A novel, simple, and compact optical fiber directional bending vector sensor based on Mach-Zehnder interferometer (MZI) is proposed and experimentally demonstrated. The device consists of a piece of seven-core photonic crystal fiber (PCF) sandwiched between two single mode fibers (SMFs) with a lateral offset splicing joint that covering two cores of PCF. Bending sensitivity of the seven-core PCF based MZI is changed by an axial rotation angle, which shows its capacity for recognizing positive and negative directions. Within a curvature range of −7.05 m−1 to 7.05 m−1, the calculated bending sensitivities of two resonant central wavelengths with opposite fiber orientations are 1.232 nm/m−1 and 1.174 nm/m−1, respectively. This novel MZI is formed by invoking interference between the LP01-like supermode and other higher order supermodes in the core, which leads to insensitive to ambient refractive index (ARI). We have also investigated the transmission characteristics of the sensor with the temperature change.
© 2013 Optical Society of America
Owing to the distinct advantages of high sensitivity, good physical strength or low cost, optical fiber bending sensors have been developed in multi-field applications, such as structural deformation, intelligent artificial limb and mechanical engineering. In the past fifteen years, some types of bending sensors have been proposed based on long period fiber grating (LPFG) , fiber Bragg grating (FBG) , tilted FBG , MZI , etc. Usually, the fabricating process of the grating-based curvature sensors, in spite of the kind of fiber where they are inscribed, is relatively complicated and high frequency CO2 laser or UV laser is usually needed [5, 6]. In this regard, the MZI-based curvature sensors as alternatives have attracted lots of attentions.
Generally, the structure of the MZI-based curvature sensor consisting of an optical fiber placed between two optical fiber mode-coupling devices, is relatively simple and easy to fabricate. Since the curvature applied on the MZI and affects the two arms differently, the optical path difference will be changed. Moreover, different types of these devices have widely been proposed and studied, such as fiber lateral-offset splicing , two identical fused fiber tapers  or multimode fiber combined with a LPFG , etc. Actually, there are few reports about direction recognition bending sensing with MZI in the past few years until S. Zhang et al. presented a fiber-optic directional bending sensor based on MZI exploiting lateral offset and up taper in SMF in 2012 . However, these MZI-based bending devices mentioned above usually excite the cladding mode, which is sensitive to ARI variation, so that the cross sensitivity of ARI is a critical disadvantage.
Multicore PCFs, because of their extreme design flexibility, decreased heat-induced beam distortions and large effective mode area, have made possible the development of new optical devices for a wide range of applications, such as nonlinear media in supercontinuum source , Q-switched  and phase-lock  multicore PCF lasers or demonstration in interconnection system . Recently, a few works utilizing multicore PCFs have been presented in the sensing field. For example, in 2009, a twin core PCF based in-line MZI sensor immunity to bend-induced intensity fluctuation was demonstrated and its strain sensitivity was negative and wavelength-dependent . An ARI sensor with a high sensitivity of 30,100 nm/RIU has been realized based on a directional coupler architecture in a post-processed PCF . And it is noteworthy that bending sensors based on LPFG are usually with a high ARI sensitivity due to the propagational property of cladding mode is sensitive to the surrounding. In addition, the design flexibility of the multicore PCF facilitates the creation of asymmetric core structure that permitting the curvature measurement .
In this paper, we demonstrated a simple and cost-effective ARI-independent bending vector sensor based on MZI using seven-core PCF. The proposed novel sensor is simply fabricated by splicing the seven-core PCF to SMF with a lateral offset splicing point that covering two cores of PCF. This technique enables the possibility to break the cylindrical symmetric geometric structure of the seven-core PCF, which in order to make the distribution of the supermode asymmetric, and thus LP01-like and higher order LP11-like supermodes in the core are separated and make interference from each other. For the first time to our knowledge, the key advantages of this sensor are related to the ARI insensitivity and the capability of bending vector sensing in one dimension. The temperature sensing characteristics of the MZI are also experimentally investigated.
2. Sensor fabrication and operation principle
The scanning electron micrograph of the cross section of seven-core PCF we utilized, which is produced by Yangtze Optical Fiber and Cable Corporation, is shown in the inset of Fig. 1. The PCF has seven pure silica cores and a high air filling micro-structured cladding formed by air holes in silica. The diameter of each silica core, the air holes, the pitch of air holes, and the outer cladding are around 3.8 μm, 1.71 μm, 2.45 μm, and 133 μm, respectively. The diameter of the microstructure which includes two adjacent cores is about 7.8 μm. It is similar to the core size (9 μm) of conventional SMF-28.
The propagation mode property considering the material dispersion of silica for seven-core PCF is carried out by the full-vector finite element method with the commercial software COMSOL Multiphysics. Simulated effective mode indices of the supermodes  versus wavelength are plotted in Fig. 1. The blue and red regions represent the LP01-like and LP11-like supermode band, respectively. The two supermode bands are distinguished by the calculated mode field distribution in the seven cores of PCF shown in Fig. 2. Some typical LP01-like and LP11-like supermodes profiles at 1550 nm of different orders are demonstrated in Figs. 2(a)-2(c) and Figs. 2(d)-2(f), respectively. Each order of supermodes in a certain band can be considered as a linear combination of modes with specific phase relationships of the electric field distribution. The black curve in Fig. 1 represents the effective index of fundamental space filling mode (nFSM) . It shows that the effective indices of LP01-like and LP11-like supermodes are higher than nFSM, thus LP01-like and LP11-like supermodes are permitted as guided supermodes in seven-core PCF.
The structure of the MZI with seven-core PCF is depicted in Fig. 3. To construct the device, a short length of unjacketed seven-core PCF is spliced between two SMFs with a commercial fusion splicing machine (FITEL S175). Light is injected into the seven-core PCF from Hi-1060 fiber (core size of ~6 μm) and some supermodes are excited at the first splice point of PCF. The mode field of Hi-1060 fiber used in our experiments is closer to that of single core of PCF than SMF-28, which is in favor of obtaining a higher coupling efficiency. At the second splice point between seven-core PCF and SMF-28, a certain intentional lateral offset fusion splicing is carried out manually with the splicer. Furthermore, to obtain the strong interference between two adjacent cores, the fiber core of SMF-28 should cover the two cores named out-core and center-core as much as possible, as shown in Fig. 3. Figure 4 shows the transmission spectrum evolution of the MZI with a ~4 mm long PCF within the lateral offset value of ~5 μm. It can be seen that the dips of interference fringe become deeper as the lateral offset increases at the beginning. A good fringe visibility of the MZI can be achieved when the lateral offset value is increased to ~4 μm. The interference strength becomes weaker with lateral offset value of ~5 μm. So, the lateral offset value is optimized to be ~4 μm in the experiments which agree well with the condition that the fiber core of SMF-28 should cover the out-core and center-core of PCF.
The excited supermodes would travel along the two cores and then are coupled back into the core of SMF-28. The difference in the effective refractive index of the supermodes that propagated along the PCF results in different optical path lengths of the interferometer arms. Therefore, a kind of MZI with seven-core PCF is formed through exciting and coupling the supermodes by lateral offset splicing. The accumulated phase difference between two supermodes can be expressed as :
The MZIs with seven-core PCF of different interference lengths (e.g. ~4 mm, ~10 mm, and ~34 mm) were fabricated at room temperature, and the transmission spectra without bend are shown in Figs. 5(a)-5(c). Strong interference pattern and good fringe visibility can be seen from Figs. 5(a)-5(c) and the interference fringes become denser with the increase of interference length. The maximum fringe visibility of the interference resonance dips exceeds 15 dB. Moreover, some minor dips inside main dips can also be observed in Figs. 5(a)-5(c), which indicated that multiple LP01-like and LP11-like supermodes contribute to the interference  and it is the interference superposition of some supermodes. The insertion loss (the minimum value of ~10 dB) is a little higher due to the lateral offset splicing and the mismatch of mode fields between SMF and seven-core PCF.
3. Experiments and discussions
The experimental setup for measuring the curvature characteristics of the MZI with seven-core PCF is shown in Fig. 6(a). A broad-band SLD optical source (1250~1700nm, B&A Technology SL3200, China) and an optical spectrum analyzer (YOKOGAWA AQ6370B) are connected to the MZI to monitor the transmission spectra as the curvature varies. The MZI under test is positioned at the middle of a section of fiber, and then two ends of the fiber are fixed at two graduated rotational fiber holders, respectively. As one translation stage moves inward to induce bending, the fiber bends toward the –Y axis direction and is normally approximated as an arc circle. Two heavy plates are placed on both sides of the fiber closely in order to ensure that the fiber does not bend to any other orientation. The resulting curvature (C) of the sensor can be defined as :Figure 6(b) shows the four fiber orientations used in the experiments.
The modes of a curved waveguide can be determined through the use of an equivalent straight waveguide (ESW) whose refractive index profile is modified from the bent waveguide’s through a conformal transformation . The geometry and refractive index profile of curved seven-core PCF along –Y axis direction are shown in Fig. 7. The refractive index distribution for y <<R can be expressed approximately by :21, 22]. Moreover, the supermodes that propagate along the center-core will experience a longer transmission path than that propagate along the out-core. Therefore, the OPD between the supermodes will increase, resulting in a red shift in the transmission spectra , as shown in Eq. (2). On the contrast, a blue shift occurs in the transmission spectra for the 180° orientation case. For this reason, the MZI with opposite OPD changes induced by the curvature of inverse axial rotation angles of the fiber makes it possible to recognize the bending direction. Thus, we use this kind of MZI to develop a one-dimensional bending vector sensor.
The MZI with a ~4 mm long seven-core PCF is used to measure the transmission spectral responses to variations of curvature for different axial rotation angles of the fiber. All the experimental data are calculated by the optical spectrum analyzer using the 3dB central wavelength method. We have traced the resonant central wavelengths at 1505.84 nm, 1536.24 nm, and 1580.15 nm of the MZI under various applied curvatures and all the measurements are carried out at room temperature. Figures 8(a) and 8(b) show the spectral responses of the MZI with curvature changed for the fiber orientation of 0° and 180°, respectively. It is clear that the bending responses of the sensor are directional sensitivity corresponding to the opposite fiber orientations. When the MZI is fixed at 0° orientation, the resonant central wavelengths are shifted to the longer wavelength as applied curvature increases, whereas experience a blue shift for the 180° orientation case. As shown in Fig. 8(a), there is a resonance dip split in the curvature range , and the splitting can be attributed to the breaking of the supermode symmetry induced by curvature compression .
Figures 9(a) and 9 (b) show the wavelength shifts with error bar of the two resonant central wavelengths, located initially at 1505.84 nm and 1580.15 nm, plotted against applied bending for inverse fiber orientations (0° and 180°), respectively. The experimental data with error bar are calculated using repeated records and standard deviation method. It could be seen that the bending responses are directionally sensitive and the spectral responses exhibit near linear features. For a curvature range from −7.05 m−1 to 7.05 m−1, the bending sensitivities of the two central wavelengths are 1.232 nm/m−1 and 1.174 nm/m−1 by linear fitting, respectively. It shows a weak dependence on wavelength. The multiple LP01-like and LP11-like supermodes interference produces main and minor dips in the same notch  and especially the supermodes splitting [23, 24] in the curvature range lead to the difficulties and inaccurate to define the central wavelength with the curvature change. Thus, as shown in Fig. 9(b), the distribution of the data points of central wavelength at 1580.15 nm shows the nonlinearity compared with Fig. 9(a), especially within the curvature of −3 m−1 to 3 m−1. We have also monitored the wavelength shifts at 1536.24 nm central wavelength with the fiber oriented at 90° and 270° as shown in Fig. 9(c). The resonant central wavelength shift with error bar is insensitive to bending for the curvature range of 0~7.05 m−1 and the bending response is found no directional sensitivity characteristics. This is because the MZI is symmetric along the X axis direction, and thus the OPD of the MZI with applied curvature will unchanged with the fiber fixed at 90° and 270° orientation. We have also tested the bending response for other orientations and find no directional sensitivity. This is also because the MZI is symmetric along the x axis, and thus bending for other orientations will induce the same phase difference changes, and result the same attenuation wavelength shifts in opposite direction .
The ARI and temperature cross sensitivity for a bending sensor is a critical issue that should be considered. We have investigated the spectral responses of the MZI to the ARI with the length of ~34 mm as shown in Fig. 10. It can be seen that the central wavelength is shifted slightly as ARI changes in a range of 1 to 1.474, thus the MZI is believed to be insensitive to the ARI. It is the result that MZI is resulted by invoking LP01-like and higher order LP11-like supermodes in the core. Those core mode fields are well confined by air holes of seven-core PCF we used. Their effective refractive indices are immune to ARI, thus the MZI sensor possesses a key advantage of ARI insensitivity. On the other hand, the MZI structures with different lengths of ~4 mm and ~34 mm are placed in a heater which controls the temperature change of the sensor, and heated from 30 °C to 120 °C with a step of 10 °C to obtain the sensitivity of temperature, as shown in Fig. 11. By linear fitting, the temperature sensitivities of ~34 mm MZI at central wavelength 1520 nm and 1584 nm are obtained to be 0.011 nm/°C and 0.020 nm/°C, respectively. Meanwhile, those of ~4 mm MZI at central wavelength 1505 nm and 1584 nm are 0.018 nm/°C and 0.016 nm/°C, respectively. It indicates that the temperature sensitivity is weakly dependent on MZI length and wavelength. Compared with the maximum bending sensitivity of 1.232 nm/m−1, the bending measurement error resulting from temperature is about 1.5 × 10−2 m−1/°C, we think it is small enough to be negligible, especially for the environment with a fluctuation of dozens of Centigrades in temperature, such as the atmospheric environment on the ground. Therefore, such a device can be a good candidate for ARI insensitive bending vector sensor in the atmospheric environment with a relative small fluctuation in temperature.
In summary, a simple, novel and cost-effective MZI based on the seven-core PCF is proposed by simply splicing a short length of seven-core PCF between two SMFs with a lateral offset splicing joint that covering two cores of PCF. The LP01-like and LP11-like supermodes are permitted as the guided supermodes in seven-core PCF. Because of the asymmetric geometric structure induced by lateral offset fusion splicing, the proposed sensor has the capability of recognizing positive and negative directions. The bending sensitivities of two resonant central wavelengths with opposite fiber orientations are 1.232 nm/m−1 and 1.174 nm/m−1 for a curvature range from −7.05 m−1 to 7.05 m−1, respectively. ARI insensitivity is the result of MZI caused by different order supermodes interference in the core. It indicates that this device can work as an ARI-independent one-dimensional bending vector sensor and have excellent potential for curvature sensing applications.
This work was supported by the National Natural Science Foundation of China (NSFC) under Grants No. 61275125, 61308055, National High Technology Research and Development Program of China under Grant No. 2013AA031501 & 2012AA041203, Shenzhen Science and Technology Project (NO. JC201005280473A, JC201104210019A, ZDSY20120612094753264) and Specialized Research Fund for the Doctoral Program of Higher Education (SRFDP, 20124408120004).
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