We proposed and experimentally demonstrated paralleled Mach-Zehnder interferometers (MZIs) in few-mode multicore fiber (FM-MCF) for temperature and strain discriminative sensing. A section of FM-MCF is sandwich-spliced between two single-mode multicore fiber (SM-MCF) with a rotational offset. The arbitrarily controlled angular misalignment generates intentional intermodal interferences in outer cores of the FM-MCF thus multiple MZI structures are implemented. Experimental results show that the temperature sensitivities are 105.8 pm/°C and 223.6 pm/°C for two outer cores, strain sensitivity is 13.96 pm/με for the outer core 1 and 11.7 pm/με for the outer core 2, respectively. Due to the low condition number of the cross coefficient matrix dependent on the temperature and strain response indexes, the temperature-strain cross sensitivity can be efficiently eliminated. In addition, the structure’s fabrication process is simple, cost effective, and repeatable. The sensing structure can be applied to a wide range of measurements and is expected to develop potentials by building a higher dimensional matrix with more cores.
© 2018 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
In physics, the Mach-Zehnder interferometer (MZI) is an intensively utilized device with variant materials and structures. It has been widely applied in aerodynamics, plasma physics, optical communication and sensing systems for many decades. Various types of fiber-based MZIs are often used in the sensing field, such as micro-cavity type MZI [1, 2], taper or waist-enlarged taper MZI structure [3–6], microfiber based MZI [7–9], and the traditional MZI structure based on conventional single mode fiber (SMF) [10, 11] or photonics crystal fiber [12, 13]. However, all these fiber-based MZIs only support limited spatial channels, and it is difficult to achieve dense integration. Meanwhile, multiple environmental parameters comprehensively affect the MZI spectra wavelength shifts and induce cross sensitivities , which makes it hard to realize an accurate measurement of a single parameter in the complex environments. Many solutions have been proposed to solve this problem. One of the most common methods is cascading dissimilar structures with distinct sensitivities to realize discriminative dual-parameter measurement. For example, a sensor which consists of hybrid FBG/LPG was proposed in . An in-line MZI cascaded with a reflective FPI was formed in special fiber for temperature and curvature discrimination . However, the fabrication processes of the whole structures mentioned above are very complicated and time-consuming. Many procedures are needed in the demodulation process. Besides the different structure cascading technique, two sensors based on SMF-MMF-SMF structure with different taper waists were proposed to realize discriminative measurement . Although they showed different responses to environmental parameter variations and could be used to achieve the discriminative measurement, it still required complex tapering technique and more than one sensor.
Comparing with those aforementioned single-channel techniques, the spatial-division multiplexed (SDM) sensing technique offers an alternative method for multi-parameter sensing. Single-mode multicore fiber (SM-MCF) based MZI structures can provide not only multiple isolated channels to implement spatially independent transmission along the whole fiber, but also paralleled and integrated cores with identical or differential responses to environmental parameter variations. It is beneficial for us to achieve the integration of MZIs in one single fiber and the discriminative multi-parameter measurement by establishing a cross coefficient matrix. For instance, multipath Mach-Zehnder interferometers structure consisting of two identical tapered regions in heterogeneous MCF was proposed . This sensor realized the integration of multipath MZIs and the discriminative measurement between the temperature and strain by dissimilar responses in different cores. However, the single mode cores only support fundamental mode and the taper regions induce coupling between core mode and uncontrolled cladding modes, making the tapered MZIs device unpredictable and less repeatable. On the other hand, the temperature and strain sensitivities of different cores are relative low and the condition number of the cross coefficient matrix is large thus leads to unwanted measurement errors .
In this paper, we have proposed and experimentally demonstrated an integration of paralleled Mach-Zehnder interferometers based on few-mode multicore fiber (FM-MCF). A segment of FM-MCF is sandwich-spliced between two SM-MCF with rotational misalignment. The arbitrarily controlled rotational offset generates intermodal interferences between lower core modes in six outer cores thus implements stable multipath MZI structures. Compared with previously reported offset splicing induced MZI structures in SMF and MCF [10, 19], the FM-MCF interferometers have the benefits of low insertion loss and high stability due to smaller rotation angle and steady intermodal interference pattern. With the help of the compact fan-in/fan-out demodulators, we measure the temperature and strain sensitivities of MZIs in selective outer cores. Then, the temperature and strain can be demodulated by solving the cross coefficient matrix with dissimilar temperature and strain coefficients. Due to smaller effective refractive index differences between guided core modes, the temperature and strain sensitivities have been efficiently improved compared with previous works [14, 19–21], as demonstrated by experimental results. Smaller matrix’s condition number also improve the demodulation accuracy . Meanwhile, the carefully controlled refractive index differences between guided modes leads to a large free spectrum range (FSR) of ~72 nm. Owing to the suitable extinction ratio and the wide FSR of the interference pattern, accurate temperature and strain measurement in a large range can be guaranteed.
2. Fabrication and operation principle
The cross section of the FM-MCF is illustrated in Fig. 1(a), the FM-MCF has seven identical cores where the outer six cores are arranged hexagonally and the cladding diameter, the core diameter and the core pitch are 150 μm, 24 μm, and 42 μm, respectively. The gradient refractive index (RI) profile of the FM-MCF is shown in Fig. 1(b). The value of the RI decreases from 1.476 in the center of the core until it approaches the cladding’s RI of 1.46.
The schematic diagram of the MZI structures based on FM-MCF is shown in Fig. 2. The device fabricated by using the fiber fusion splicer (Fujikura FSM-100P + ) is a sandwich structure: the center section is a FM-MCF segment with length of L while the two sides are SM-MCF connected to the spatial fan-in/fan-out devices. The spatial fan-in/fan-out devices are featured with chemical etching process and fiber bundle technique . Before splicing, a rotation of angle θ for FM-MCF is introduced which can be arbitrarily controlled by the fiber fusion splicer, the rotation accuracy is 0.1 degree. The symmetrical structure of the FM-MCF enables us to achieve the off-center launching in every outer core. Each outer core of the FM-MCF can be served as an independent MZI. At the first splicing point, the light is off-center launched from one of outer cores in the SM-MCF, multiple guided modes are excited in the FM-MCF. At the second splicing point, different guide modes couple back into the lead-out core of the SM-MCF after propagating through the FM-MCF. Due to the mode refractive index differences, optical path differences between guided modes accumulate over the whole FM-MCF. Consequently, paralleled Mach-Zehnder interferometers can be realized in six outer cores. During the fabrication process, many splicing parameters will affect the performance of the FM-MCF based fiber sensor, such as the rotation angle θ, overlap length, discharge power, and discharge time. For example, long overlap length and high discharge power will lead to the deformation of the splicing points. Different θ will influence the insertion loss and the extinction ratio of the transmission spectra. Too large or too small rotation angle will result in the imbalance of the optical power of two guide modes involved in the dominant intermodal interference and lead to lower extinction ratio. Thus, it is important to select an appropriate rotation angle θ. After optimization, when the rotation angle θ for FM-MCF is about 3°, suitable extinction ratio (fringe visibility) and relative low insertion loss are achieved.
After the fabrication process, we use the supercontinuum optical laser (SCS, from YSL Photonics) as the light source and the optical spectrum analyzer (OSA, YOKOGAWA AQ6370C) to monitor the MZI transmission spectra in selective outer cores. Figure 3(a) shows the transmission spectra of three different outer cores with a 36.5 cm MZI segment. The interferometric fringes are quite clear for each outer core. A wide FSR of ~72 nm and the extinction ratios of 5 ~15 dB have been obtained. However, the extinction ratios of other three outer cores’ spectra are less than 2 dB, which means that they are not suitable for the sensing applications and the power of the stimulated lower core mode is very low . The spectra differences are mainly because there is a deviation in the geometrical distribution of outer cores which are supposed to be distributed in the six vertices of the regular hexagon. Figure 3(b) depicts the transmission spectra in outer core 1 with MZI segment length L of 36.5 cm, 43.6 cm, and 68.8 cm, respectively. It’s obvious that the FSR decreases as the length L increases, which can be explained by using the following equation :
In order to investigate the propagating modes contributing to the inter-modal interferences, we prepared several samples with the FM-MCF of different lengths L. The spatial frequency spectrums are obtained by taking Fourier transform (FT) of different transmission spectrums shown in Fig. 3(b). As shown in Figs. 4(a)-4(c), the spatial frequencies are presented as 0.0225 nm−1, 0.0146 nm−1, and 0.0133 nm−1, with the length L of 68.8 cm, 43,6 cm, and 36.5 cm, respectively. Hence, the can be easily derived by using the relation between the effective refractive index difference and the spatial frequency :Fig. 4(c), for the L of 36.5 cm, comparing with those weak peaks in the spatial frequency spectrum, one peak plays the leading role, which indicates that there are mainly two kinds of lower core modes participating in the interference. The of the dominant peak is calculated to be at 10−5 orders of magnitude. From the COMSOL finite element method (FEM) simulation, it corresponds to the refractive index difference between LP21 mode and LP02 mode in the same mode group. Figures 4(a) and 4(b) show the spatial frequency analyses with the length L of 68.8 cm and 43.6 cm, which are consistent with the situation for the length L of 36.5 cm.
To further discuss its working principle, we analyze the sensor’s responses to temperature. The intensity at the output of the corresponding outer core of the fan-out device can be described as:
The phase term of Eq. (3) represents the phase difference between two modes after transmission in the fiber, and it can be described as:23]:23]:
According to Eq. (7), the temperature sensitivity is determined by the and the . To improve the temperature sensitivity, large and smallare necessary. Hence, two guide modes involved in the interference with closer effective refractive indices are preferred. The previously reported SM-MCF based multipath MZIs mainly incorporate core-cladding interferences and the between the core mode and cladding modes are at orders of magnitude [14, 19]. In this experiment, the are calculated to be at orders of magnitude which is relative small. Therefore, this multipath MZIs device has much higher temperature sensitivities. Furthermore, higher sensitivities also can be anticipated by increasing the doping concentration. In practical situation, there is slightly difference in the doping concentrations of outer cores of the FM-MCF and a deviation in the geometrical distribution of outer cores. According to Eq. (7), a slightly change in the will lead to a big change in the temperature sensitivity. So in this case, different outer cores exhibit distinct temperature sensitivities, which are suitable elements for a cross coefficient matrix.
3. Experimental results and discussion
In order to realize the discriminative measurement between the temperature and strain, we chose FM-MCF based MZI structures with the length L of 36.5 cm as the sensor head. The system setup is illustrated in Fig. 5. Light emitting from a YSL Photonics was off-center launched into the outer core of the FM-MCF through the spatial fan-in device, then propagated into the corresponding outer core of the spatial fan-out device. The output spectrum was monitored by the OSA. The sensing structure was placed between two copper plates and the temperature was adjusted by the thermoelectric cooler (TEC). In the meantime, two ends of the sensing structure were clamped to two translation stages which allowed for precise control of the axial strain.
The temperature dependence of the sensor’s spectral characteristic was investigated when the strain was fixed at 0.0 με and the temperature range in our measurements was adjusted from 20 °C to 60 °C with steps of 10 °C. The resonant wavelength dip near 1636.85 nm of the outer core 1 and the wavelength dip near 1659.73 nm of the outer core 2 were selected for discriminative sensing. Figures 6(a) and 6(b) show the wavelength shifts of the selected outer cores (outer core 1, outer core 2). For both outer cores, the wavelength dips linearly shift to the shorter wavelength with the increase of temperature. The spectral response curves are linearly fitted as shown in Fig. 6(c). The temperature sensitivity is 105.8 pm/°C for the outer core 1 and 223.6 pm/°C for the outer core 2. The R-square of both curves are above 0.998. It can be seen from the Fig. 3(a) that the large FSR of ~72 nm guarantees a wide measuring range and effectively avoids the overlapping reading problem. Meanwhile, we also analyzed the strain dependence of the sensor’s spectral characteristic when the temperature is fixed at 30 °C. Figures 7(a) and 7(b) depict the wavelength shifts of two different outer cores with the axial strain increasing from 0.0 με to 1111.1 με with steps of 222.2 με. The wavelength dips for outer core 1 and outer core 2 exhibit blue shift and the wavelength shifts follow a linear behavior with the axial strain increasing. From the linear fitting results in Fig. 7(c), the strain sensitivity is 13.96 pm/με for the outer core 1 and 11.7 pm/με for the outer core 2 and the R-square of each curve is 0.998 and 0.996, respectively.
Owing to the fact that two different outer cores have distinct responses to strain and temperature, the cross sensitivities of temperature and strain can be discriminated by establishing a cross coefficient matrix, as given by :17]. The smaller the condition number of the matrix, the higher the discrimination accuracy. To improve the sensing accuracy, the matrix with small condition number is preferred. In this experiment, the condition number of the cross coefficient matrix is calculated to be 32. It is smaller than the temperature-strain fiber sensors in [14, 25–27]. In order to verify the effectiveness of the temperature and strain discrimination, the fiber sensor was put in a stable environment with the setting temperature is 30 °C and the applied strain is 444.4 με as a reference. Then the temperature was set to be 45 °C and the strain was set to be 66.7 με for detection. and are the wavelength shifts of the outer core 1 and outer core 2 under two conditions, as shown in Figs. 8(a) and 8(b). According to the above-mentioned discriminative measurement theory, Eq. (8) becomes:Eq. (9). The relative error for temperature is 4.8% and for strain is 8.7%. This multipath MZIs device successfully achieves the discriminative measurement between the temperature and strain.
In summary, we designed and fabricated integrated and paralleled Mach-Zehnder interferometers in few-mode multicore fiber (FM-MCF). Thanks to the SDM characteristic of the FM-MCF, this proposed fiber sensor successfully achieves the integration of several MZIs in one single fiber by offset splicing a section of FM-MCF between two SM-MCFs. With the help of the acceptable extinction ratio of 5 ~15 dB and the wide FSR of ~72 nm, the range of temperature and strain measurement can be efficiently improved. The temperature sensitivity of 105.8 pm/°C for the outer core 1 and 223.6 pm/°C for the outer core 2, and the strain sensitivity of 13.96 pm/με for the outer core 1 and 11.7 pm/με for the outer core 2 have been obtained. We successfully realize the discriminative measurement between the temperature and strain by building up a cross coefficient matrix, and the small condition number of the matrix significantly improved the discrimination accuracy. What’s more, the simple structure, cost-effective fabrication process, high sensitivities, and wide measurement range make this compact device a good candidate for practical application. In the future, introducing the offset in X and Y axis in the original basis, improving the FM-MCF manufacturing process such as using the drilling technology  and optimizing the parameters of FM-MCF will enhance the device’s performance and provide more possibilities for the field of multi-parameter discriminative sensing.
National Natural Science Foundation of China (Grant No. 61331010, 61722108, 61775138); Major Program of the Technical Innovation of Hubei Province of China (2016AAA014); the Open Fund of State Key Laboratory of Optical Fiber and Cable Manufacture Technology; YOFC under Grant SKLD1601 and SKLD1706.
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