Abstract

A reflective optic-fiber orientation-dependant inclinometer, in which a short piece of polarization-maintaining photonic crystal fiber (PM-PCF) is spliced with a lead-in single mode fiber (SMF) without any offset, is proposed and experimentally demonstrated. The hollow holes within the PM-PCF are partly collapsed due to the directional arc-heating splicing and couple two linearly polarized (LP) modes into the downstream PM-PCF. Then two LP-modes are reflected at the end face of PM-PCF and recoupled back into the lead-in SMF again via the collapsed splicing cross section. A well-defined interference pattern is obtained as the result of polarized modes interference. Both orientation and sensitivity of bending is determined unambiguously with this compact PM-PCF configuration.

©2013 Optical Society of America

1. Introduction

Photonic crystal fibers (PCFs) have been a new generation of optical fibers currently being widely researched and developed for many applications [14]. Polarization-maintaining photonic crystal fibers (PM-PCFs), as one group of PCF community, have also been attracting much more attention due to their inherent advantages. Compared with conventional PMFs including Panda-type PMF, bow-tie type PMF and elliptical core PMF [5], PM-PCF has shown higher birefringence and lower temperature sensitivity [6]. PM-PCFs have been used to equip the fiber laser and fiber sensors, such as highly polarized PCF fiber laser [7], Sagnac loops for temperature-insensitive strain measurement [8], transmission type sensor for torsion measurement [9], cladding to core re-coupling interferometer for curvature measurement [10] and cladding-mode resonance device for simultaneous temperature and strain measurements [11], etc. These fiber components mainly focus on polarization-maintaining (resulting from its high birefringence) and temperature-insensitive properties of PM-PCF, but do not perform a further study on the excitation and coupling of polarized modes. Recently, a fiber optic interferometer based on intermodal coupling of two-LP-modes in PM-PCF has been proposed for torsion measurement [12], which is a good start for polarized mode coupling of PM-PCF. However, the interferometer worked on transmission and the small contrast of interference fringe limit its sensitivity.

Bending is an important physical parameter due to its multi-area applications including security monitoring and structural engineering. Fiber-optic inclinometers for measuring bending angle have been developed in various schemes. A hollow core photonic crystal fiber (HC-PCF) sensor has been reported as an orientation-independence inclinometer [13]. Besides, multiple fiber grating based components also have been employed as inclinometers, such as a single fiber Bragg grating (FBG) with a segment of etched fiber [14], a Mach-Zehnder interferometer incorporating a taper cascaded with a long period grating (LPG) [15], and a taper combined with a titled fiber Bragg grating (TFBG) [16], etc. Above reported techniques take the advantages of compact size and well-controlled fabrication technologies but suffer from the weakened mechanical strength caused by tapering and etching processes.

In this paper, we propose and experimentally demonstrate an interferometer using a simple configuration: a short piece of PM-PCF alignment splicing with a lead-in single mode fiber (SMF). By controlling the heat-splicing direction and strength, the hollow holes of PM-PCF are partly collapsed over the cross-section of splicing region. Two linearly polarized (LP) modes are excited into the PM-PCF via splicing region. They transmit a round trip along the PM-PCF, and induce a phase difference between their orthogonal polarizations due to the intrinsic high-birefringence of PM-PCF. A well-defined superimposed interference pattern is obtained as the result of polarized modes interference. The free spectrum range (FSR) can be easily tailored by changing the length of PM-PCF tip. The sensitivity of interference pattern shows a symmetric response for bending angles ranging from −80° and 80° and high orientation-dependence ranging from 0 to 360°.

2. Sensing system and theoretical analysis

Figure 1(a) shows the schematic diagram of the bending angle sensing system. The light generated by an amplified spontaneous emission (ASE) propagates through a linear polarizer to obtain the highly linearly polarized light. A polarization controller (PC1) following with the polarizer is used to modulate the polarization state of input light. The polarized light is leaded into the sensing fiber and then reflected at the smooth end of PM-PCF. The output light is demonstrated by an optical spectrum analysis (OSA) with a resolution of 0.02 nm. The sensing device consists of a section of PM-PCF alignment splicing with a standard SMF by a commercial fusion splicer (Fujikura FSM-60S), as shown at the left of insert in Fig. 1(b). The cross-section of PM-PCF is partly collapsed at the arc discharge condition of I = 20 units and t = 300 ms. Optical microscope image of PM-PCF cross-section is shown at the right of insert in Fig. 1(b). It has the following structural characteristics: all-silica, 2 large holes with 7.7 µm diameters, 5-layers hollow holes, 88 small holes with 3.2 µm diameters, 2.3 µm pitch between two small holes, and one elliptical core with 4.0 μm and 7.5 μm diameters corresponding to the two orthogonal axes, respectively. The diameters of air holes in the cladding of PM-PCF are different, making the six-fold rotational symmetry transform into the two-fold rotational symmetry. The two-LP-modes coupling operation can be understood as a system that is analogous to a quasi-Michelson interferometer [17], of which the collapsing region can be seen as the multi-mode fiber. The first spatial modes, i.e. the fundamental mode of LP01 and the second mode of LP11, are excited and coupled into the downstream PM-PCF via the collapsed region. The multiple polarizations of LP01(x) and LP01(y), LP11(x) and LP11(y) are generated when the light is launched at certain direction relatively to the eigenaxes of PM-PCF. Azimuth of input light can be flexibly adjusted by changing the angular orientations of three wave-plates (used as polarization controller). When the LP light is launched at 45° relatively to the eigenaxes of PM-PCF, LP01 (x and y) and LP11 (x and y) are simultaneously excited, generating multi-beam interference.Besides, when LP light is parallel with the eigenaxes of PM-PCF, only x- or y-polarization of LP01 and x- or y-polarization of LP11 are excited, generating double-beam interference. Therefore, the polarizations of light injected into PM-PCF can be adjusted by the PC. When both x- and y-polarizations of the two-LP-modes are simultaneously excited, a superimposed spectrum pattern formed by multi-beams interference can be obtained, as shown in Fig. 2(a). Its maximum fringe contrast is 9.54 dB, which is about larger than 12 times that in [12], O. Frazão et al. Modulating PC can control the LP modes coupling efficiency between each other. For example, at one selected PC state, just y-polarization of LP01 and x-polarization of LP11 are excited and generate a clear double-beam interference spectra profile, as shown in Fig. 2(b).

 

Fig. 1 Schematic diagram of PM-PCF based orientation-dependant inclinometer sensing system. Inset (a) shows the sensing configuration of PM-PCF sensing probe, and (b) shows the photograph of the splicing point between SMF and (PM-PCF), and the cross section of PM-PCF.

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Fig. 2 Experimentally measured interference spectra, (a) between LP01 (x and y) and LP11 (x and y), (b) between LP01 (y) and LP11 (x); (c) shows the spatial frequency domain of interference in (a) and (b), (d) shows the field orientation-dependant plots which demonstrated the construction of LP11 modes, i.e. TM01 + HE21 rotated 45° = LP11(y), and -TE01 + HE21 = LP11(x).

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In order to analyze the characteristics of interference patterns, the wavelength spectra in Figs. 2(a) and 2(b) are fast Fourier transformed (FFT) to the spatial frequency domain (as shown in Fig. 2(c)) and the further modes coupling scheme is studied. The frequency spectrum presents the relationship between the frequency of the fringes of channeled spectrum and their amplitude. It clearly shows that the interference spectrum in Fig. 2(a) mainly results from three waves of LP01(y), LP11(y) and LP11(x) interference. The intensity of LP01(x) is weak and just participate in modifying the main interference. Besides, the spectrum in Fig. 2(b) is as the result of the double-beam interference between LP01(y) and LP11(x) only. According to the Fig. 2(c), the group birefringence can be calculated and the values are B1 = 3.4315 × 10−3 between LP01(y) and LP11(x), B2 = 2.9168 × 10−3 between LP01(y) and LP11(y), and B3 = 5.148 × 10−4 between LP11(x) and LP11(y), respectively. The spatial beat length for x-polarization (between LP01(x) and LP11(x)) and for the y-polarization (between LP01(y) and LP11(y)) is deduced and the values are 265.70 μm and 265.65 μm. Moreover, we plot and calculate the vectorial presentation of polarized modes by the commercial BEAMPROP® software. LP01 mode is expressed as HE11, and LP11 comprises four degenerate modes of TE01, TM01, HE21 (even) and HE21 (odd) with the approximately same propagation constant. As shown in Fig. 2(d), TE01 mode has an electric field tangential to the waveguide boundary, while TM01 mode is normally incident. The two modes present high polarization-dependence [18]. The even and odd modes can be defined with a perpendicular electric field of y-orientation (x-orientation is similar) in the polar coordinates as

E11(r,φ)=y^AJ1(X11ra){sin(mφ),(even)cos(mφ),(odd)
where A, J1(X11) are the amplitude of electric field and the 1th zero of 1th Bessel function. Through the field vector plots, Fig. 2(d) demonstrates the relationship between the orthogonal polarizations of LP11 and TE01, TM01 and HE21 modes: the LP11(y) mode is constructed by adding the TM01 mode and HE21 mode, rotated by 45°; LP11(x) mode is constructed by adding the -TE01 mode and HE21 mode. It shows that HE21 mode for each polarization presents clear orientation-dependence and makes the LP11 profile not cylindrical symmetry.

The transmission characteristics of light described above are further analyzed by Jones matrix as follows. The sensing system can be defined as in-line Sagnac interference. The transmission scheme of light is shown in Fig. 3, where F and S are with respect to the birefringence fast- and slow-axis. The linear polarizer is at an angle of α with respect to the vertical F-axis. To simplify the calculation, the pass axis of the linear polarizer is assumed to be parallel with the F-axis, i.e. α = 0, the Jones matrix MIP of polarizer is singular. The all-fiber PC is made of a half-wave plate (HWP) coil sandwiched two quarter-wave plates (QWPs) coils. We define θ1, θ2 and θ3 as the angular orientations of the three wave-plates. The Jones matrix of PC when light travels through QWP, HWP, and QWP forward is written as [19]

Mpc(θ1,θ2,θ3)=i2[a+ib,c+idcid,a+ib]
a=cos(2θ2)cos(2θ32θ2+2θ1)b=cos(2θ32θ2)cos(2θ22θ1)c=sin(2θ2)sin(2θ32θ2+2θ1)d=sin(2θ32θ2)sin(2θ22θ1)
After propagating forward and backward a single optical path along L-long PM-PCF singly, the birefringence between polarized-modes induce phase differences, Δφ1 = 2πB1L/λm, Δφ2 = 2πB2L/λm and Δφ3 = Δφ1-Δφ2 = 2πB3L/λm, where λm is the signal wavelength in vacuum. The Jones matrixes of PM-PCF and its end-face reflection can be written as
MPMPCF=[100eiΔφ1+eiΔφ2]
MEF=[r00r]
where r is reflectivity of PM-PCF end-face which is based on Fresnel reflection. Eventually the output light electric field is represented as
[EoutxEouty]=MIP'MPC'(θj)MPMPCF'MEFMPMPCFMPC(θj)MIP[Ein0]
M' is transpose Jones matrix of the corresponding optical component when light transmits backward. According to the Eq. (2a-4), the transmission function in the x-orientation (that of y-orientation is similar) is deduced as

 

Fig. 3 Scheme illustration of light transmitting in the system shown in Fig. 1(a).

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T=|Eoutx|2|Ein|2=r4[(a+ib)2(ei2Δφ1+ei2Δφ2)+(c+id)2]×[(a+ib)2(ei2Δφ1+ei2Δφ2)+(c+id)2]*

According to the Eq. (5), the transmission dependence for PC is theoretically simulated, as shown in Fig. 4. The length of the PM-PCF is 0.14 m, its end-face is well cut with reflectivity of 4%, and PC states are (θ1, π/6, π/4), (π/6, θ2, π/4) and (π/2, π/4, θ3). As shown in Figs. 4(a)-4(c), the superimposed interference spectra are clearly presented, and the transmission pattern change with θj (j = 1,2,3) change from –π/2 to π/2 and wavelength change from 1545 nm to 1565 nm, respectively. Since HWP variation affects the orientation of input linearly polarized light, Fig. 4(b) mainly depicts interference fringe contrast change with θ2. Besides, QWPs change impact the polarization state of light and thus results in the polarization component variation. Therefore, the fringe contrast and pattern of interference spectra clearly change with θ1 and θ3 in Figs. 4(a) and 4(c). The spectrum is confirmed with a certain PC state, with that conclusion, we can obtain the expected interference pattern by adjusting the three plates of PC.

 

Fig. 4 Simulated transmission spectra of PM-PCF in the states of (a) PC (θ1, π/6, π/4), (b) PC (π/6, θ2, π/4), (c) PC (π/2, π/4, θ3).

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In the certain constant PC state, the aforementioned superimposed interference spectrum can be simplified as a result of a three-wave interference model [20]. The intensity of output light can be represented as follow

I=|E1+E2eiΔφ1+E3eiΔφ2|2=E12+E22+E32+2E1E2cosΔφ1+2E1E3cosΔφ2+2E2E3cosΔφ3
where E1, E2 and E3 are the amplitudes of LP01(y), LP11(y) and LP11(x), whose normalized intensity can be determined by Fig. 2(c), respectively. When the sensing fiber subjects to bending at the certain orientation, the PM-PCF materials at the inner side of the bending axis will be compressed and that at the outside will be stretched. It can compel the refractive index of fused silica to decrease at one side and increase at the opposite side. Therefore, the presence of the bending breaks the fiber’s circular symmetry and the profiles of LP modes. The corresponding bending-induced birefringence change between polarized-modes can be written as [2123]
Bj(j=1,2,3)(β)=Bj|β=0+δBj
δBj=ni3(p11p12)(1+v)1(R0cosβ)2r2
where β is the bending angle, δBj is bending-induced adding birefringence, ν = 0.17 denotes Poisson’s ratio, (p11-p12) = −0.15 represents the strain-optical coefficient, n1, 2 = 1.4575, 1.4546 are the refractive indices for LP01 and LP11 modes, R0 = 0.5 mm is original bending curvature radius, and r = 4 μm is the radius of PM-PCF core. To simplify further simulated calculation, it is assumed that the bending axis is at the y-polarization axis, and the adding birefringence at the PM-PCF core region is just considered. By substituting the Eq. (7) into the Eq. (6), the interference intensity variation with β can be deduced as

I=|E1+E2eiΔφ1+E3eiΔφ2|2=E12+E22+E32+2E1E2cos2πλ(B11.08×1061cos2β)+2E1E3cos2πλ(B21.08×1061cos2β)+2E2E3cos2πλ(B31061cos2β)

The birefringence change will cause the optical phase differences variation between polarizations and eventually results in the shift of interference spectrum. According to Eq. (8), the interference pattern and its shift with bending angle are simulated. As shown in Fig. 5, when bending angle changes from π/9 to 4π/9, the interference pattern shows a blue-shift (from red interference pattern to blue one). The wavelength near 1567 nm is employed as an indicator and presents a significant wavelength shift of 2 nm. Moreover, since the vectorial degenerate modes of HE21 (even) and HE21 (odd) for each polarization present orientation-dependence, the index profiles change of the x- and y-LP11 modes at the bending axis is different. It allows the orientation sensitivity of the PM-PCF to bending.

 

Fig. 5 Simulated interference pattern shifts with bending-angle change.

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3. Experiments and discussion

The fabrication and properties of PM-PCF sensing device have been described above. In this section, we experimentally demonstrate it as an orientation-dependant inclinometer with 18cm-long PM-PCF. The coating material on the PM-PCF is not striped for two benefits: one is that the coating can effectively protect the sensing fiber and enhance the measurement range; the other is that it also can absorb the higher-order modes disturbing the main interference pattern. As shown in Fig. 6(a), two capillary tubes are employed to protect the fiber on both sides of the rotating axis, as well as to keep it straight for any bending angle. The distance between two capillary tubes, i.e. the length of bending fiber section, is 1.5 cm. In the experiment, one of the capillary tubes is held at a fixed stage, and the other capillary tube is held on the turn table. The interference valley near 1567 nm as an indicator is used to measure bending angle change. Figure 6(b) depicts that the spectrum shifts to shorter wavelength with increasing bending angle. While, due to the lower birefringence between LP11(x) and LP11(y), the larger interference enveloping of interference spectrum depicts lower bending angle sensitivity, and thus it will be a filter band and tailor the intensity of narrowband dips. Meanwhile, bending the fiber will induce part of light emitting out of fiber core and thus result in the core intensity loss.

 

Fig. 6 (a) Schematic diagram of the bending angle, (b) spectral blue shifting versus bending.

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To measure the device’s bending angle response, the fiber is bent from 0° to +/−80° with a step of 4°. The measureable bending angle is very hard to reach +/−90° due to the bending loss. The angle range is larger than that of aforementioned the literatures [1316]. The change relationship of the selected valley versus bending angle is shown in the red points of Fig. 7(a). The experimental data can be fitted by a quadratic function of λ = −5 × 10−4β2 + 4 × 10−4β + 1567.7. According to the Fig. 7(a), at the small angle range around 20°, the inclinometer presents a low sensitivity of −0.0163 nm/deg. When the fiber is bent to a larger angle around 60°, the spectrum sharply shifts to shorter wavelength and a higher sensitivity of −0.0775 nm/deg is obtained. To analyze the length of fiber bending section how to influence the inclinometer’s response, the distance between two capillary tubes is changed to 1 cm and 2 cm, respectively. And then the same fiber bending process is performed. The results are shown in the black and blue points of Fig. 7(a). The different bending angle responses present that the shorter bending length has a higher sensitivity around 60°. To study the orientation-dependant property of the inclinometer, its bending angle responses over the orientations ranging from 0° to 360° are demonstrated. Of which, the inclinometer is rotated at a step of 20° after finishing each set of bending angle measurement. The sensitivity around 60° of each measurement is as the function of rotated orientations. As shown in Fig. 7(b), strong angular (oriented) dependences of the sensitivity response have been achieved for interferometer. The maximum sensitivity results from that the bending axis is at the polarization axis, and the minimum sensitivity is due to that each polarization is independent of bending occurring in the orthogonal direction. The orientation function is not perfectly symmetry which may result from the following reasons: the relationship of wavelength versus bending angle is incomplete linear around 60°; two capillary tubes is incompletely set on the same horizon plane, which may add a walk-off angle to the bending; the experimental setup including calibrated inclinometer and rotator may bring in some errors. Besides, bending angle responses for different wavelength dips are investigated, the experimental results are given in Fig. 7(c). In this process, the length of bending fiber is 1 cm and the bending axis is at the polarization axis. It indicates that the two wavelength dips of 1542 nm and 1571 nm have the approximately same bending angle sensitivity around the whole angle range. It is attributed to that the group birefringence is independent on the interference wavelengths.

 

Fig. 7 (a) Wavelength response to the bending angle, (b) angular dependence of the inclinometer versus different orientations, (c) compared with two wavelengths’ response to the bending angle.

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The temperature response for the proposed sensor has also been characterized with a 6 cm-long PM-PCF. As shown in Fig. 8(a), over the heating range from 20 °C to 100 °C, an exactly linear spectral shift (recorded resonance at 1562.7 nm) has been achieved with the sensitivity of 10.5 pm/°C. Most importantly, over the whole heating process, the interference spectrum keeps its shape but only shifts its wavelength (as shown in Fig. 8(b)), which identifies the good thermal stability of our proposed sensor. For the in-field applications, the temperature fluctuations can be effectively cancelled out by induce one commercial fiber Bragg grating for calibration.

 

Fig. 8 The temperature response of the PM-PCF, (a) the dip wavelength response to temperature, (b) spectral red shifting versus temperature.

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4. Conclusion

We propose and experimentally demonstrate a compact and reflective interferometer as orientation-dependant inclinometer. The proposed device is easily fabricated by alignment splicing a section of PM-PCF with a lead-in SMF. A superimposed interference pattern is obtained as the result of the intermodal coupling and interference of two-LP-modes. The interference valleys are selected as the indicator to measure the bending angle change, and its sensitivity shows high angular dependence. Moreover, the inclinometer can provide remote sensing as a reflection probe, and the fabrication is simple and cost effective, making it a good candidate for structural health monitoring.

Acknowledgments

This work was supported by the National Natural Science Foundation of China (Nos. 60727004, 61077060, 61205080), National High Technology Research and Development Program 863(Nos. 2007AA03Z413, 2009AA06Z203), Ministry of Education Project of Science and Technology Innovation (No. Z08119), Ministry of Science and Technology Project of International Cooperation (No. 2008CR1063), Shanxi Province Project of Science and Technology Innovation (Nos. 2009ZKC01-19, 2008ZDGC-14), Guangdong Natural Science Foundation of China (Nos. S2011010001631, S2012010008385), Doctoral Program of Higher Education of China (No. 20114401120006), Pearl River Scholar for Distinguished Young Scientist (No. 2011J2200014).

References and links

1. P. Russell, “Photonic crystal fibers,” Science 299(5605), 358–362 (2003). [CrossRef]   [PubMed]  

2. J. C. Knight, “Photonic crystal fibres,” Nature 424(6950), 847–851 (2003). [CrossRef]   [PubMed]  

3. G. Coviello, V. Finazzi, J. Villatoro, and V. Pruneri, “Thermally stabilized PCF-based sensor for temperature measurements up to 1000 ° C,” Opt. Express 17(24), 21551–21559 (2009). [CrossRef]   [PubMed]  

4. B. H. Lee, J. B. Eom, J. Kim, D. S. Moon, U. C. Paek, and G. H. Yang, “Photonic crystal fiber coupler,” Opt. Lett. 27(10), 812–814 (2002). [CrossRef]   [PubMed]  

5. O. Frazão, J. M. Baptista, and J. L. Santos, “Recent advances in high-birefringence fiber loop mirror sensors,” Sensors (Basel Switzerland) 7(11), 2970–2983 (2007). [CrossRef]  

6. H. Y. Fu, A. C. L. Wong, P. A. Childs, H. Y. Tam, Y. B. Liao, C. Lu, and P. K. Wai, “Multiplexing of polarization-maintaining photonic crystal fiber based Sagnac interferometric sensors,” Opt. Express 17(21), 18501–18512 (2009). [CrossRef]   [PubMed]  

7. F. C. McNeillie, E. Riis, J. Broeng, J. R. Folkenberg, A. Petersson, H. Simonsen, and C. Jacobsen, “Highly polarized photonic crystal fiber laser,” Opt. Express 12(17), 3981–3987 (2004). [CrossRef]   [PubMed]  

8. X. Y. Dong, H. Y. Tam, and P. Shum, “Temperature-insensitive strain sensor with polarization-maintaining photonic crystal fiber based Sagnac interferometer,” Appl. Phys. Lett. 90(15), 151113 (2007). [CrossRef]  

9. H. Y. Fu, S. K. Khijwania, H. Y. Tam, P. K. A. Wai, and C. Lu, “Polarization-maintaining photonic-crystal-fiber-based all-optical polarimetric torsion sensor,” Appl. Opt. 49(31), 5954–5958 (2010).

10. B. Dong, J. Z. Hao, and Z. W. Xu, “Temperature insensitive curvature measurement with a core-offset polarization maintaining photonic crystal fiber based interferometer,” Opt. Fiber Technol. 17(3), 233–235 (2011). [CrossRef]  

11. B. Dong, J. Z. Hao, C. Y. Liaw, and Z. W. Xu, “Cladding-mode resonance in polarization-maintaining photonic-crystal-fiber-based Sagnac interferometer and its Application for fiber sensor,” J. Lightwave Technol. 29(12), 1759–1763 (2011).

12. O. Frazão, C. Jesus, J. M. Baptista, J. L. Santos, and P. Roy, “Fiber-optic interferometric torsion sensor based on a two-LP-mode operation in birefringent fiber,” IEEE Photon. Technol. Lett. 21(17), 1277–1279 (2009). [CrossRef]  

13. S. H. Liu, N. L. Liu, M. X. Hou, J. T. Guo, Z. H. Li, and P. X. Lu, “Direction-independent fiber inclinometer based on simplified hollow core photonic crystal fiber,” Opt. Lett. 38(4), 449–451 (2013). [CrossRef]   [PubMed]  

14. A. Rauf, J. L. Zhao, B. Q. Jiang, Y. J. Jiang, and W. Jiang, “Bend measurement using an etched fiber incorporating a fiber Bragg grating,” Opt. Lett. 38(2), 214–216 (2013). [CrossRef]   [PubMed]  

15. O. Frazão, R. Falate, J. L. Fabris, J. L. Santos, L. A. Ferreira, and F. M. Araújo, “Optical inclinometer based on a single long-period fiber grating combined with a fused taper,” Opt. Lett. 31(20), 2960–2962 (2006). [CrossRef]   [PubMed]  

16. L. Y. Shao and J. Albert, “Compact fiber-optic vector inclinometer,” Opt. Lett. 35(7), 1034–1036 (2010). [CrossRef]   [PubMed]  

17. Q. Z. Rong, X. G. Qiao, Y. Y. Du, D. Y. Feng, R. H. Wang, Y. Ma, H. Sun, M. L. Hu, and Z. Y. Feng, “In-fiber quasi-Michelson interferometer with a core-cladding-mode fiber end-face mirror,” Appl. Opt. 52(7), 1441–1447 (2013). [CrossRef]   [PubMed]  

18. S. Ramachandran, S. Golowich, M. F. Yan, E. Monberg, F. V. Dimarcello, J. Fleming, S. Ghalmi, and P. Wisk, “Lifting polarization degeneracy of modes by fiber design: a platform for polarization-insensitive microbend fiber gratings,” Opt. Lett. 30(21), 2864–2866 (2005). [CrossRef]   [PubMed]  

19. J. Wang, K. Zheng, J. Peng, L. S. Liu, J. Li, and S. S. Jian, “Theory and experiment of a fiber loop mirror filter of two-stage polarization-maintaining fibers and polarization controllers for multiwavelength fiber ring laser,” Opt. Express 17(13), 10573–10583 (2009). [CrossRef]   [PubMed]  

20. Y. Z. Zhu, K. L. Cooper, G. R. Pickrell, and A. B. Wang, “High-temperature fiber-tip pressure sensor,” J. Lightwave Technol. 24(2), 861–869 (2006).

21. S. C. Rashleigh and R. Ulrich, “High birefringence in tension-coiled single-mode fibers,” Opt. Lett. 5(8), 354–356 (1980). [CrossRef]   [PubMed]  

22. U. L. Block, M. J. F. Digonnet, M. M. Fejer, and V. Dangui, “Bending-induced birefringence of optical fiber cladding modes,” J. Lightwave Technol. 24(6), 2336–2339 (2006). [CrossRef]  

23. R. Ulrich, S. C. Rashleigh, and W. Eickhoff, “Bending-induced birefringence in single-mode fibers,” Opt. Lett. 5(6), 273–275 (1980). [CrossRef]   [PubMed]  

References

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  1. P. Russell, “Photonic crystal fibers,” Science 299(5605), 358–362 (2003).
    [Crossref] [PubMed]
  2. J. C. Knight, “Photonic crystal fibres,” Nature 424(6950), 847–851 (2003).
    [Crossref] [PubMed]
  3. G. Coviello, V. Finazzi, J. Villatoro, and V. Pruneri, “Thermally stabilized PCF-based sensor for temperature measurements up to 1000 ° C,” Opt. Express 17(24), 21551–21559 (2009).
    [Crossref] [PubMed]
  4. B. H. Lee, J. B. Eom, J. Kim, D. S. Moon, U. C. Paek, and G. H. Yang, “Photonic crystal fiber coupler,” Opt. Lett. 27(10), 812–814 (2002).
    [Crossref] [PubMed]
  5. O. Frazão, J. M. Baptista, and J. L. Santos, “Recent advances in high-birefringence fiber loop mirror sensors,” Sensors (Basel Switzerland) 7(11), 2970–2983 (2007).
    [Crossref]
  6. H. Y. Fu, A. C. L. Wong, P. A. Childs, H. Y. Tam, Y. B. Liao, C. Lu, and P. K. Wai, “Multiplexing of polarization-maintaining photonic crystal fiber based Sagnac interferometric sensors,” Opt. Express 17(21), 18501–18512 (2009).
    [Crossref] [PubMed]
  7. F. C. McNeillie, E. Riis, J. Broeng, J. R. Folkenberg, A. Petersson, H. Simonsen, and C. Jacobsen, “Highly polarized photonic crystal fiber laser,” Opt. Express 12(17), 3981–3987 (2004).
    [Crossref] [PubMed]
  8. X. Y. Dong, H. Y. Tam, and P. Shum, “Temperature-insensitive strain sensor with polarization-maintaining photonic crystal fiber based Sagnac interferometer,” Appl. Phys. Lett. 90(15), 151113 (2007).
    [Crossref]
  9. H. Y. Fu, S. K. Khijwania, H. Y. Tam, P. K. A. Wai, and C. Lu, “Polarization-maintaining photonic-crystal-fiber-based all-optical polarimetric torsion sensor,” Appl. Opt. 49(31), 5954–5958 (2010).
  10. B. Dong, J. Z. Hao, and Z. W. Xu, “Temperature insensitive curvature measurement with a core-offset polarization maintaining photonic crystal fiber based interferometer,” Opt. Fiber Technol. 17(3), 233–235 (2011).
    [Crossref]
  11. B. Dong, J. Z. Hao, C. Y. Liaw, and Z. W. Xu, “Cladding-mode resonance in polarization-maintaining photonic-crystal-fiber-based Sagnac interferometer and its Application for fiber sensor,” J. Lightwave Technol. 29(12), 1759–1763 (2011).
  12. O. Frazão, C. Jesus, J. M. Baptista, J. L. Santos, and P. Roy, “Fiber-optic interferometric torsion sensor based on a two-LP-mode operation in birefringent fiber,” IEEE Photon. Technol. Lett. 21(17), 1277–1279 (2009).
    [Crossref]
  13. S. H. Liu, N. L. Liu, M. X. Hou, J. T. Guo, Z. H. Li, and P. X. Lu, “Direction-independent fiber inclinometer based on simplified hollow core photonic crystal fiber,” Opt. Lett. 38(4), 449–451 (2013).
    [Crossref] [PubMed]
  14. A. Rauf, J. L. Zhao, B. Q. Jiang, Y. J. Jiang, and W. Jiang, “Bend measurement using an etched fiber incorporating a fiber Bragg grating,” Opt. Lett. 38(2), 214–216 (2013).
    [Crossref] [PubMed]
  15. O. Frazão, R. Falate, J. L. Fabris, J. L. Santos, L. A. Ferreira, and F. M. Araújo, “Optical inclinometer based on a single long-period fiber grating combined with a fused taper,” Opt. Lett. 31(20), 2960–2962 (2006).
    [Crossref] [PubMed]
  16. L. Y. Shao and J. Albert, “Compact fiber-optic vector inclinometer,” Opt. Lett. 35(7), 1034–1036 (2010).
    [Crossref] [PubMed]
  17. Q. Z. Rong, X. G. Qiao, Y. Y. Du, D. Y. Feng, R. H. Wang, Y. Ma, H. Sun, M. L. Hu, and Z. Y. Feng, “In-fiber quasi-Michelson interferometer with a core-cladding-mode fiber end-face mirror,” Appl. Opt. 52(7), 1441–1447 (2013).
    [Crossref] [PubMed]
  18. S. Ramachandran, S. Golowich, M. F. Yan, E. Monberg, F. V. Dimarcello, J. Fleming, S. Ghalmi, and P. Wisk, “Lifting polarization degeneracy of modes by fiber design: a platform for polarization-insensitive microbend fiber gratings,” Opt. Lett. 30(21), 2864–2866 (2005).
    [Crossref] [PubMed]
  19. J. Wang, K. Zheng, J. Peng, L. S. Liu, J. Li, and S. S. Jian, “Theory and experiment of a fiber loop mirror filter of two-stage polarization-maintaining fibers and polarization controllers for multiwavelength fiber ring laser,” Opt. Express 17(13), 10573–10583 (2009).
    [Crossref] [PubMed]
  20. Y. Z. Zhu, K. L. Cooper, G. R. Pickrell, and A. B. Wang, “High-temperature fiber-tip pressure sensor,” J. Lightwave Technol. 24(2), 861–869 (2006).
  21. S. C. Rashleigh and R. Ulrich, “High birefringence in tension-coiled single-mode fibers,” Opt. Lett. 5(8), 354–356 (1980).
    [Crossref] [PubMed]
  22. U. L. Block, M. J. F. Digonnet, M. M. Fejer, and V. Dangui, “Bending-induced birefringence of optical fiber cladding modes,” J. Lightwave Technol. 24(6), 2336–2339 (2006).
    [Crossref]
  23. R. Ulrich, S. C. Rashleigh, and W. Eickhoff, “Bending-induced birefringence in single-mode fibers,” Opt. Lett. 5(6), 273–275 (1980).
    [Crossref] [PubMed]

2013 (3)

2011 (2)

B. Dong, J. Z. Hao, and Z. W. Xu, “Temperature insensitive curvature measurement with a core-offset polarization maintaining photonic crystal fiber based interferometer,” Opt. Fiber Technol. 17(3), 233–235 (2011).
[Crossref]

B. Dong, J. Z. Hao, C. Y. Liaw, and Z. W. Xu, “Cladding-mode resonance in polarization-maintaining photonic-crystal-fiber-based Sagnac interferometer and its Application for fiber sensor,” J. Lightwave Technol. 29(12), 1759–1763 (2011).

2010 (2)

2009 (4)

2007 (2)

O. Frazão, J. M. Baptista, and J. L. Santos, “Recent advances in high-birefringence fiber loop mirror sensors,” Sensors (Basel Switzerland) 7(11), 2970–2983 (2007).
[Crossref]

X. Y. Dong, H. Y. Tam, and P. Shum, “Temperature-insensitive strain sensor with polarization-maintaining photonic crystal fiber based Sagnac interferometer,” Appl. Phys. Lett. 90(15), 151113 (2007).
[Crossref]

2006 (3)

2005 (1)

2004 (1)

2003 (2)

P. Russell, “Photonic crystal fibers,” Science 299(5605), 358–362 (2003).
[Crossref] [PubMed]

J. C. Knight, “Photonic crystal fibres,” Nature 424(6950), 847–851 (2003).
[Crossref] [PubMed]

2002 (1)

1980 (2)

Albert, J.

Araújo, F. M.

Baptista, J. M.

O. Frazão, C. Jesus, J. M. Baptista, J. L. Santos, and P. Roy, “Fiber-optic interferometric torsion sensor based on a two-LP-mode operation in birefringent fiber,” IEEE Photon. Technol. Lett. 21(17), 1277–1279 (2009).
[Crossref]

O. Frazão, J. M. Baptista, and J. L. Santos, “Recent advances in high-birefringence fiber loop mirror sensors,” Sensors (Basel Switzerland) 7(11), 2970–2983 (2007).
[Crossref]

Block, U. L.

Broeng, J.

Childs, P. A.

Cooper, K. L.

Coviello, G.

Dangui, V.

Digonnet, M. J. F.

Dimarcello, F. V.

Dong, B.

B. Dong, J. Z. Hao, and Z. W. Xu, “Temperature insensitive curvature measurement with a core-offset polarization maintaining photonic crystal fiber based interferometer,” Opt. Fiber Technol. 17(3), 233–235 (2011).
[Crossref]

B. Dong, J. Z. Hao, C. Y. Liaw, and Z. W. Xu, “Cladding-mode resonance in polarization-maintaining photonic-crystal-fiber-based Sagnac interferometer and its Application for fiber sensor,” J. Lightwave Technol. 29(12), 1759–1763 (2011).

Dong, X. Y.

X. Y. Dong, H. Y. Tam, and P. Shum, “Temperature-insensitive strain sensor with polarization-maintaining photonic crystal fiber based Sagnac interferometer,” Appl. Phys. Lett. 90(15), 151113 (2007).
[Crossref]

Du, Y. Y.

Eickhoff, W.

Eom, J. B.

Fabris, J. L.

Falate, R.

Fejer, M. M.

Feng, D. Y.

Feng, Z. Y.

Ferreira, L. A.

Finazzi, V.

Fleming, J.

Folkenberg, J. R.

Frazão, O.

O. Frazão, C. Jesus, J. M. Baptista, J. L. Santos, and P. Roy, “Fiber-optic interferometric torsion sensor based on a two-LP-mode operation in birefringent fiber,” IEEE Photon. Technol. Lett. 21(17), 1277–1279 (2009).
[Crossref]

O. Frazão, J. M. Baptista, and J. L. Santos, “Recent advances in high-birefringence fiber loop mirror sensors,” Sensors (Basel Switzerland) 7(11), 2970–2983 (2007).
[Crossref]

O. Frazão, R. Falate, J. L. Fabris, J. L. Santos, L. A. Ferreira, and F. M. Araújo, “Optical inclinometer based on a single long-period fiber grating combined with a fused taper,” Opt. Lett. 31(20), 2960–2962 (2006).
[Crossref] [PubMed]

Fu, H. Y.

Ghalmi, S.

Golowich, S.

Guo, J. T.

Hao, J. Z.

B. Dong, J. Z. Hao, C. Y. Liaw, and Z. W. Xu, “Cladding-mode resonance in polarization-maintaining photonic-crystal-fiber-based Sagnac interferometer and its Application for fiber sensor,” J. Lightwave Technol. 29(12), 1759–1763 (2011).

B. Dong, J. Z. Hao, and Z. W. Xu, “Temperature insensitive curvature measurement with a core-offset polarization maintaining photonic crystal fiber based interferometer,” Opt. Fiber Technol. 17(3), 233–235 (2011).
[Crossref]

Hou, M. X.

Hu, M. L.

Jacobsen, C.

Jesus, C.

O. Frazão, C. Jesus, J. M. Baptista, J. L. Santos, and P. Roy, “Fiber-optic interferometric torsion sensor based on a two-LP-mode operation in birefringent fiber,” IEEE Photon. Technol. Lett. 21(17), 1277–1279 (2009).
[Crossref]

Jian, S. S.

Jiang, B. Q.

Jiang, W.

Jiang, Y. J.

Khijwania, S. K.

Kim, J.

Knight, J. C.

J. C. Knight, “Photonic crystal fibres,” Nature 424(6950), 847–851 (2003).
[Crossref] [PubMed]

Lee, B. H.

Li, J.

Li, Z. H.

Liao, Y. B.

Liaw, C. Y.

Liu, L. S.

Liu, N. L.

Liu, S. H.

Lu, C.

Lu, P. X.

Ma, Y.

McNeillie, F. C.

Monberg, E.

Moon, D. S.

Paek, U. C.

Peng, J.

Petersson, A.

Pickrell, G. R.

Pruneri, V.

Qiao, X. G.

Ramachandran, S.

Rashleigh, S. C.

Rauf, A.

Riis, E.

Rong, Q. Z.

Roy, P.

O. Frazão, C. Jesus, J. M. Baptista, J. L. Santos, and P. Roy, “Fiber-optic interferometric torsion sensor based on a two-LP-mode operation in birefringent fiber,” IEEE Photon. Technol. Lett. 21(17), 1277–1279 (2009).
[Crossref]

Russell, P.

P. Russell, “Photonic crystal fibers,” Science 299(5605), 358–362 (2003).
[Crossref] [PubMed]

Santos, J. L.

O. Frazão, C. Jesus, J. M. Baptista, J. L. Santos, and P. Roy, “Fiber-optic interferometric torsion sensor based on a two-LP-mode operation in birefringent fiber,” IEEE Photon. Technol. Lett. 21(17), 1277–1279 (2009).
[Crossref]

O. Frazão, J. M. Baptista, and J. L. Santos, “Recent advances in high-birefringence fiber loop mirror sensors,” Sensors (Basel Switzerland) 7(11), 2970–2983 (2007).
[Crossref]

O. Frazão, R. Falate, J. L. Fabris, J. L. Santos, L. A. Ferreira, and F. M. Araújo, “Optical inclinometer based on a single long-period fiber grating combined with a fused taper,” Opt. Lett. 31(20), 2960–2962 (2006).
[Crossref] [PubMed]

Shao, L. Y.

Shum, P.

X. Y. Dong, H. Y. Tam, and P. Shum, “Temperature-insensitive strain sensor with polarization-maintaining photonic crystal fiber based Sagnac interferometer,” Appl. Phys. Lett. 90(15), 151113 (2007).
[Crossref]

Simonsen, H.

Sun, H.

Tam, H. Y.

Ulrich, R.

Villatoro, J.

Wai, P. K.

Wai, P. K. A.

Wang, A. B.

Wang, J.

Wang, R. H.

Wisk, P.

Wong, A. C. L.

Xu, Z. W.

B. Dong, J. Z. Hao, and Z. W. Xu, “Temperature insensitive curvature measurement with a core-offset polarization maintaining photonic crystal fiber based interferometer,” Opt. Fiber Technol. 17(3), 233–235 (2011).
[Crossref]

B. Dong, J. Z. Hao, C. Y. Liaw, and Z. W. Xu, “Cladding-mode resonance in polarization-maintaining photonic-crystal-fiber-based Sagnac interferometer and its Application for fiber sensor,” J. Lightwave Technol. 29(12), 1759–1763 (2011).

Yan, M. F.

Yang, G. H.

Zhao, J. L.

Zheng, K.

Zhu, Y. Z.

Appl. Opt. (2)

Appl. Phys. Lett. (1)

X. Y. Dong, H. Y. Tam, and P. Shum, “Temperature-insensitive strain sensor with polarization-maintaining photonic crystal fiber based Sagnac interferometer,” Appl. Phys. Lett. 90(15), 151113 (2007).
[Crossref]

IEEE Photon. Technol. Lett. (1)

O. Frazão, C. Jesus, J. M. Baptista, J. L. Santos, and P. Roy, “Fiber-optic interferometric torsion sensor based on a two-LP-mode operation in birefringent fiber,” IEEE Photon. Technol. Lett. 21(17), 1277–1279 (2009).
[Crossref]

J. Lightwave Technol. (3)

Nature (1)

J. C. Knight, “Photonic crystal fibres,” Nature 424(6950), 847–851 (2003).
[Crossref] [PubMed]

Opt. Express (4)

Opt. Fiber Technol. (1)

B. Dong, J. Z. Hao, and Z. W. Xu, “Temperature insensitive curvature measurement with a core-offset polarization maintaining photonic crystal fiber based interferometer,” Opt. Fiber Technol. 17(3), 233–235 (2011).
[Crossref]

Opt. Lett. (8)

S. Ramachandran, S. Golowich, M. F. Yan, E. Monberg, F. V. Dimarcello, J. Fleming, S. Ghalmi, and P. Wisk, “Lifting polarization degeneracy of modes by fiber design: a platform for polarization-insensitive microbend fiber gratings,” Opt. Lett. 30(21), 2864–2866 (2005).
[Crossref] [PubMed]

S. H. Liu, N. L. Liu, M. X. Hou, J. T. Guo, Z. H. Li, and P. X. Lu, “Direction-independent fiber inclinometer based on simplified hollow core photonic crystal fiber,” Opt. Lett. 38(4), 449–451 (2013).
[Crossref] [PubMed]

A. Rauf, J. L. Zhao, B. Q. Jiang, Y. J. Jiang, and W. Jiang, “Bend measurement using an etched fiber incorporating a fiber Bragg grating,” Opt. Lett. 38(2), 214–216 (2013).
[Crossref] [PubMed]

O. Frazão, R. Falate, J. L. Fabris, J. L. Santos, L. A. Ferreira, and F. M. Araújo, “Optical inclinometer based on a single long-period fiber grating combined with a fused taper,” Opt. Lett. 31(20), 2960–2962 (2006).
[Crossref] [PubMed]

L. Y. Shao and J. Albert, “Compact fiber-optic vector inclinometer,” Opt. Lett. 35(7), 1034–1036 (2010).
[Crossref] [PubMed]

B. H. Lee, J. B. Eom, J. Kim, D. S. Moon, U. C. Paek, and G. H. Yang, “Photonic crystal fiber coupler,” Opt. Lett. 27(10), 812–814 (2002).
[Crossref] [PubMed]

S. C. Rashleigh and R. Ulrich, “High birefringence in tension-coiled single-mode fibers,” Opt. Lett. 5(8), 354–356 (1980).
[Crossref] [PubMed]

R. Ulrich, S. C. Rashleigh, and W. Eickhoff, “Bending-induced birefringence in single-mode fibers,” Opt. Lett. 5(6), 273–275 (1980).
[Crossref] [PubMed]

Science (1)

P. Russell, “Photonic crystal fibers,” Science 299(5605), 358–362 (2003).
[Crossref] [PubMed]

Sensors (Basel Switzerland) (1)

O. Frazão, J. M. Baptista, and J. L. Santos, “Recent advances in high-birefringence fiber loop mirror sensors,” Sensors (Basel Switzerland) 7(11), 2970–2983 (2007).
[Crossref]

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Figures (8)

Fig. 1
Fig. 1 Schematic diagram of PM-PCF based orientation-dependant inclinometer sensing system. Inset (a) shows the sensing configuration of PM-PCF sensing probe, and (b) shows the photograph of the splicing point between SMF and (PM-PCF), and the cross section of PM-PCF.
Fig. 2
Fig. 2 Experimentally measured interference spectra, (a) between LP01 (x and y) and LP11 (x and y), (b) between LP01 (y) and LP11 (x); (c) shows the spatial frequency domain of interference in (a) and (b), (d) shows the field orientation-dependant plots which demonstrated the construction of LP11 modes, i.e. TM01 + HE21 rotated 45° = LP11(y), and -TE01 + HE21 = LP11(x).
Fig. 3
Fig. 3 Scheme illustration of light transmitting in the system shown in Fig. 1(a).
Fig. 4
Fig. 4 Simulated transmission spectra of PM-PCF in the states of (a) PC (θ1, π/6, π/4), (b) PC (π/6, θ2, π/4), (c) PC (π/2, π/4, θ3).
Fig. 5
Fig. 5 Simulated interference pattern shifts with bending-angle change.
Fig. 6
Fig. 6 (a) Schematic diagram of the bending angle, (b) spectral blue shifting versus bending.
Fig. 7
Fig. 7 (a) Wavelength response to the bending angle, (b) angular dependence of the inclinometer versus different orientations, (c) compared with two wavelengths’ response to the bending angle.
Fig. 8
Fig. 8 The temperature response of the PM-PCF, (a) the dip wavelength response to temperature, (b) spectral red shifting versus temperature.

Equations (11)

Equations on this page are rendered with MathJax. Learn more.

E 11 (r,φ)= y ^ A J 1 ( X 11 r a ){ sin(mφ),(even) cos(mφ),(odd)
M pc ( θ 1 , θ 2 , θ 3 )= i 2 [ a+ib,c+id cid,a+ib ]
a=cos(2 θ 2 )cos(2 θ 3 2 θ 2 +2 θ 1 ) b=cos(2 θ 3 2 θ 2 )cos(2 θ 2 2 θ 1 ) c=sin(2 θ 2 )sin(2 θ 3 2 θ 2 +2 θ 1 ) d=sin(2 θ 3 2 θ 2 )sin(2 θ 2 2 θ 1 )
M PMPCF =[ 10 0 e iΔ φ 1 + e iΔ φ 2 ]
M EF =[ r0 0r ]
[ E outx E outy ]= M IP ' M PC ' ( θ j ) M PMPCF ' M EF M PMPCF M PC ( θ j ) M IP [ E in 0 ]
T= | E outx | 2 | E in | 2 = r 4 [ (a+ib) 2 ( e i2Δ φ 1 + e i2Δ φ 2 )+ (c+id) 2 ] × [ (a+ib) 2 ( e i2Δ φ 1 + e i2Δ φ 2 )+ (c+id) 2 ] *
I= | E 1 + E 2 e iΔ φ 1 + E 3 e iΔ φ 2 | 2 = E 1 2 + E 2 2 + E 3 2 +2 E 1 E 2 cosΔ φ 1 +2 E 1 E 3 cosΔ φ 2 +2 E 2 E 3 cosΔ φ 3
B j(j=1,2,3) (β)= B j | β=0 +δ B j
δ B j = n i 3 ( p 11 p 12 )(1+v) 1 ( R 0 cosβ) 2 r 2
I= | E 1 + E 2 e iΔ φ 1 + E 3 e iΔ φ 2 | 2 = E 1 2 + E 2 2 + E 3 2 +2 E 1 E 2 cos 2π λ ( B 1 1.08× 10 6 1 cos 2 β ) +2 E 1 E 3 cos 2π λ ( B 2 1.08× 10 6 1 cos 2 β ) +2 E 2 E 3 cos 2π λ ( B 3 10 6 1 cos 2 β )

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