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Abstract
In this paper, we report a novel in-fiber Mach-Zehnder interferometer based directional torsion sensor, in which a section of two-mode fiber is sandwiched between two single mode fibers by over core-offset splicing technique. The variety of fringe visibility demonstrates the strong dependence on offset and fiber length. For the first time the near zero visibility at 0° rotating state is obtained by fine offset-modulation. The experimental results show that, with 0° turning point, the counter-clockwise to the clockwise direction can be recognized by the reversal from peak to dip of fringes. Moreover, a competitive sensitivity of 21.485 dB/(rad/cm) is gained with high linearity and low-temperature crosstalk in the range from −40 rad/m to 40 rad/m. Without any pre-twisting, our fiber torsion sensor is small size, ease of fabrication, cost efficiency and very potential in the applications of industrial and artificial intelligence.
© 2019 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
Fiber torsion sensors have been widely used in the fields of aerospace engineering, industrial monitoring and artificial intelligence due to the merits of low-cost, ease of fabrication and immunity to electromagnetic interference. Various schemes based on long-period fiber grating (LPFG) [1–3], polarization-maintaining fiber (PMF) [4], multicore fiber [5,6], photonic crystal fiber (PCF) [7–9], Sagnac interferometer (SI) [10,11] have been extensively reported and investigated. Wherein, the Sagnac-loop structure is viewed as one of the stable and practical schemes with direction discrimination by means of measuring the twist-induced birefringence changes in non-circular symmetric fiber-core (e.g., PMF) [12]. The highest sensitivity of 3.2565 nm per degree is demonstrated in a SI structure based on a piece of femtosecond laser-induced low birefringence single-mode fiber (SMF) [13]. Recently, the novel helix/twisted PCFs have been developed and present the unique capability in torsion sensing and helical grating based schemes are continuously studied to further enhance the torsion sensitivity [14–16]. It is worth noting that the above wavelength-modulated schemes need monitoring the changes of transmission spectrum by an expensive spectrometer and may be accompanied by the crosstalk from temperature and strain.
Comparatively, the intensity-modulation based schemes are more practical for actual measurement through a cost-effective power meter. By introducing a simple fiber Lyot filter, the torsion sensitivity of 20.34 dB/rad is exhibited in [17]. And the direction-discrimination capability is realized in the structures based on elliptical-core few-mode fiber (FMF) and partially silver coated hollow core fiber [18,19]. Furthermore, Fu. et al. reported a promising directional torsion sensor based on intensity modulation, in which the asymmetric helical LPFG is fabricated by CO2 laser [20]. And under a pre-torsion angle of 73°, the twist direction is easily recognized by the turning of fringe visibility in the range from −50 rad/m to 50 rad/m.
In this paper, to reduce the limitation of pre-twisting, an in-fiber Mach-Zehnder interferometer (MZI) based directional torsion sensor is theoretically and experimentally demonstrated, in which a core-offset two-mode fiber (TMF) is sandwiched between two SMFs. The comprehensive torsion measurement is performed and the dependence of fringe visibility on offset and fiber length is theoretically and experimentally investigated. For the first time the near zero visibility at 0° rotating state is obtained by fine offset-modulation. The experimental results show that, with 0° turning point, the counter-clockwise (CCW) to clockwise (CW) direction can be recognized by the reversal from peak to dip of fringes. And under the matched offset and fiber length, a competitive sensitivity of 21.485 dB/(rad/cm) is gained in the range from −40 rad/m to 40 rad/m, with high linearity and low-temperature crosstalk.
2. Principle
FMFs have been frequently adopted in the studies of mode converter and excitation of orbital angular momentum [21–24]. For fiber-optic sensing, FMF based modal interferometers are completed by means of the techniques of side-polishing, etching, tapering and gratings [25–29]. We here fabricate the TMF based in-fiber MZIs by core-offset splicing technique and the distribution of guide and cladding modes are simulated by beam propagation method. As shown in Fig. 1, a piece of TMF (LP01 and LP11 modes, http://www.yofc.com) is respectively spliced to the lead-in and lead-out SMFs with the symmetric core-offset value (α) by a commercial fusion splicer (KL 300T). Then the incident light is split into the core and cladding of TMF at the first offset joint. The excited cladding mode (LP21 mode) and core mode (LP01 mode) are recombined and interfered at the 2nd offset joint. Due to the difference of refractive indexes (RIs), a stable MZI is formed in lead-out SMF. Additionally, the inset shows the adopted TMF consists of the fiber-core (p1), inner-cladding (p2), ring (p3) and outer-cladding (p4), and their diameters are 14, 26, 38, and 125 µm. The corresponding RIs at the wavelength of 1550 nm are given as 1.4485, 1.444, 1.435336, and 1.444, respectively [27].
Fig. 1. Schematic diagram of TMF-MZI. The insets: cross-section at splicing point and the excited modes in fiber core and cladding.
We then define Ico and Icl as the intensities of the fiber core and cladding modes, k1 and k2 as the split and combine ratios, respectively. Considering the symmetry of structure, we set k1= k2= k (where k is a constant), accordingly $ {I_{cl}} = {k^2}{I_{co}}$. Thus the light intensity of TMF-MZI is expressed as
Fig. 2. (a) The relationship between visibility and split ratio; simulated transmission spectra with (b) 0 < k ≤ 5 and (c) 10 ≤ k ≤ 100; the torsion response of visibility with different (d) split ratio and (e) fiber length.
3. Experiment and results
As shown in Fig. 3, the fabricated sensor head is connected with a broadband source (BBS, with the range of 1300-1700 nm) and an optical spectrum analyzer (OSA, Agilent 86142B, with a resolution of 0.06 nm/0.01 dB). Three samples are prepared for comparison and characterization with a similar core-offset (α = ∼6 µm) but different length of TMF (L = 7, 10 and 14 cm, respectively). The TMFs are tightly fixed by fiber holders to prevent the effect of curvature and these TMF-MZIs are respectively rotated by an electric rotator in the range from −200° to 200° with the step of 20°. The distance between the holder and rotator is l = 35 mm to get a large range of torsion. For clarity, their transmission spectra under twisting are illustrated only in the range of 1500-1600 nm.
In Figs. 4(a)–4(c), the periodical fluctuations of fringe intensity are observed with the varied θ, which is consistent with Eq. (4). Also similar to [7] and [9], the variations of fringe intensity and their corresponding frequency spectra in linear response range are given in Figs. 4(d)–4(f). In detail, for a small L (=7 cm), four island-like fringes are linked together and Fig. 4(a) shows their intensities almost vertically decrease/increase during the clockwise/counter-clockwise twisting. Furthermore, in CW direction, for the fringe located at ∼1550 nm, it gradually drops from the peak to dip and the intensity decreases from −8.454 to −24.525 dBm. So the variation of fringe visibility (ΔV) is equal to 16.071 dB. Comparatively, the wavelength red shifts ∼2.2 nm (from 1552.4 to 1554.6 nm). Similarly, as shown in Fig. 4(d), the intensity of fringe at 1530 nm is monotonously increased from −23.914 to −8.054 dBm (ΔV = 14.86 dB), but with a larger wavelength shift (∼5.4 nm). Moreover, two near zero visibility curves (ΔV < ±0.5 dB) at θ = 0° and −60° are found in these two fringes. This means that, without any pre-twisting, the torsion direction can be easily discriminated by the fringe turning from dip/peak to peak/dip.
Fig. 4. Transmission and frequency spectra of different fiber lengths with α = ∼6 µm. (a) and (d) L = 7 cm, (b) and (e) L = 10 cm, (c) and (f) L = 14 cm. The insets in (d), (e) and (f) show the variations of fringe intensity.
Further, in Fig. 4(b), we observe the “four islands” change to be “three butterflies” when L = 10 cm because the large variations in terms of intensity and wavelength are simultaneously generated with the added shear strain. More interestingly, when L is increased to 14 cm, a trade-off spectrum is presented in Fig. 4(c) where Δλ or ΔV has a great but alternative variation in each sub-region (∼20 nm). From the insets of Figs. 4(e) and 4(f), the variations of fringe visibility are 8.11 (at ∼1540 nm) and 7.32 dB (at ∼1545 nm), respectively. It is fortunate that the near zero visibility curves are also found in Figs. 4(b) and 4(c). From Table 1, the turning points of three sensor heads respectively appear at 0°/−60°, 100° and 120°. The maximum average of visibility variation (Ave.ΔV) occurs when L = 7 cm but with the large ranges of >20 nm. Inversely, when L = 10 and 14 cm, the effective near zero visibility curves are obviously compressed within the ranges of ∼10 nm, although the smaller values of Ave.ΔV are presented.
Table 1. Positions and ranges at turning points
The above experimental results indicate that the positions of turning points are highly related to L and α. To reveal this, through fine offset-modulation, series of experiments are performed with the varied α (=5∼12 µm) for the given L. From the results in Figs. 5(a)–5(c), multiple turning points of V${\approx} $0 are gotten by offset-modulation in all tested samples, but the 0° turning points are found only for the matched L and α. Their detail values are [7-cm, 6.02-µm], [10-cm, 12.3-µm] and [14-cm, 10.51-µm], respectively. It is obvious that for most samples the pre-torsion is necessary for being as a directional torsion sensor, but the samples with 0° turning points are able to discriminate the twisting direction without any pre-torsion. Further, according to this nonlinear relation between L and α, new 0° turning points are predicted and experimentally gained in the sensor heads with the parameters of [8.2-cm, 8.85-µm], [12-cm, 14.1-µm], [16-cm, 6.72-µm] and [18-cm, 7.3-µm]. These values of L and α are then fitted in Fig. 5(d) and an approximate sine-function is satisfied with the correlation coefficient R2=0.922, that can be written as
where B = 3.9, w = 5.2 and L0=8.9, respectively. Assuming ${\theta _k} = \frac{\pi }{w}({L - {L_0}} )$ and $k = \gamma \alpha $ (where $\gamma $ is a constant), we then get $k = \gamma B\textrm{sin}{\theta _k}.$ Therefore, the initial visibility can be expressed as $V = \frac{{2\gamma Bsin{\theta _k}}}{{1 + {{({\gamma Bsin{\theta_k}} )}^2}}}$. Under the state of over-core-offset, Eq. (4) is changed as Equations (6) and (7) show that V is related to fiber length and the introduced ${\theta _k}$ by core-offset splicing may partly compensate the variations of coupling coefficient and insertion loss under rotating state [20].Fig. 5. Turning points by offset-modulation at (a) L = 7 cm, (b) L = 10 cm and (c) L = 14 cm; (d) the relationship of fiber length and offset.
Further, the sensor heads with 0° turning point (denoted by S1 [7-cm, 6.02-µm], S2 [10-cm, 12.3-µm] and S3 [14-cm, 10.51-µm]) are selected out and their normalized intensities response to the varied torsion are compared in terms of sensitivity and linear response range. As shown in Fig. 6(a), the visibility of S1 is slightly increased (< 1.1 dB) in the region −80 ∼ −60 rad/m, but decreased in the region 40 ∼ 80 rad/m. Comparatively, in the range of −60 ∼ 40 rad/m, its visibility quickly grows from −9.39 to 4.42 dB, the corresponding sensitivity is 13.81 dB/(rad/cm) with high linearity (>0.99). Similarly, in Fig. 6(b), S2 has two insensitive regions (−70 to −40 rad/m) and (40 to 70 rad/m), but ΔV reaches 17.118 dB in the sensitive range from −40 to 40 rad/m. Thus the torsion sensitivity of S2 reaches 21.485 dB/(rad/cm) with the linearity of >0.98. Nevertheless, Fig. 6(c) shows that S3 has a wide linear-response range from −60 to 60 rad/m, but the sensitivity is merely about 8.92 dB/(rad/cm).
The transmission spectra of S2 are then shown in Fig. 7. Similar to Fig. 4(a), four linked “islands” (denoted by dip-A to dip-D, respectively) are uniformly distributed in the range of 1510-1570 nm with a more flat near zero visibility curve at 0 degrees. By calculation, for dip-A (1514 nm), dip-B (1528 nm), dip-C (1545 nm) and dip-D (1559 nm), their fluctuations of near zero visibility curves are 0.53, 0.68, 0.72 and 0.43 dB, respectively. So the average fluctuation is about ±0.59 dB covered in the whole 60-nm range. According to Eq. (5), the calculated k is equal to 28.57, and the deviation of near zero visibility curves from the theoretical value in Fig. 2(c) is about ±0.3 dB.
In addition, four “islands” present high consistence in terms of intensity and wavelength. As shown in Fig. 8(a), in CW direction, dip-B gradually decays from −0.47 to −18.06 dBm. And in CCW direction, the intensity of dip-C is reduced from −0.44 to −17.614 dBm. This small difference of ΔV (0.416 dB) guarantees the measurement precision of torsion is restrained within 0.005 dB/(rad/m). Besides, the fabricated sensor is almost insensitive to torsion in term of wavelength. The small difference of wavelength changes among the dips may be resulted from the difference of λdip (see Eq. (3)) and the possible device dependence [33]. Figure 8(b) shows dip-B has the maximum shift of wavelength (∼3.05 nm) in the range from −40 to 40 rad/m. The corresponding wavelength response of our sensor is less than 0.038 nm/(rad/m).
Additionally, the fabricated torsion sensor (including the lead-in and lead-out fibers) is placed into a temperature chamber (LICHEN, 202-00T, China) with a resolution of ±0.5°C and its response of temperature is tested and characterized. Figure 9(a) shows the transmission spectra of dip-B (located at 1526.955 nm) under different temperature. It is worth noting that the initial fringe visibility is about 8.344 dB under a loose state. From Fig. 9(b), the fringe is hardly wavelength-shifted with the increased temperature, but there is a slight visibility-increment of ∼1.211 dB in the range from 20 to 80 °C. The calculated temperature response is 0.02016 dB/°C with the linearity of 0.998. Thus in our sensor the cross-sensitivity from temperature is constrained within ∼0.00094 (rad/cm)/°C. Moreover, the performance comparisons among the reported torsion sensors are given in Table 2. It is obvious that, besides the feature of non-pre-torsion and direction-discrimination, our sensor achieves the competitive sensitivity and low-temperature crosstalk within a wide linear response range (from −40 rad/m to 40 rad/m), simultaneously.
Fig. 9. (a) Transmission spectra of S2 and (b) responses of wavelength and visibility with the varied temperature.
Table 2. Performance comparison of the reported torsion sensors
4. Conclusions
In conclusion, a TMF-MZI based directional torsion sensor is proposed and fabricated by over-core-offset splicing technique. The comprehensive numerical simulation and tests on twisting are conducted and multiple 0° turning points are theoretically and experimentally obtained under the matched fiber length and offset. The experimental results show that, without any pre-twisting, the torsion direction can be easily distinguished by the reversal from peak to dip at 0° turning point. The obtained near-zero visibility curve has the fluctuation of ±0.59 dB. Moreover, the torsion sensitivity up to 21.485 dB/(rad/cm) is gained with high linearity in the range from −40 rad/m to 40 rad/m. the crosstalk from temperature is constrained within 0.00094 (rad/cm)/°C. Besides, our sensor has the merits of compactness, ease of fabrication, cost-efficiency, which is very practical for the applications of torsion sensing and measurement.
Funding
National Natural Science Foundation of China (61302075, 61675066); Natural Science Foundation of Heilongjiang Province (QC2015068).
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