are 10kHz and 46.6kHz, respectively. The resonator’s output waveform when the laser frequency adjusts to the resonance frequency are shown in Fig. 4. The original output waveforms of the photodetectors are quite consistent with the theory. A backreflection coefficient of 2 × 10−5 (−47dB) is obtained from the fit shown in Fig. 4(a).
Fig. 4 Experimental results of resonator’s output waveform under a) CPM and b) IPM. The bias is −1.03V when the laser is turned off.
The process of amplitude demodulation, including sampling, accumulating, subtracting, filtering and etc., can be accomplished with the help of A/D + FPGA. The demodulated and filtered signal of CCW photodetector is used to adjust the laser frequency to the CCW resonance frequency of the resonator, then the demodulated and filtered signal of CW photodetector is used as the open-loop gyro output. The comparison of gyro test results under IPM and CPM is shown in Fig. 5. The scale factor of the gyro apparatus was obtained by pseudo-input method at first, as shown in Fig. 5(a). Then a stationary test was performed on a static table. The test time was 60s and the integration time was 0.01s. At this sampling rate, it can be clearly seen that the noise under IPM is obviously lower than the CPM, as shown in Fig. 5(b). Power spectrum density (PSD) analysis is introduced to evaluate the noise quantatively. The mean value of the PSD value in the range [3, 10] Hz can be taken as the estimated value of ARW. ARWs of about 3deg/h1/2 and 0.8deg/h1/2 are achieved under CPM and IPM, respectively, as shown in Fig. 5(c). The Allan variance analysis also shows that the noise level is obviously reduced under IPM because the curve of IPM lies below when integration time is less than one second. And when integration time increases, the two curves get close to each other, which shows that the IPM and CPM stand at parity to some extent in suppressing the backreflection induced bias drift.
Fig. 5 Stationary test results of RIOG. a) pseudo-input test; b) stationary test; c) power spectrum density of the stationary test data; d) Allan variance of the data.
However, since IPM has lower ARW than CPM, can it improve the bias stability obviously rather than remain in the same level with CPM? Further theoretical analysis and experimental results have given a positive answer, and a manuscript is in preparation.
4. Conclusion
We have proposed and demonstrated the IPM technique applied to the RIOG. This technique is effective to reduce the gyro ARW, because the resonator’s original output signal is ripple-free when IPM is applied. The gyro’s ARW is obviously reduced from 3 to 0.8 deg/h1/2 compared to that of CPM. This also enlightens a new way to design the scheme of backreflection/backscattering suppression. Other noise sources, such as laser frequency noise and frequency-lock noise, are considered to be suppressed to reduce the ARW of the RIOG.
Acknowledgments
The authors would like to acknowledge the financial support from National Natural Science Foundation of China (NSFC) (No. 61171004).
References and links
1. C. Ciminelli, F. Dell’Olio, C. E. Campanella, and M. N. Armenise, “Photonic technologies for angular velocity sensing,” Adv. Opt. Photonics 2(3), 370–404 (2010). [CrossRef]
2. F. Dell’Olio, T. Tatoli, C. Ciminelli, and M. N. Armenise, “Recent advances in miniaturized optical gyroscopes,” J. Eur. Opt. Soc. Rap. Public. 9, 14013 (2014). [CrossRef]
3. L. Feng, J. Wang, Y. Zhi, Y. Tang, Q. Wang, H. Li, and W. Wang, “Transmissive resonator optic gyro based on silica waveguide ring resonator,” Opt. Express 22(22), 27565–27575 (2014). [CrossRef] [PubMed]
4. J. Wang, L. Feng, Y. Tang, and Y. Zhi, “Resonator integrated optic gyro employing trapezoidal phase modulation technique,” Opt. Lett. 40(2), 155–158 (2015). [CrossRef] [PubMed]
5. H. Ma, J. Zhang, L. Wang, and Z. Jin, “Double closed-loop resonant micro optic gyro using hybrid digital phase modulation,” Opt. Express 23(12), 15088–15097 (2015). [CrossRef] [PubMed]
6. C. Ciminelli, F. Dell’Olio, M. N. Armenise, F. M. Soares, and W. Passenberg, “High performance InP ring resonator for new generation monolithically integrated optical gyroscopes,” Opt. Express 21(1), 556–564 (2013). [CrossRef] [PubMed]
7. C. Ciminelli, F. Dell’Olio, and M. N. Armenise, “High-Q spiral resonator for optical gyroscope applications: numerical and experimental investigation,” IEEE Photonics J. 4(5), 1844–1854 (2012). [CrossRef]
8. D. D’Agostino, G. Carnicella, C. Ciminelli, P. Thijs, P. J. Veldhoven, H. Ambrosius, and M. Smit, “Low-loss passive waveguides in a generic InP foundry process via local diffusion of zinc,” Opt. Express 23(19), 25143–25157 (2015). [CrossRef] [PubMed]
9. J. Li, M. Suh, and K. Vahala, “Microresonator Brillouin gyroscope,” Opt. Soc. of Am., pp. h2A–h3A (2015).
10. J. Li, H. Lee, and K. J. Vahala, “Microwave synthesizer using an on-chip Brillouin oscillator,” Nat. Commun. 4, 2097 (2013). [PubMed]
11. H. Lee, T. Chen, J. Li, K. Y. Yang, S. Jeon, O. Painter, and K. J. Vahala, “Chemically etched ultrahigh-Q wedge-resonator on a silicon chip,” Nat. Photonics 6(6), 369–373 (2012). [CrossRef]
12. J. Wang, L. Feng, Y. Zhi, H. Liu, W. Wang, and M. Lei, “Reduction of backreflection noise in resonator micro-optic gyro by integer period sampling,” Appl. Opt. 52(32), 7712–7717 (2013). [CrossRef] [PubMed]
13. K. Iwatsuki, K. Hotate, and M. Higashiguchi, “Effect of Rayleigh backscattering in an optical passive ring-resonator gyro,” Appl. Opt. 23(21), 3916–3924 (1984). [CrossRef] [PubMed]
14. Y. Yan, H. Ma, and Z. Jin, “Reducing polarization-fluctuation induced drift in resonant fiber optic gyro by using single-polarization fiber,” Opt. Express 23(3), 2002–2009 (2015). [CrossRef] [PubMed]
15. X. Wang, Z. He, and K. Hotate, “Reduction of polarization-fluctuation induced drift in resonator fiber optic gyro by a resonator with twin 90 degrees polarization-axis rotated splices,” Opt. Express 18(2), 1677–1683 (2010). [CrossRef] [PubMed]
16. H. Ma, X. Li, G. Zhang, and Z. Jin, “Reduction of optical Kerr-effect induced error in a resonant micro-optic gyro by light-intensity feedback technique,” Appl. Opt. 53(16), 3465–3472 (2014). [CrossRef] [PubMed]
17. E. Jaatinen and D. J. Hopper, “Compensating for frequency shifts in modulation transfer spectroscopy caused by residual amplitude modulation,” Opt. Lasers Eng. 46(1), 69–74 (2008). [CrossRef]
18. K. Hotate and K. Tabe, “Drift of an optical fiber gyroscope caused by the Faraday effect: influence of the earth’s magnetic field,” Appl. Opt. 25(7), 1086–1092 (1986). [CrossRef] [PubMed]
19. H. C. Lefevre, The fiber-optic gyroscope (Artech house, 2014).
20. H. Ma, Z. He, and K. Hotate, “Reduction of backscattering induced noise by carrier suppression in waveguide-type optical ring resonator gyro,” J. Lightwave Technol. 29(1), 85–90 (2011). [CrossRef]
21. Y. Zhi, L. Feng, J. Wang, and Y. Tang, “Reduction of backscattering noise in a resonator integrated optic gyro by double triangular phase modulation,” Appl. Opt. 54(1), 114–122 (2015). [CrossRef] [PubMed]
