MA Honghao ,LI Hui ,FENG Changkun ,FENG Lishuang,2,* ,GAO Shoufei ,WANG Yingying ,and WANG Pu
1.School of Instrumentation and Optoelectronics Engineering,Beihang University,Beijing 100191,China;2.Key Laboratory of Intelligent Sensing Materials and Chip Integration Technology of Zhejiang Province,Hangzhou Innovation Institute of Beihang University,Hangzhou 310053,China;3.Institute of Photonics Technology,Jinan University,Guangzhou 510632,China;4.Institute of Laser Engineering,Beijing University of Technology,Beijing 100124,China
Abstract:The coupling efficiency of hollow-core fiber changes with temperature,which leads to the decrease of the finesse (F)of fiber resonator and limits the performance of the resonant fiber optic gyroscope (R-FOG) system.Negative-curvature antiresonant fiber (ARF) can maintain single-mode characteristics under the condition of large mode field diameter,achieve efficient and stable fiber coupling,and significantly improve the consistency of the F of the spatial coupling resonator in variable temperature environment.A new type of ARF with a mode field diameter (MFD) of 25 μm is used to fabricate a fiber resonator with a length of 5.14 m.In the range of 25 °C-75 °C,the average F is 31.45.The ARF resonator is used to construct an R-FOG system that shows long-term bias stability (3 600 s) of 3.1 °/h at room temperature,4.6 °/h at 75 °C.To our knowledge,this is the best reported index of hollow-core fiber resonator and R-FOG system within the temperature variation range of 50 °C test.
Keywords:negative-curvature anti-resonant fiber (ARF),fiber resonator,temperature stability.
Resonator fiber optic gyroscope (R-FOG) has been one of the key research directions of inertial navigation system since the scheme was put forward because of its potential to achieve high precision and miniaturization at the same time [1].
Anti-resonant fiber (ARF) is a new type of hollow-core fiber (HCF) [2,3].It has similar advantages to the photonic band-gap fiber (PBF),which can eliminate the Kerr effect [4],Faraday effect [5] and Brillouin scattering [6]of the traditional polarization-maintaining fiber (PMF),and exhibit lower radiosensitivity [7].Different from the light guiding mechanism of PBF [8],ARF uses anti resonant effect to bind the light field [9,10].By changing the wall thickness of the anti-resonant layer,ARF suitable for light guiding in different bands from ultraviolet [11] to mid infrared [12] can be obtained,which can meet the needs of different application fields.Given the small overlapping area between the transmitted light field and the surrounding glass cladding structure,the theoretical loss limit of ARF is very low.In the early stage of the research,the transmission loss of ARF did not decrease rapidly.During this period,optical fiber researchers and users generally focused on PBF.Until 2018,the loss of ARF dropped to 2 dB/km [13],and further decreased to 0.28 dB/km two years later [14].The lowest loss of ARF reported up to now is 0.174 dB/km [15].ARF has the advantages of low loss of traditional optical fiber and anti radiation of hollow-core optical fiber,and has become the focus of researchers in the field of communication and sensing.
Kagome structured fiber,the first generation of ARF,was applied in hollow-core R-FOG system shortly after its development [16].Using the efficient lens coupling technology,the coupling loss between Kagome fibers is reduced to 0.1 dB [17],enabling the HCF resonator to obtain a high finesse (F),and the overall performance of the hollow-core R-FOG system is greatly improved.In further research,ARF shows the advantages of low polarization crosstalk,strong temperature stability [18] and small backscattering [19],making it especially suitable for fiber sensing system.The Fabry-Perot interferometers made of ARF has significantly improved itsFand the stability of transmission peak frequency at variable temperature [20].The resonator in known hollow-core R-FOG system with the best long-term stability is also composed of ARF and polarization maintaining fiber coupler [21].
In order to translate the principle prototype of hollowcore R-FOG into engineering prototype,improving its temperature stability is a critical step.Fiber resonator is the core sensitive unit of hollow-core R-FOG.The consistency of its optical parameters under different temperature environments is the key factor affecting the temperature stability of the R-FOG system.At present,HCF resonators are mostly fabricated by the spatial optical alignment method [22,23],and adhesive needs to be used between the optical fiber and the coupling substrate.When the temperature changes,the thermal expansion coefficients of optical fiber,coupling substrate and adhesive are inconsistent,which leads to the drop of coupling efficiency between optical fibers and changes the optical parameters of the resonator,thus affecting the overall performance of the hollow-core R-FOG system.
In this paper,we analyze the source of fiber coupling loss in the resonator fabricated by the spatial optical alignment method.Then,we compare and analyze the coupling efficiency of a new small core diameter conjoined tube ARF and a PBF under different alignment deviations.It is determined that the resonator made of ARF will have better temperature stability.After that,we build the ARF resonator and R-FOG system,and test it in the temperature range of 25 °C-75 °C,and test results show that ARF can greatly improve the temperature stability of R-FOG.
In the spatial optical alignment method,the resonator uses the coupling lens to complete the closed-loop connection of the fiber,and uses the light splitter to complete the connection between the resonator and other optical devices of the R-FOG system.Increasing the coupling efficiency between fibers can significantly improve theFof the resonator,hence improving the detection accuracy of the R-FOG system.The coupling efficiency between fibers can be evaluated by calculating the matching degree of spatial light field,that is,the overlapping integral of the transmission light fieldEreaching the receiving end face and the near Gaussian mode of the fiber end face.
At present,the fibers used in the optical path of R-FOG system are single-mode polarization maintaining fibers.After the HCF in the resonator is wound into a certain diameter,only the fundamental modeefcan be transmitted.Therefore,the transmission light fieldEof the receiving end face can be expressed as
whereeh_ jis the radiation mode or dissipation mode of the optical fiber,xjis the mode proportion of radiation mode or dissipation mode.
The mode proportionxfcan be expressed as
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The coupling efficiencyCcan be expressed as
Er(x,y) is used to represent the transverse vector field distribution of the incident light field,andef(x,y) is used to represent the transverse vector field distribution of the fundamental mode of the optical fiber,then the analytical expression of the coupling efficiencyCis
Fig.1 is the schematic diagram of the spatial optical alignment method for the same kind of fiber.The light field of the fiber at the outgoing end becomes an approximately parallel beam after passing through the collimating lens.After transmitting for a certain distance,it is focused by the second collimating lens and finally transmitted to the fiber at the receiving end.Ideally,the spatial optical alignment method can efficiently complete the optical field coupling between fibers,the coupling efficiency is typically more than 95%,and the loss merely comes from the reflection of the lens and air interface and the absorption of lens materials.
Fig.1 Schematic diagram of the spatial optical alignment method
The quartz platform integrated coupling method uses the high concentricity quartz tube to replace the fine-tuning frame in the traditional spatial optical alignment method to fix the position of the fiber and the coupling lens.Other optical devices in the optical path are also pasted on the quartz block in advance,and these quartz tubes and quartz blocks are fixed on the quartz plate substrate.This method uses the high precision and high flatness of quartz processing to ensure the coaxiality of the optical path,which can effectively reduce the size of the resonator coupling structure and improve the design flexibility.
Fig.2 shows four common fiber coupling mismatches in quartz platform integrated fiber coupling method.The radial offset of fiber as shown in Fig.2(a) mainly comes from the machining tolerance of quartz concentric tube used in the collimator.It can be compensated for its impact on the overall coupling efficiency by adjusting the radial position and deflection angle of the collimator during the closed-loop coupling of the resonator.The axial offset of fiber as shown in Fig.2(b) mainly comes from the insufficient adjustment resolution of the displacement adjusting frame used in the manufacture of fiber collimator.Moreover,in the packaging process of collimator,the tensile stress caused by adhesive curing will also change the position of fiber end face.The influence of fiber axial offset on coupling efficiency cannot be compensated by later adjustment,which must be avoided when the collimator is made.
Fig.2 Schematic diagram of the fiber coupling mismatches in quartz platform integrated coupling method
The quartz platform integrated coupling method requires the use of adhesive to fix the fine-tuned fiber,coupling lens,spectroscope and other optical devices on the quartz base plate.The amount of adhesive is determined by the processing tolerance of quartz concentric tube and base plate.Both radial offset and angle offset of collimator as shown in Fig.2(c) and Fig.2(d) come from the linear expansion of materials at different ambient temperatures.Due to the different linear expansion coefficients of adhesive and quartz,when the resonator is at different ambient temperatures,the relative position between optical devices will change slightly,resulting in the decrease of coupling efficiency.The influence can be reduced by selecting an adhesive with a linear expansion coefficient as close as possible that of quartz substrate.This is the first factor limiting the temperature stability of R-FOG system.
When choosing the type of fiber to make the resonator,we must first ensure that the transmission mode of the optical fiber is single-mode.The high-order modes transmitted in the resonator made of multimode fiber will interfere with the resonant state of the fundamental mode.
Traditional PBF can completely suppress the highorder mode only when the core air hole is compressed below 10 μm and the MFD is about 6 μm [24].Further compression of the core air hole size will increase the transmission loss of optical fiber.Thus the second fiber selected is a PBF (HC-1 550-PM-02-FUD) from NKT Photonics,referred to below as “PBF”.The MFD of this PBF is 6.5 μm.
The main parameters of the two fiber samples are listed in Table 1,and the structures are shown in Fig.3.
Fig.3 SEM image of two fiber samples
Table 1 Main parameters of two fiber samples
When selecting lens,we first consider the coupling efficiency between collimators made of two identical optical fibers (ARF or PBF).In order to facilitate the connection between the resonator and other optical paths of the R-FOG system,the output light field of the two kinds of fibers needs to be well matched with the light field of the common polarization maintaining fiber collimator after being collimated by the lens.Therefore,the 354550 C-lens with a focal length of 6.1 mm and the 355150 Clens with a focal length of 2 mm produced by Lightpath are selected as the coupling lenses of ARF and PBF respectively.
Fig.4 shows the simulation results of coupling efficiency of HCFs in the case of four fiber coupling mismatches.The coupling tolerance of ARF in the case of fiber radial offset and fiber axial offset is much larger than that of PBF,which shows that using ARF can greatly reduce the process difficulty of making fiber collimator.In the case of collimator radial offset and collimator angle offset,the coupling efficiency of ARF and PBF collimator has a certain stability range,and the stability range of ARF collimator is larger.This shows that the resonator made of ARF collimator will have better temperature stability.
Fig.4 Simulation results of coupling efficiency of ARF and PBF in fiber coupling mismatches
We fabricate two pairs of fiber collimators using ARF and PBF to test the coupling efficiency of the two fibers.The test system is shown in Fig.5.The fiber laser works at 1 550 nm,and outputs by polarization maintaining fiber.In order to ensure that only the fundamental mode is transmitted in the optical fiber,the tail fiber of collimator 1 is coiled into a ring with a length of more than 5 m and a diameter of 20 cm.The length of tail fiber of collimator 2 is 1 m.The same photodetector is used to measure the output power of collimator 1 and the power at the tail fiber of collimator 2 respectively.The tail fiber of collimator 2 is very short,and the transmission loss of this section of optical fiber can be ignored.The power ratio measured by the two photodetectors is the coupling efficiency of a pair of optical fiber collimators.
Fig.5 Test system for collimator coupling efficiency
Table 2 shows the test results of the coupling efficiency of the collimators.The coupling efficiency of the ARF collimator reaches 0.96,while the coupling efficiency of the PBF collimator is only 0.82.The large coupling loss of PBF mainly comes from three parts.The first is that PBF is more sensitive to the error source of optical fiber axial offset.The minimum scale of the displacement table used to adjust the axial position of the fiber is 10 μm.The resolution of manual mediation is 3-5 μm.It is difficult to make the end face of the fiber in the most ideal axial position.The stress caused by the uneven curing speed of the adhesive in all directions will cause the axial position of the end face of the fiber to shift again.The second is that the honeycomb cladding structure of PBF is more likely to be damaged by stress cutting.During cutting,the fracture surface extends in two directions along the torus composed of quartz outer layer of the optical fiber from the stress point,and the optical fiber is completely broken at the symmetrical point of the stress point.However,this cutting method cannot ensure that the two fracture directions are in the same plane,so a stepped fracture will generally be formed at the termination position.The tepped fracture will lead to the wavefront distortion of the output optical field of PBF and increase the coupling loss.The third is that the mode shape of the PBF will also affect the coupling efficiency.
Table 2 Coupling efficiency of collimator
The collimator is baked at 60 °C for four hours to improve its stability.During the baking process,we detect that the output optical power of the collimator fluctuates greatly,and the lowest is less than 70% of the original output power.The optical power fluctuation disappears after the heating stops for a period of time,and the output power of the collimator returs to the original state.We believe that this phenomenon is because the air hole in the HCF is mixed with the atmosphere,and the air in the HCF will flow when the temperature changes unevenly at different positions of the resonator.The irregular flow of this medium will have a great impact on the intensity,phase and directivity of the light field [25],thus affecting theFand polarization extinction ratio of the resonator in the variable temperature environment,which is the second main factor limiting the temperature stability of the hollow-core R-FOG system.
In order to solve this problem,we optimize the manufacturing process of the collimator,and past a cover sheet with a thickness of 0.3 mm and double-sided antireflection film at the front end of the HCF to isolate the air hole of the fiber from the atmosphere,as shown in Fig.6.The output optical power of ARF collimators made by this method hardly fluctuates in the baking process.This manufacturing process can effectively improve the stability of hollow-core R-FOG system in variable temperature environment.
Fig.6 A cover sheet and the HCF with quartz concentric tube
We use the quartz platform integrated coupling method to fabricate ARF resonator.The length of ARF is 5.14 m and is coiled with a diameter of 20 cm.The structure of the ARF is centrosymmetric.After bending it into a fiber ring,the stress will make the ARF appear a polarization axis,and the direction of the polarization axis is determined by the bending shape of the ARF.After the resonator coupling is completed and fully solidified,the polarization axis direction of the optical fiber and the main polarization direction of the resonator can be finally determined.Therefore,the splitting ratios of the splitter in S and P directions are both designed to be 95:5,so as to ensure that the splitting ratio of the resonator will not change when the final main polarization direction of the resonator is any direction.The focal length of the coupling lens is 6.1 mm.After all collimators are coupled and fixed,rotate theλ/2 wave plate inside the resonator to make the polarization direction at both ends of ARF consistent and ensure the alignment of polarization direction in the resonator.Then rotate the twoλ/2 wave plates outside the resonator to align the polarization direction of the light field emitted by the two circulators with the main polarization direction of the resonator.The circulators used in the R-FOG system work on two axes,so after the light field emitted from the resonator passes through theλ/2 wave plate again,the light field in any polarization direction can reach the detector through the circulator.
The structure diagram of the resonator and R-FOG system is shown in Fig.7.
Fig.7 Structure diagram of the ARF resonator and R-FOG system
In the temperature range of 25 °C to 75 °C,the resonator is tested at 10 °C intervals.The resonance curve test results are shown in Fig.8.The averageFof ARF resonator at each temperature point is 31.45,and the maximum deviation is 9.4%.To our knowledge,this is the best reported index of quartz platform integrated coupling resonator within the temperature variation range of 50 °C test.
Fig.8 Resonance curves of ARF resonator at different temperatures
According to the simulation analysis in Fig.4(c),the ARF collimator can maintain high coupling efficiency when the radial offset is less than 0.5 mm,which is far greater than the μm expansion limit of quartz based coupling platform.Therefore,we believe that the change of coupling efficiency mainly comes from the angle offset of the collimator,which is due to the uneven thickness of the adhesive between the fixed component of the collimator and the quartz plate and the different expansions at different positions.
The measurement results of output of the R-FOG when the ARF resonator is placed in the room environment(25 °C) is shown in Fig.9(a).A long-term (3 600 s) bias stability of 3.1°/h is successfully demonstrated from the Allan variance analysis result.The measurement results when the ARF resonator is heated to 75 °C is shown in Fig.9(b),with the long-term (3 600 s) bias stability of 4.6°/h.Although the temperature stability of ARF resonator has been improved compared with PBF resonator,theFof the resonator still changes by nearly 10% under the temperature difference of 50 ℃,which is the main reason why the test results of R-FOG system at high temperature are worse than those at room temperature.In the future research,we will try to further optimize the coupling process of the resonator and compensate the temperature of the R-FOG system to improve its temperature stability.
Fig.9 Allan deviation of open-loop output of the R-FOG
In summary,an ARF resonator within the temperature variation range of 50 °C is proposed and demonstrated.The main reason for the change of coupling efficiency of the spatial optical path coupling scheme in variable temperature environment is analyzed.Because of the larger MFD,ARF has the advantages of large coupling tolerance and low transmission loss compared with traditional PBF,which can effectively improve the optical performance of the HCF resonator at different temperatures.For the resonator sample made of ARF,the measuredFis greater than 30 in the temperature range of 25 °C to 75 °C.In the test of R-FOG system,bias stability of 3.1°/h at the room environment and 4.6°/h at 75 °C are obtained.This shows that ARF is an important breakthrough to realize hollow-core R-FOG system with high detection precision and temperature stability.At present,many research institutions are committed to developing ARF with polarization maintaining performance [26],which will further improve long-term stability of R-FOG.