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Air-core photonic bandgap fiber (PBF) is a good choice for fiber-optic gyroscopes (FOGs) owing to the fact that it can be adapted to a wide variety of environments. However, its multimode properties are disadvantageous for the application to FOGs. An interference-based method is proposed to precisely determine the secondary waves caused by the high-order modes and their coupling. Based on the method, two groups of secondary waves have been found, having optical path differences (OPDs) of ~1.859 m and ~0.85 m, respectively, relative to the primary waves in a PBFOG that consists of a 7-cell PBF coil, approximately 180 m in length. Multi-turn bends of the PBF at both ends of the PBF coil after the fusion splicing points are shown to suppress the intensity of these secondary waves by approximately 10 dB.
© 2016 Optical Society of America
1. Introduction
Fiber-optic gyroscope (FOG) is a kind of angle velocity sensor developed about 30 years ago. In the last decade, the emergence of photonic bandgap fibers (PBFs) injects new vitality to the FOGs, and those novel air-core resonant fiber-optic gyroscopes (RFOGs) and photonic bandgap fiber optic gyroscopes (PBFOGs) have shown great potentials. For the RFOG, PBFs offer a novel approach to overcome the main problems (Kerr-induced drift and temperature-driven polarization instability) present in conventional solid-core RFOGs, and it may allow the RFOG to be commercialized and make the RFOG a perfect choice in the family of miniaturized optical gyroscopes which includes such as MEMS gyroscope, resonant micro-optic gyro (RMOG) and so on at present [1–4]. For the PBFOG, which is first proposed by a group in Stanford University [5–7], it is a relatively new member in the family of interferometric fiber-optic gyroscopes (FOGs). As illustrated in Fig. 1(a), the PBFOG includes an amplified spontaneous emission (ASE) source having a high power and broad spectrum, a coupler, an integrated optic chip (IOC), and a photonic bandgap fiber (PBF) coil that is connected to the pigtails of the IOC through angle-cleaved fusion splicing to suppress reflections [6, 7]. The PBFOG has dramatic reductions in the errors caused by the Kerr effect, Shupe effect, and Faraday effect when compared with the corresponding error values in a conventional fiber-optic gyroscope (FOG), because the light propagates in the air in the PBF and air is much more stable than conventional silica [7]. However, high-order modes are inevitable for most of the state-of-the-art PBFs having hexagonal air holes triangularly arranged in the cladding except 3-cell PBF or specially-designed single-mode PBF which may have a relatively higher loss [8, 9]. For the 7-cell PBF [see Fig. 1(b)] that has been reported to be applied in the PBFOG, there exist 10-12 high-order modes [10]. In fact, there have been no prior studies regarding the behavior of those modes when they propagate along such a large number of optical segments including the PBF coil, the IOC, the coupler and the conventional pigtail fibers in the PBFOG. Unquestionably, it is true that single-mode operation is essential for the proper performance of a FOG [11]. Therefore, a better understanding of the high-order modes in the PBFOG is very important for the improvement of the PBFOG performance and optimization of the PBF.
Fig. 1 (a) Schematic diagram of a photonic bandgap fiber-optic gyroscope; (b) Cross section of the photonic bandgap fiber used in the coil.
At present, there are two methods to measure modes in the PBFs: the spatial and spectrum (S2) method and the time-of-flight (TOF) method. Nicholson et al. [12] have studied the high-order modes in PBFs with the S2 image method, and Gray et al. [13] have investigated the modes in a long (260 m) 19-cell PBF with the TOF method. However, these two methods are not suitable for the precise determination of the modes in a complete PBFOG. First, the source in the PBFOG is a broad-spectrum ASE source, which makes the measuring range of the S2 technique very small, but the PBF in the coil is as long as a few hundreds to thousands of meters, so the S2 image method is not feasible. Second, optical loss is very high in the PBFOG, and the high-order modes are very weak when they exit from the PBFOG; hence, it is difficult for the TOF method to maintain a background noise level that is low enough to directly determine such weak high-order modes. Therefore, we propose an interference-based method to precisely measure the high-order modes in a complete PBFOG without disassembling any optical components.
2. Measurement of the secondary waves caused by high-order modes in PBFOGs
In the PBFOG shown in Fig. 1(a), the PBF in the coil has a length of ~180 m, and is wound with a quadrupole symmetric winding method, which is an internationally popular method to reduce the temperature sensitivity in a FOG [11]. The high-order modes are generated in the PBF coil when light waves from the IOC are launched into the coil through the fusion splicing points, but we do not know what will happen to those high-order modes when they propagate through the IOC, the coupler, the conventional pigtail fibers, and the PBF coil that has complicated properties including the effects of bending, twist, and stress caused by glue and tension. It is possible that some high-order modes may cause parasitic secondary waves in the output of the PBFOG, or some may disappear owing to the high loss. Therefore, an interference-based method is proposed, and the corresponding experimental setup has been established (see Fig. 2), to investigate the evolution of the high-order modes in the PBFOG. In Fig. 2, a Mach–Zehnder (MZ) interferometer is formed at the output end of the PBFOG. In the signal arm of the MZ interferometer, the light waves exit from the PBFOG; these include primary waves Ws generated by fundamental modes and secondary waves W1 caused by high-order modes. In the reference arm, the light wave (WR) from the ASE source is launched from one port of the coupler, an attenuator is applied to adjust the power, and a delay coil is used to adjust the optical path difference (OPD) between WR and WS or W1. At the end of the MZ interferometer, all of the waves (WR, WS, and W1) enter the wavetrain analysis module (WAM) that is applied to determine the OPD between WR, WS, and W1, as well as the relative intensities of these light waves. The WAM is actually a Michelson interferometer or white light interferometer, in which WR is much larger than WS and W1, so that WR can be used as a local oscillator to interfere with WS and W1 [11]. The position of reflector B is adjusted until interference occurs. The output of the WAM is the envelope of the interference fringes, from which the relative position and intensity of WS and W1 can be determined. The reflector B moves on a guiding rail that has a range of travel that is only 60 cm (in air), so the length of the delay coil has to be adjusted if the OPD between WR and WS, W1 needs to be changed by more than 60 cm.
Fig. 2 Measurement setup of the secondary waves caused by high order modes in the photonic bandgap fiber-optic gyroscope. In the wavetrain analysis module, D denotes a semi-transparent mirror.
Prior to initiating the test of the secondary waves caused by high-order modes in the PBFOG, the WAM was first used to determine the high-order modes in a PBF with a length of approximately 10 m so that we could obtain the approximate index difference between the high-order modes and the fundamental mode and make a reasonable choice for the starting length of the delay coil. The fundamental modes and high-order modes are excited when the light from the ASE source is launched into the ~10-m PBF, and these modes directly enter the WAM. As shown in Fig. 3, there are two main groups of high-order modes existing at the positions ~100 mm and ~200 mm from the fundamental mode; this reveals that the index difference (∆n) between the fundamental modes and these high-order modes in the PBF is ~0.01 and ~0.02, respectively.
Fig. 3 Test results of the high-order modes in the PBF with a length of approximately 10 m, obtained by using the wavetrain analysis module.
Considering the index difference between the fundamental modes and high-order modes, as well as the length of the pigtails of the IOC and coupler, we chose a delay coil composed of ~150 m of conventional single mode (SM) fiber to connect into the reference arm of the MZ interferometer in Fig. 2. First, we tried the TOF method to directly determine the light waves in the experimental setup, as illustrated in Fig. 4(a), the 89.8-ns time difference between the reference light wave WR0 and WS indicates that the optical path of WR0 is ~26.94 m (in air) larger than that of WS. It is obvious that W1 must be located somewhere between WS and WR0, because the OPD between W1 and WS cannot exceed 26.94 m even for the high-order mode of ∆n = ~0.02. We gradually decreased the optical path of WR0 to bring it close to that of W1 so that they can then interfere with each other, and the relative position and intensity of W1 can be determined from the interference results. Considering that the range-of-travel of the reflector B is only 60 cm (in air), we reduced the length of the delay coil in 40-cm steps (corresponding to ~58 cm in air; the refractive index of the SM fiber is ~1.4527) in order to gradually decrease the optical path of WR0. On the other hand, note that no high-order modes can be seen between WS and WR0 in Fig. 4(a), which can be explained by the fact that the high-order modes are too weak to be observed with the TOF method after they propagate such a long distance and encounter so many high-loss optical components in the PBFOG. Hence, the interference-based method must be employed to investigate those high-order modes.
Fig. 4 Test results of the secondary waves caused by high-order modes in the photonic bandgap fiber-optic gyroscope (PBFOG). (a) The original relative position between the reference light wave WR0 and the primary waves WS in the PBFOG when 0 m of single mode fiber is cut away from the delay coil; this was obtained by the time-of-flight method. Output of the wavetrain analysis module when (b) 0 m; (c) ~17 m; and (d) ~18.34 m of single-mode fiber has been cut away from the delay coil.
In its original state, the delay coil was composed of ~150 m of SM fiber; the output of the WAM is shown in Fig. 4(b), indicating that the reference light wave WR0 has not interfered with W1 when the reflector B moved from 0 to 60 cm; in other words, the OPD between WR and W1 was larger than 60 cm (in air). Then, 40 cm of SM fiber was cut away from the delay coil, so that the optical path of the reference light wave decreased by ~58 cm (in air). Under this condition, we measured the interference situation again, but the result was the same as Fig. 4(b) and no interference fringes were found when the reflector B moved from 0 to 60 cm. In fact, we could not see any signs of interference until ~17 m of SM fiber (corresponding to ~24.7 m in air) had been cut away [see Fig. 4(c)], indicating that there are no secondary waves whose OPD is between ~26.94 m and ~2.24 m relative to the primary waves WS. In Fig. 4(c), the peaks are induced by the interference between the reference light waves WR1 and the secondary waves (W1) caused by high-order modes. When ~18.34 m of SM fiber (corresponding to ~26.65 m in air) were cut away from the delay coil, the interference results are shown in Fig. 4(d) where the largest peak is caused by the interference between the reference light wave WR2 and the primary waves WS, and the other peak is caused by the interference between WR2 and the secondary waves W′1. During the experiment, the power arriving at the detector was held constant by adjusting the attenuator, so that WR0, WR1 and WR2 had the same intensity but different optical paths.
As a result, we have found only two groups of secondary waves W1 and W′1 in the PBFOG; the relative position relationship between those light waves was analyzed and is presented in Fig. 5 based on the experimental results. The secondary waves W1 and W′1 have an OPD of ~1.859 and ~0.85 m, respectively, compared to the primary wave. W1 is caused by high-order modes that have an index difference of ~0.01 as found in the test results for 10-m PBF; W′1 has an index difference of ~0.0047, but we have not found any high-order modes that have the same index difference in the 10-m PBF, so these secondary waves may be caused by mode coupling between WS and W1 somewhere in the optical circuit. Moreover, the high-order modes with an index difference of ~0.02 have not been found either; this might be because those high-order modes have higher loss.
Fig. 5 The relative position relationship (the distance is calculated in air) between the light waves in the experiment. WR0, WR1, and WR2 denote the reference light wave when 0 m, ~17 m, and ~18.34 m, respectively, of single-mode fiber is cut away from the delay coil (The refractive index of the single-mode fiber is 1.4527). W1 and W′1 are the secondary waves induced by high-order modes and their coupling in the PBFOG. WS is the primary wave generated by fundamental modes in the PBFOG.
3. Suppression of the secondary waves caused by high-order modes in PBFOG
The secondary waves (W1 and W′1) caused by high-order modes are found to still exist in the PBFOG, even though they have encountered so many optical segments including the approximately 180-m-long PBF coil, the IOC, the coupler, and the conventional pigtail fibers. In a conventional FOG, the studies by [14–16] showed that the parasitic modes can have some deleterious effects on the FOG performance; the influencing mechanism of W1 and W′1 is actually the same for the PBFOG, so they must be suppressed to obtain better performance of the PBFOG. It is well known that the fundamental mode of the PBF is typically quite robust against macrobending, but high-order modes may be more sensitive to macrobending [12, 17]; therefore, bending might be a simple method to suppress the secondary waves caused by high-order modes in a real PBFOG [18].
Immediately after the fusion splicing points A and B in the PBFOG, we introduced 3-turn bends with a radius-of-curvature of ~5 mm in each of the two pigtails of the PBF coil, as shown in Fig. 6(a). The secondary waves were significantly suppressed (by ~10 dB) compared to their values before the PBF pigtails were bent, as illustrated in Figs. 6(b) and 6(c) where the black curves are the same as Figs. 4(c) and 4(d), respectively, and the red curves were obtained under the same conditions, except that the two PBF pigtails of the coil had been bent. 10-dB suppression of those secondary waves caused by the high-order modes means ~10-times reduction of the secondary-waves-induced nonreciprocal phase error and ~√10-times decrease of the secondary-waves-induced random walk coefficient (RWC) [14–16, 19]. Moreover, Fig. 6(c) shows that the primary wave WS has not been affected, also indicating that the fundamental mode is very robust against bending in the PBF. Therefore, moderately bending the PBF pigtails is effective and feasible to suppress the secondary waves caused by high-order modes in a real PBFOG.
Fig. 6 (a) Multi-turn bends of the PBF at both ends of the fiber coil are applied to suppress the secondary waves caused by high-order modes in the PBFOG. The corresponding suppression effect of (b) the secondary waves W1 and (c) the secondary waves W′1 after both the ends of the PBF coil were subjected to the ~10-mm (3-turn) bends.
4. Conclusion
In summary, we have proposed an interference-based method to measure the secondary-waves induced by high-order modes and their coupling in the PBFOG. It is generally thought that few secondary waves are caused by high-order modes in the PBFOG, because the PBF coil is long enough (~180 m) to attenuate the high-order modes; moreover, they have to propagate through so many optical components and more than 10 m of conventional single-mode fiber including the pigtails of the integrated optic chip and the coupler. However, after investigating the secondary-waves within the range of ~26.94-m (in air) OPD compared to the primary waves, we still found the existence of two groups of secondary waves, having an OPD of ~1.859 m and ~0.85 m, respectively, compared to the primary waves in the PBFOG. Those secondary waves are one of the factors affecting the PBFOG performance. Therefore, multi-turn bends of the PBF at both ends of the PBF coil were proposed to suppress the secondary waves caused by high-order modes in the PBFOG; these bends were found to be effective and feasible, because they reduced the intensity of the secondary waves by ~10 dB.
In fact, the promoted methods provide a tool to investigate the secondary waves caused by high order modes in the PBFOG. In the future, we will try to use the methods to investigate the secondary-waves induced by high-order modes in PBFOG made of other PBFs.
Acknowledgments
This work was supported by the National Natural Science Foundation of China (NSFC) under grants No. 61575012 and 61575013.
References and links
1. M. A. Terrel, M. J. F. Digonnet, and S. Fan, “Resonant fiber optic gyroscope using an air-core fiber,” J. Lightwave Technol. 30(7), 931–937 (2012). [CrossRef]
2. Y. Yan, H. Ma, L. Wang, H. Li, and Z. Jin, “Effect of Fresnel reflections in a hybrid air-core photonic-bandgap fiber ring-resonator gyro,” Opt. Express 23(24), 31384–31392 (2015). [CrossRef] [PubMed]
3. F. Dell’Olio, T. Tatoli, C. Ciminelli, and M. N. Armenise, “Recent advances in miniaturized optical gyroscopes,” J. Europ. Opt. Sov. Rap. Public. 9, 14013 (2014).
4. C. Ciminelli, D. D’Agostino, G. Carnicella, F. Dell’Olio, D. Conteduca, H. P. M. M. Ambrosius, M. K. Smit, and M. N. Armenise, “A high-Q InP resonant angular velocity sensor for a monolithically integrated optical gyroscope,” IEEE Photonics J. 8(1), 6800418 (2016). [CrossRef]
5. H. K. Kim, V. Dangui, M. Digonnet, and G. Kino, “Fiber-optic gyroscope using an air-core photonic-bandgap fiber,” Proc. SPIE 5855, 198–201 (2005). [CrossRef]
6. H. K. Kim, M. J. F. Digonnet, and G. S. Kino, “Air-core photonic-bandgap fiber-optic gyroscope,” J. Lightwave Technol. 24(8), 3169–3174 (2006). [CrossRef]
7. M. Digonnet, S. Blin, H. K. Kim, V. Dangui, and G. Kino, “Sensitivity and stability of an air-core fibre-optic gyroscope,” Meas. Sci. Technol. 18(10), 3089–3097 (2007). [CrossRef]
8. F. Poletti, M. N. Petrovich, A. van Brakel, and D. J. Richardson, “Hollow core photonic bandgap fibre for truly single mode operation,” in IEEE/LEOS Winter Topical Meeting Series (IEEE, 2008), pp. 182–183.
9. J. M. Fini, J. W. Nicholson, B. Mangan, L. Meng, R. S. Windeler, E. M. Monberg, A. DeSantolo, F. V. DiMarcello, and K. Mukasa, “Polarization maintaining single-mode low-loss hollow-core fibres,” Nat. Commun. 5, 5085 (2014). [CrossRef] [PubMed]
10. F. Poletti, M. N. Petrovich, and D. J. Richardson, “Hollow-core photonic bandgap fibers: technology and applications,” Nanophotonics 2(5–6), 315–340 (2013).
11. H. C. Lefèvre, The Fiber-Optic Gyroscope (Artech House, 1993).
12. J. W. Nicholson, L. Meng, J. M. Fini, R. S. Windeler, A. DeSantolo, E. Monberg, F. DiMarcello, Y. Dulashko, M. Hassan, and R. Ortiz, “Measuring higher-order modes in a low-loss, hollow-core, photonic-bandgap fiber,” Opt. Express 20(18), 20494–20505 (2012). [CrossRef] [PubMed]
13. D. R. Gray, Z. Li, F. Poletti, R. Slavik, N. V. Wheeler, N. K. Baddela, M. N. Petrovich, A. Obeysekara, and D. J. Richardson, “Complementary analysis of modal content and properties in a 19-cell hollow core photonic band gap fiber using time-of-flight and S2 techniques,” in European Conference and Exhibition on Optical Communication, Technical Digest (Optical Society of America, 2012), paper Mo.2.F.1. [CrossRef]
14. H. Medjadba, S. Lecler, L. M. Simohamed, J. Fontaine, and P. Meyrueis, “Investigation of mode coupling effects on sensitivity and bias of a multimode fiber loop interferometer: Application to an optimal design of a multimode fiber gyroscope,” Opt. Fiber Technol. 17(1), 50–58 (2011). [CrossRef]
15. H. Medjadba, S. Lecler, L. M. Simohamed, and A. Chakari, “Modeling a multimode sagnac interferometer: application for an embarked fiber optic gyroscope,” Proc. SPIE 7003, 700310 (2008). [CrossRef]
16. S. Ezekiel and H. J. Arditty, Fiber-Optic Rotation Sensors and Related Technologies (Springer-Verlag, 1982).
17. T. P. Hansen, J. Broeng, C. Jakobsen, G. Vienne, H. R. Simonsen, M. D. Nielsen, P. M. W. Skovgaard, J. R. Folkenberg, and A. Bjarklev, “Air-guiding photonic bandgap fibers: spectral properties, macrobending loss, and practical handling,” J. Lightwave Technol. 22(1), 11–15 (2004). [CrossRef]
18. S. Moon and Z. Chen, “Mode-filtered large-core fiber for optical coherence tomography,” Appl. Opt. 51(34), 8262–8270 (2012). [CrossRef] [PubMed]
19. W. K. Burns, R. P. Moeller, and A. Dandridge, “Excess noise in fiber gyroscope sources,” IEEE Photonics Technol. Lett. 2(8), 606–608 (1990). [CrossRef]
