A novel temperature- and strain-independent optical fiber torsion sensor based on a phase-shifted fiber Bragg grating (PSFBG) inscribed by the line-by-line (LbL) technique in a standard single-mode fiber with a femtosecond laser has been proposed and experimentally demonstrated. The strong birefringence created by the LbL inscription technique leads to the significant polarization splitting of the transmission peak of the PSFBG. By simply monitoring the variation of the amplitude difference between the two polarization-peaks, the fiber torsion angle and the fiber torsion direction can be simultaneously deduced without temperature and strain confusion. The torsion sensor exhibits a high torsion sensitivity of up to −1032.71 dB/(rad/mm), with the distinct advantages of low manufacture cost, small dimension (just ~1.72mm), and extremely robust and simple structure, which make it very attractive for practical applications. To the best of our knowledge, this is the smallest torsion sensor ever reported.
© 2016 Optical Society of America
Torsion, as a physical parameter reflects the stress state and internal injury of the structure, has become one of the most important mechanical parameters for modern smart structure monitoring and recently its measurement has attracted increasing research interest. Among the various torsion sensors developed before, fiber-based torsion sensors have been widely applied due to their excellent advantages of compactness, low cost, excellent flexibility, and strong immunity to electromagnetic interference [1–22].
Currently, a considerable amount of optical fiber torsion sensors have been constructed based on different fiber optic devices. One common fiber optic device employed to fabricate fiber torsion sensor is fiber grating. Long-period fiber gratings (LPGs) fabricated by etching a fiber  or high-frequency CO2 laser pulses radiation [2–4], machinery  have been used as torsion sensors. However, the torsion sensors based on conventional long-period fiber gratings mentioned above present the cross sensitivities from the axial strain and temperature. To address this issue, a multi-phase-shifted helical long period fiber grating , a paired helical long-period fiber gratings with opposite helicities , structured polarization maintaining chirped fiber Bragg grating  and an 81° tilted fiber Bragg grating  have been used to develop torsion sensors. And yet, the fabrication of the sensors are relatively complex. Then, the torsion sensors based on a polarization maintaining fiber Bragg grating , a Bragg grating in a single mode fiber by utilizing analysis of polarization dependent loss  have been reported. Even though simple as the structures of the sensors are, the highest torsion sensitivity of the two sensors is ~28.65 dB/(rad/mm), which is remaining to be improved. The other common fiber optic device employed to fabricate fiber torsion sensor is fiber interferometer [12–22]. In many related studies, some proposed fiber torsion sensors are based on a multimode interferometer (MMI) employing the square no-core fiber , a dual polarized Mach-Zehnder interferometer , a Mach-Zehnder interferometer constituted by a twisted taper in polarization-maintaining fiber  and a Mach Zehnder interferometer based on helical waveguides . In addition, some achieved torsion sensors are based on the Sagnac interferometers constructed with different kinds of asymmetric photonic crystal fibers (PCFs), including suspended twin-core fibers , highly birefringent PCFs , low-birefringence PCFs , side-leakage PCF  and polarization-maintaining elliptical core fibers(PM-ECFs) . However, it is well known that the PCFs are lossy and expensive, which are the barriers to their large-scale applications. In addition, these special fibers are usually spliced in the torsion structures, which make the sensors are relatively fragile.
In this Letter, we propose and demonstrate a novel temperature- and strain-independent optical fiber torsion sensor based on a phase-shift fiber Bragg grating (PSFBG) written in a standard single-mode fiber. A fourth-order π-PSFBG with a length of ~1.72mm is fabricated by the line-by-line (LbL) technique with a femtosecond laser. This is also the first time, to the best of our knowledge, that a phase-shift fiber Bragg grating fabricated with line-by-line technique is reported. In terms of PSFBG fabrication, the LbL technique is extremely simple since a phase-shift can be simply designed and realized by setting an appropriate line gap (e.g. Half-period is corresponding to π-phase-shift) at the structure center. For the point-by-point (PbP) technique demonstrated in , it is difficult to fabricate a PSFBG in a single step and a post-tuning has to be used. Also with lines in the core instead of points, stronger mode coupling can be realized, which allows one to fabricate strong gratings with shorter length. Moreover, since the refractive index is modified along only one axis in the cross-section of the fiber, it is much easier to create a strong birefringence compared with the PbP technique. The line-by-line generated structure here shows a strong birefringence, which leads to the transmission peak of the π-PSFBG to split into two polarization dependent peaks. By simply monitoring the amplitude difference between the two polarization-peaks, the fiber torsion angle and the fiber torsion direction can be simultaneously deduced without temperature and strain confusion. A good agreement of theoretical prediction and experimental results can be reached. The torsion sensor exhibits a high torsion sensitivity of up to −1032.71 dB/(rad/mm), which is almost 36 times higher than that of the current similar existing torsion sensor . Since the PSFBG used here has an extremely short length (only ~1.72mm), to the best of our knowledge, this is the smallest torsion sensor ever reported.
2. LbL fabrication of PSFBG
The schematic of the experimental setup used for the LbL writing of PSFBGs is shown in Fig. 1. A femtosecond laser amplifier emitting laser pulses at a center wavelength of 1040 nm with a pulse duration of <400 fs at a repetition rate of 200 kHz is frequency doubled to 520 nm. A variable attenuator composed by the half-wave plate and the polarizer is used at the output of the laser to realize the adjustment of the pulse energy. The diameter of the beam is adjusted by a laser beam expander composed by a convex lens and a concave lens. A 63 × oil-immersion lens is used to focus the laser pulses into the core of the fiber. To minimize the distortion of the focal point introduced by the curved surface of the fiber, the objective and the fiber are both immersed in index-matching oil. The fiber used in the experiment is a nonphotosensitized standard telcom single-mode fiber (from YOFC Ltd) with a core diameter of ~8.2 μm and a cladding diameter of 125 μm, respectively. The fiber is positioned on a three-axis translating stage, which is controlled by a computer to translate the fiber with respect to the focal spot of the fs-laser beam according to a designed pattern. The transmission spectrum is real-time monitored by employing a broadband light source, a fiber polarizer, a polarization controller and an optical spectrum analyzer (OSA, with a resolution of 0.02 nm). The fiber polarizer and the polarization controller are used for controlling the polarization of the light transmitting in the fiber.
The principle of the LbL inscription technique and the pattern designed in the computer are schematically illustrated in Fig. 2(a). For each line, the inscription process consists of scanning the focused fs-laser beam along the direction of the arrowhead marked in the line and perpendicular to the fiber axis (x). Then moving the focus in the x direction with a small distance, which is equal to the Bragg period Λ of the grating, another parallel line is inscribed repeatedly, and so on until the whole designed pattern is written. The shutter of the laser is closed during the movement between lines. The LbL PSFBG is formed by two identical uniform FBGs with a grating period of Λ, separated by a gap of ΔΛ. The phase shift is introduced by the gap ΔΛ between the two uniform FBGs. A PSFBG inscribed in this way is schematically shown in Fig. 2(b). In the experiment, the period Λ of the PSFBGs is designed to be 2.144 μm, corresponding to a fourth-order Bragg resonant wavelength of ~1552.3 nm. Here the m-th order Bragg resonance wavelength is estimated with the phase match equation mλB = 2neffΛ, where neff is effective refractive index (~1.448). To obtain the phase-shift variable of π, the gap ΔΛ is set to 0.268 μm. The length of each line is 8 μm, which roughly equals to the diameter of the fiber core. The inscription process runs automatically and normally takes a few minutes. To characterize the PSFBG, the polarized transmission spectra are recorded.
Figure 3 shows the transmission spectra of a ~1.72-mm-long π-PSFBG, measured with input light of different polarizations. It is clearly seen that the spectrum of the LbL-inscribed PSFBG is strongly dependent on the polarization state of the input light. The reason for this dependence is due to the birefringence induced by the line-by-line inscribed grating structures. Only one transmission peak can be observed in the transmission spectra when the polarization state of the input light is corresponding to the fast or the slow axis of the fiber grating. However, the transmission peak splits into two peaks (labeled as P1 and P2) for the input polarization of 45°. The polarization-induced spectral shift between the narrow transmission bands measured in orthogonal polarization states is 232 pm for the π-PSFBG, corresponding to a birefringence of 2.16 × 10−4. As the refractive index modification by the LbL inscribing technique is only along the y-axis shown in Fig. 2(b), there is an asymmetry of the induced index profile with respect to the circular cross-sectional area of the fiber core, and then resulting in the high birefringence of the PSFBG.
3. Torsion sensing experiment
The schematic diagram of the torsion sensing arrangement using a π-PSFBG is shown in Fig. 4. The fiber containing the π-PSFBG under test is mounted between a fiber holder and a fiber rotator with a separation length (L) of 20cm. The distance L0 between the fiber holder and the end of the PSFBG is 12cm. In order to eliminate possible measurement errors from axial strain and bending effects, the test fiber is kept straight by applying a small axial tension. The initial polarized light is provided by a broadband light source, a fiber polarizer, a polarization controller (similar to Fig. 1). The OSA is used to record the spectral evolution of the PSFBG sensor to the fiber torsion. The original polarization state of the input light is set to ~45° by adjusting the polarization controller and thus the observed resonance splits into two peaks with almost equal transmittance.
In order to investigate the torsion response of the sensor, the transmission spectra are recorded by increasing the torsion angle from 0° to 360° with an interval of 10° in the clockwise direction and anticlockwise direction, respectively. Figure 5(a) shows the transmission spectra evolution of π-PSFBG under torsion in clockwise direction from 0° to 80° in an elevation step of 20°. From Fig. 5(a), one can note that the amplitudes of the two polarization-peaks labeled as P1 and P2 respectively depend on the value of the torsion angle. In order to eliminate the amplitude measurement errors caused by the optical power fluctuations of the broadband light source, the torsion sensor is encoded in the amplitude difference between P1 and P2. Figure 5(b) represents the relationship between the value of P1-P2 and the applied torsion angle in clockwise and anticlockwise directions. It can be obviously seen that P1-P2 changes periodically with the torsion angle as a sine-like function. The slopes in the linear fitting region from 140° to 240° in clockwise direction and 100° to 210° in anticlockwise direction are 0.0819, −0.08778, corresponding to the torsion sensitivities of 963.53 dB/(rad/mm), −1032.71 dB/(rad/mm), respectively. In practical application, the sensor can be pre-twist to these linear ranges for achieving a high sensitivity measurement.
To characterize the temperature and strain cross-sensitivity of the torsion sensor, the differences between P1 and P2 versus temperature and strain are measured by heating the pre-twisted sensor from 20°C to 70°C and increasing the applied strain from 0 με to 500 με, respectively. Figure 6 shows the value of P1-P2 as a function of temperature and strain when the pre-torsion angles are set at 0°, 30° and 60° in clockwise direction. It can be observed from Fig. 6(a)-6(b) that the differences between P1 and P2 almost keep same, with the maximal coefficient of only 0.0036 dB/°C and 0.000218 dB/με, respectively. The maximal temperature and strain cross-sensitivities of the torsion sensor are calculated to be 3.7 × 10−6 (rad/mm)/°C and 2.26 × 10−7 (rad/mm)/με respectively, indicating the torsion sensor is nearly independent of the temperature and strain.
We also investigate the birefringence induced in the PSFBG when the fiber is under torsion. The birefringence is characterized by monitoring the wavelength separation of the two polarization-peaks of the PSFBG. Figure 7 shows the measured birefringence of the π-PSFBG versus the torsion angle. The original birefringence of the π-PSFBG tested without torsion is 2.16 × 10−4. As seen in Fig. 7, when changing the torsion angle from 0° to 360° with an interval of 30° in the clockwise direction, the measured birefringence exhibits only small fluctuations of within 1.31 × 10−5, indicating that the amplitude difference variations of the two polarization-peaks P1 and P2 are mainly resulted from the change of the state of polarization (SOP) of the input light induced by the fiber torsion. In practical applications, the original polarization state of the input light should be carefully chosen (can be adjusted and defined by the fiber polarizer and the polarization controller) to ensure both of the two polarization dependent peaks can be observed at the same time, otherwise it might be difficult to use their amplitude difference if only one peak can be observed.
4. Analysis and discussion
For a fiber under linear twist (θ = ωz, ω is the twist-rate) shown in Fig. 8, the twisted fiber is regard as a stack of plates with the thickness of δz. Assuming that the optical axes of each plate are at an angle of δθ to the preceding plate and taking the limit δz → 0, the electric field amplitudes (Ax, Ay) of the successive segments at the boundary can be matched, the coupled-mode equations describing the state of polarization of light are obtained :25]:26].
The electric field amplitudes (Ax (L), Ay (L)) of the output light can be described as:
For the input polarization of 45°, the output polarization θ´ of the twisted fiber is:
In the experiment, the π-PSFBG is located in the middle of the twisted fiber, so the output polarization α of the π-PSFBG is:
Consequently, the amplitudes of the two polarization-peaks labeled as P1 and P2 are:
The amplitude difference in linear scale caused by the twist between the two polarization-peaks of the π-PSFBG can be described as:
In the experiment, we then replot the evolution process for P1-P2 under torsion from −360° to + 360° in linear scale in Fig. 9 and use a sine function to fit the data. The curve-fitting result of the experimental data is I = −0.101 + 0.313sin(1.071θ-197°), which basically agrees with the result of the theoretical estimation shown in Eq. (9). The small difference between the theoretical calculation and the experiment might result from the following reasons: In the theoretical calculation, we do not consider the influence of the linear birefringence in the twist fiber. Moreover, the tension of the fiber changes with the twist angle applied on the fiber in the experiment, which also result in the change of the state of polarization.
In conclusion, a novel temperature- and strain- independent optical fiber torsion sensor based on a PSFBG written in a standard single-mode fiber has been proposed and demonstrated in this Letter. By accurately controlling the gap ΔΛ between uniform FBGs, a fourth-order π-PSFBG with a birefringence of 2.16 × 10−4 is fabricated by the line-by-line technique with a femtosecond laser. The responses of the PSFBG sensor to the torsion, temperature and strain are characterized respectively. By simply monitoring the amplitude difference between two polarization-peaks of the PSFBG, the fiber torsion angle and the fiber torsion direction can be simultaneously deduced without temperature and strain confusion. The torsion sensor exhibits a high torsion sensitivity of up to −1032.71 dB/(rad/mm), with the distinct advantages of low cost (no PM fiber or other special fibers needed), small dimension (just ~1.72mm, smallest torsion sensor reported so far), and extremely simple and robust structure (compared with those fragile ones that need splicing a section of special fiber [12–22]), which makes it very attractive for practical applications.
Director Fund of WNLO; National 1000 Young Talents Program, China.
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