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This paper presents a novel optical fiber torsion sensor based on dual polarized Mach-Zehnder interference (DPMZI). Unlike the conventional fiber sensor, the proposed sensor is composed of a sensor part and a demodulator. The demodulator is made by a bared single mode fiber (SMF) loop, and the sensor part is a segment of a coated SMF placed before the loop. A mathematical model is proposed based on DPMZI mechanism and from the model when the sensor part is twisted, the E-field rotational angle will bring a quasi-linear impact on the resonance dip wavelength in their matched detecting range. A proof-of-concept experiment was performed to verify the theoretical prediction. From the experimental data, a sensitivity of −0.3703, −1.00962, and −0.59881 nm•m/rad is achieved with the determining range of 12.0936, 7.6959, and 10.4444 rad/m respectively. The sensor which is composed only of the SMF has the advantages of low insertion loss (~-2dB), healthy structure, low manufacture cost, and easy assembly and application.
© 2014 Optical Society of America
1. Introduction
Torsion is one of the most important mechanical parameters of engineering and recently its measurement has attracted considerable research interest. Compared with conventional torsion sensors [1], fiber-optic sensors offer excellent performance for the measurement of various mechanical parameters under quite challenging environments, due to their unique ease of integration and compatibility with the subjects being tested. Consequently, a variety of optical fiber torsion sensors have been reported in recent years [2–22].
The universal principle for the common fiber torsion sensors is based on a segment of birefringence fiber to support circular birefringence in the optical path. When the birefringence fiber is twisted, an additional circular birefringence induced by elasto-optic effect would make the transmission resonance dip shift with the torsion angle [2–9]. For example, the authors embed two segments of multimode fiber and polarization maintain fiber into a Sagnac loop and obtain a sensitivity of 1.630 nm•m/rad within a range of 8.726 rad/m [2]. Hyun-Min Kim et al insert a highly birefringent photonic crystal fiber (PCF) into a Sagnac loop and the measured torsion sensitivity is about 1.014 nm•m/rad within a range of 10.471 rad/m [3]. Weiguo Chen et al splice a segment of side leakage PCF into a Sagnac loop and achieve a maximum sensitivity of 7.959 nm•m/rad with a relatively poor linear fit [5]. Yangying Du et al, based on the polarization-dependent in-line quasi-Michelson interferometer, achieved a torsion sensor with a sensitivity of 0.220 nm•m/rad within a range of 6.283 nm/rad [8]. In another similar scheme, a segment of birefringence fiber that guides linearly polarization mode is spliced between two single-mode fibers. When the birefringence fiber is twisted, the mode field redistributes. And therefore, the transmission resonance dip depth changes with the applied torsion angle [10–13] and the conventional fast Fourier transform (FFT for short) is employed for the torsion rate measurement [14–16]. For example, Zhengyong Liu et al spliced a segment of high-birefringence suspended-core PCF and achieved a torsion sensor. The sensitivity is 16243/rad using the FFT technique within a range of 3.490 rad/m [15]. Orlando Frazão et al spliced a segment of suspended twin-core fiber and achieved a 0.179 dB•m/rad and 0.003/rad using the FFT technique and visibility approaches, respectively [16]. Additionally, the active [17], mechanical [18], and grating-based torsion sensors [19–22] have been reported as well. Their sensing principles are based on pure geometrical deformation.
So far, most of the proposed sensors insert a microstructure into the optical path, i.e., a sandwich structure. However, the inserted part is a relatively weak structure and in most cases they cannot be encapsulated in the polymer coat because the commonly used polymer coat refractive index is higher than that of cladding. Then the cladding mode might be affected and the sensor would be damaged or even lose the ability to sense torsion. In addition to this, different types of fiber might give rise to a large insertion loss and would definitely lead to difficulty in splicing.
To circumvent the aforementioned disadvantages, in this paper, based on the dual polarized Mach-Zehnder interference (DPMZI) principle, we propose a novel fiber torsion sensor. Unlike the conventional fiber sensor, the proposed sensor is composed of a sensor part and a demodulator. The demodulator is made by a bared single mode fiber (SMF) loop and the sensor part is a segment of coated SMF before the loop. The sensor part, i.e., the coated fiber, is very robust, and can effectively overcome the disadvantage of the weakness of its conventional counterpart. Moreover, due to the proposed sensor being composed of SMF only, the insertion loss (the maximum insertion loss is about −2dB in the experiment) can be dramatically improved compared with the conventional counterpart. A mathematical model is proposed for the proposed structure. According to the established model, (a) interference phenomenon can be expected in the transmitted spectrum; (b) the resonance dip wavelength is dependent on the E-field rotational angle, which can be adjusted by torsion performance; (c) the resonance dip wavelength in a matched detecting range possesses a quasi-linear relation with E-field rotational angle; (d) the larger partition coefficient difference value causes resonance dip intensity function asymmetry. A proof-of-concept experiment was performed and in the experiment, a segment of coated SMF is twisted to chirp the E-field rotational angle from 0 to π. A good agreement of theoretical prediction and experimental results can be reached. From the experimental data, the sensitivities in torsion are −0.3703, −1.00962, and −0.59881 nm•m/rad respectively and the determining ranges in torsion are 12.0936, 7.6959, and 10.4444 rad/m respectively. Moreover, other than healthy structure and low insertion loss, the sensor also has the advantages of low manufacture cost, and easy assembly and application.
2. Principle
The bared fiber loop is fabricated by bending a segment of SMF. It is known that the bend fiber is intrinsically leaky and the source of the leakage can be explained by the mismatched velocity problem. We know that two degenerate HE11 core modes propagate inside the straight SMF. When the fiber is bent with a radius of curvature, the core modes will suffer from a disturbance. In order to maintain their mode field in the bend fiber, the wavefront on the outer evanescent tail must travel faster than the wavefront at the centre of the core. Therefore a radiation mode can be coupled from a core mode when the required wavefront velocity on the outer evanescent tail is greater than core mode limitation. The coupled radiation mode will be further confined by the boundary between the cladding and air, and thus a cladding mode can be created. For the SMF, i.e., the cylinder bounder condition, the stimulated cladding mode is cladding LP01. To help our point of view be understood, we use the full vector finite element method [23] to solve the eigenmode in the SMF structure, and the supported LP01 modes in core and cladding are shown in Fig. 1.
Fig. 1 Normalized electric field of the four modes supported by the SMF at a wavelength of 1.55 μm with the red arrows indicating the electric field directions of the four modes.
From Fig. 1, we notice that cladding LP01 mode (see Figs. 1(a) and 1(b)) has a little difference with the core mode LP01 (see Figs. 1(c) and 1(d)). The polarization status in the core region is the opposite of that of the outside cladding region. As a matter of fact, the so-called cladding LP01 mode is a supermode. The outside cladding and air are composed of a waveguide, and the cladding and core are composed of a waveguide as well. In addition, the centre of these two waveguides and their own LP01 mode are both superimposed. So the two modes can create a supermode set based on the theory of supermode. Usually we cannot find the odd modes solution in a SMF structure, because the odd modes have degenerated and become LP01 in the core. This kind of degeneration is not unconditional and it occurs only when the refractive index in the core region is higher than that of the cladding region. As a consequence, only even supermode LP01 can be viewed in the simulation results. Due to the special characteristics of the cladding mode LP01, it can easily be stimulated, when the fiber is bent to a certain value of radius. In addition to this, due to bending resulting in a second-order elasto-optic effect and geometry deformation occurring in the fiber, the two effects modify the refractive index of the fiber and induce birefringence [24]. This birefringence and the cladding mode characteristics give rise to the fast and slow axes of the fiber.
For the proposed sensor, the fast and the slow axes are set along the respective directions of parallel and perpendicular to the bending radius. Therefore, two orthogonal polarized cladding modes can be stimulated with different propagation velocities when a degenerate core mode propagates through the bare fiber loop. One set of lights, including one core mode and one cladding mode, is polarized along the radial direction while the other set is normal to the bending plane. After propagating through the fiber loop, the two set of beams will recombine respectively, and the accumulated optical path difference will cause interference at the output of the fiber loop [25]. Therefore, the bending-induced fast and slow axes will cause DPMZI in the spectrum, and as far as the authors know, this new mechanism is the first of its kind to be proposed. The aforementioned process can be described by the following formula:
where Is and If stand for the light intensity in the slow and fast axes respectively, which equal (Es1)2 + (Es2)2 + 2Es1Es2cos(2πΔnsL/λ) and (Ef1)2 + (Ef2)2 + 2Ef1Ef2cos(2πΔnfL/λ), respectively. The I stands for the light intensity summation in the slow and fast axes. The terms Es1, Es2, Ef1, and Ef2 are the core mode and cladding mode electronic complex amplitudes in slow and fast axes. The Δns and Δnf are the differences of the effective refractive indices between the core mode and cladding mode in the slow and fast axes respectively; the λ is the operating wavelength; the L stands for the traveled distance of the core mode and cladding mode in the slow and fast axes. We assume the light polarization is linear polarization and the E-field rotational angle is φ. As a consequence, the electronic complex amplitude in slow and fast axes are related and their amplitudes are determined by φ. Furthermore, assuming that the partition coefficients between the core mode and cladding mode along fast and slow axes are α and β, then the core mode and cladding mode electronic complex amplitude in fast and slow axes can be written as Es1 = αsin(φ), Es2 = (1-α)sin(φ), Ef1 = βcos(φ), and Ef2 = (1-β)cos(φ). Therefore, the spectrum interference can be described as:here Idc stands for the direct current component, which equals (Es1)2 + (Es2)2 + (Ef1)2 + (Ef2)2. In the simulation, we ignore the impact on Idc. The numerical solution is used to analyze Eq. (2) because it is impossible to obtain an analytical solution. We analyze the E-field rotational angle φ impact on the resonance dip wavelength shift and the resonance dip intensity based on the two parameters—the intrinsic phase difference (Δϕ = 2πΔnsL/λ-2πΔnfL/λ) and the partition coefficient difference (α-β). As shown in the following sections, the bared fiber loop spectrum resonance dip wavelength is dependent on φ, and its value possesses a linear trend with twisting fiber before the loop [26]. Consequently, the torsion sensor can be achieved by the proposed structure.2.1 Intrinsic phase difference
We set Δns = 10−3 + κλ/L and Δnf = 10−3, R = 7.5 mm and L = 2πR, λ ranging from 1530 nm to 1570 nm, and α = β = 0.5 for convenience. The parameter κ determines the intrinsic phase difference and its value ranges from 0 to 0.5 corresponding to 0 to π, i.e, Δϕ = 2πκ. The E-field rotational angle φ ranges from 0 to π/2 corresponding with x polarization to y polarization. The simulation results are shown in Figs. 2(a) and 2(b). The Y axis in Fig. 2(a) normalizes to the free spectrum range for comparing with other κ values. It can be seen from Fig. 2(a) that the resonance dip wavelength is a monotonically increasing function with the φ increasing, and the increasing rate is determined by Δϕ, i.e., the larger value, the faster increasing rate. Notice that these curves possess a quasi-linear trend in the center of them and these sections can be used for sensing torsion. Figure 2(b) exhibits the changes in intensity with φ increasing and a peak shows up in the center part. The peak values are also determined by Δϕ, and a larger Δϕ has a sharper peak. Furthermore, it can be seen that it is a trade-off between the sensitivity and the determining range. For making the resonance dip shift processing clearly, we exhibit an example (Δϕ = π/2) in Fig. 3. It can be found that the resonance dip wavelength has a red shift with the φ increasing and its intensity first increasing and then decreasing.
Fig. 2 Resonance dip wavelength and intensity changing with E-field rotational angle φ increasing in a series of Δϕ (a) resonance wavelength as functions of E-field rotational angle; (b) resonance intensity as functions of E-field rotational angle.
2.1 Partition coefficient difference
In order to investigate the effects of the partition coefficient difference, α-β, on the spectrum dips, we fix κ = 0.125 and chirp β from 0.1 to 0.5, and keep the same value for the other parameters in section 2.1. The resonance dip wavelength and intensity information are extracted and shown in Figs. 4(a) and 4(b). In Fig. 4(a) we can see that the resonance dip shifting possesses a monotonically increasing trend with the φ increasing, which remains the same with Fig. 2(a). In contrast, a slight shift at the center point can be noticed, especially when the partition coefficient difference α-β is close to 0.4. The center point position with α-β decreasing is shown in the inset of Fig. 4(a). Notice that the center point shift means the quasi-linear section moves, but fortunately whatever the partition coefficient changes to (except for α-β = 0.5), a quasi-linear section can be found. In Fig. 4(b) we can see that a larger partition coefficient difference causes a more asymmetrical intensity curve. For example, when α-β is close to 0, the curve is a non-monotonic function of E-field rotational angle and the curve is an asymmetrical function. With the α-β value increasing, the asymmetry trend becomes more apparent. Especially when α-β is close to 0.4, the curve becomes a monotonic function with the E-field rotational angle increasing. In order to show these two kinds of processes intuitively, we take α-β = 0.4 and 0 respectively as two examples and shown them in Figs. 5(a) and 5(b). It can be seen from Fig. 5 that when α-β = 0.4, the resonance dip wavelength gets a red shift with φ increasing, and its corresponding intensity has a monotonic decrease with φ increasing. In contrast, when α-β = 0, the resonance dip wavelength gets a red shift with φ increasing as well, but its corresponding intensity is a non-monotonic change with φ increasing.
Fig. 4 Resonance dip wavelength and intensity change with E-field rotational angle φ in a series of α-β (a) resonance dip wavelength as functions of E-field rotational angle; (b) resonance dip intensity as functions of E-field rotational angle.
Fig. 5 Resonance dip shifting processes when (a) κ = 0.125 and α-β = 0.4; (b) κ = 0.125 and α-β = 0.
In conclusion, whatever values the intrinsic phase difference and the partition coefficient difference are, the resonance dip wavelength possesses a quasi-linear relation with the E-field rotational angle in its matched E-field rotational angle range. Therefore this kind of quasi-linear range can be utilized to sense torsion performance. The intrinsic phase difference and the partition coefficient difference have an effect on the detecting range, the sensitivity, the center position of the quasi-linear relation, and the resonance dip intensity. A larger intrinsic phase difference value causes a larger detecting range and a smaller sensitivity, and vice versa. A larger difference between two polarized partition coefficient differences gives rise to a smaller detecting range, a large sensitivity, and a more severely asymmetrical function of intensity, and vice versa. In addition, notice that it is a trade-off between the detecting range and the sensitivity.
3. Experimental test
The mechanical twister consists of a fiber holder attached to the translation stage and a dial with a cooper pillar (reference to Fig. 6 and [27] for details). In order to decrease tension and fraction force, we pre-process the cooper pillar and make it move smoothly in the dial by applying 0.3 N [28]. Tension and fraction force can be decreased but cannot be avoided in the measurement setup. Fortunately, 0.3 N is very small and it has little impact on the experimental results. During the measurement process, the fiber is fixed on the fiber holder while the fiber is kept straight by moving the translation stage. In the experiment, considering the fragility of the fiber loop, a minimum radius size of 7.5 mm is determined to acquire the spectral interference. That is to say, if the fiber loop radius is larger than 8 mm, the interference will not occur. However, the bare fiber is very fragile when its radius is less than 7 mm. The length l between the dial and fiber holder is about 6.35 cm and the twist angle is turned from −32° to 32°. According to the definition of twist rate [18], the calculated value of twist rate should be about −8.8 rad/m to 8.8 rad/m.
Fig. 6 Schematic diagram of the proposed torsion sensing system. (a) Experimental setup. (b) Photograph of the sensor.
The experimental results are shown in Fig. 7. In order to observe the three dips in detail, we magnify and plot them in Fig. 8. From Fig. 7, it should be noted that three dips are presented in the transmission spectra, and for clarity they are respectively specified as dips a, b, and c from left to right. When the dial turns counterclockwise or clockwise, the transmission spectrum exhibits red shift or blue shift accordingly. We find that the three dips’ wavelength shift satisfies the aforementioned principle. Then we extract the dips’ wavelength and intensity information, and perform a linear fitting on the central part of the experimental data (see Figs. 9(a)-9(c)).
Notice that the dip a has a slight ripple wave (see Fig. 8(a)) and consequently the resonance dip wavelength shift has a relatively worse linear trend than the others. The reason is in the short wavelength region, the high order cladding modes can be stimulated easily than long wavelength region. For comparing the sensitivity and the determining range, we make a list of the three dips’ information in Table 1. From Table 1, we can see that the largest linear rate has the smallest range, and the smallest linear rate possesses the largest range. The measured trade-off between sensitivity and detecting range is consistent with theoretical derivation.
Table 1. Sensitivity and detecting range for dip a, b, and c
4. Conclusion
In conclusion, a novel torsion sensor based on the DPMZI mechanism has been proposed and experimentally demonstrated. Unlike the conventional fiber sensor, the proposed sensor is composed of a sensor part and a demodulator. The demodulator is made by a bared SMF loop, and the sensor part is a segment of coated SMF placed before the loop. A mathematical model is proposed for the sensor. According to the model, several resonance dips show up in the transmission spectrum and the resonance dips’ wavelengths possess a quasi-linear relation with the E-field rotational angle in its matched detecting range. It is known that the twist performance can adjust the E-field rotational angle. As a consequence, the sensor part, i.e., the coated SMF, can sense torsion performance by tracing the dips’ wavelengths. An intuitive method can help us have a better understanding of the proposed sensor structure. Due to the sensor consisting of only one type of fiber, the power distribution in the two linear polarizations is dependent on the E-field rotational angle only. Therefore the resonance dip wavelength dependent on the E-field rotational angle can be founded in theory. The proof-of-concept experiment shows that the torsion sensitivities are −0.3703, −1.00962, and −0.59881 nm•m/rad respectively, and the torsion determining ranges are 12.0936, 7.6959, and 10.4444 rad/m respectively. Moreover, the sensor has the advantages of low insertion loss (~-2dB), robust structure, low manufacture cost, and easy assembly and application.
Acknowledgments
This work was jointly supported by the National Natural Science Foundation under Grant Nos. 11274181, 10974100, 10674075, 11274182, 61405179, 61203204, 11004110, the Doctoral Scientific Fund Project of the Ministry of Education under Grant No. 20120031110033 and by the Tianjin Key Program of Application Foundations and Future Technology Research Project under Grant No.10JCZDJC24300, the 863 National High Technology Program of China under Grant No. 2013AA014201, the Opening Project of Key laboratory of Optical Information Science and Technology, Ministry of Education under Grant No. 2014KFKT001.
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