## Abstract

A one-dimensional micro-bending vector sensor based on two-mode interference has been introduced. This device was fabricated by lateral offset splicing a piece of six-air-hole grapefruit microstructure fiber (GMF) with single mode fiber (SMF). Variation of effective mode index occurred by micro-bending was investigated in simulation and experiment. This device exhibits micro-bending sensitivities of 0.441 nm/m^{−1} and −0.754 nm/m^{−1} at 0° and 180° bending orientations, respectively. Moreover, this sensor is immune to surrounding refractive index (SRI) and presents a low crosstalk of temperature.

© 2015 Optical Society of America

## 1. Introduction

Bending measurement has been extensively investigating and developing in various areas of mechanical engineering, structural deformation, and automotive industries. Comparing with electronic or mechanical sensor, fiber-optic sensors are of great merits because of their compact size, high sensitivity, immunity to electromagnetic interference, and easy access to sensing network. So far, many types of fiber-optic bending sensor based on different optical fiber devices have been reported, such as long period fiber gratings (LPFGs) [1, 2], fiber Bragg gratings (FBGs) [3], fiber tapers [4, 5], fiber lateral offset splicing [6, 7], photonic crystal fiber (PCF) collapsing [8], hybrid structure [5], two-core [9, 10], three-core [11] and multicore [12] interference in photonic crystal fiber (PCF) and so on. Among these methods, process of fabricating gratings is usually complicated, and expensive equipment is needed, such as femtosecond or UV lasers [2, 13, 14]. Fiber tapers based bending sensors are usually sensitive to surrounding refractive index (SRI) [4, 15], which limits the practical environment. PCF collapsing usually brings in high insertion loss that costs much more energy for signal detection [16]. Some ultra-sensitive bending sensors of these kinds have been reported recently, for instance, Pouneh et al [2] reported an ultra-sensitive vector bending sensor for low curvature with a maximum sensitivity of 1.23 nm/m^{−1}, but the fabrication of this asymmetric LPFGs is rather complicated. Li et al [17] presented a bending sensor based on intermodal interference of fundamental mode and high order modes and its average sensitivity is about 1 nm/m^{−1}, but the limitation of this sensor is that it cannot detect bending orientation. Monzon-Hernandez et al [4] introduced optical fiber curvature sensor based on concatenating two tapers, however, its fringe visibility hardly changes in micro-bending range and the crosstalk of SRI seems a little big, et al. We consider method of two core modes interference by lateral offset splicing microstructure fiber with standard single mode fibers (SMFs) that can solve the problems above. Besides, relative intermodal interference was reported [18] and had been applied in temperature sensor [16, 19], modal coupler [20], modal filter [21], interferometer, and amplitude modulator [22]. However, as far as we know, few two core modes interference based interferometer by lateral offset splicing for micro-bending sensing has been reported.

In this paper, we have presented a one-dimensional micro-bending vector sensor based on two core modes interference, which was fabricated by lateral offset splicing a piece of six-air-hole grapefruit microstructure fiber (GMF) with SMF. The interference pattern is generated by the coupling of LP_{01} and LP_{11} modes back to the core of SMF. Effective mode indices of LP_{01} and LP_{11} were analyzed in theory when different curvature applied. This device exhibits sensitivities of 0.441 nm/m^{−1} and −0.754 nm/m^{−1} for the micro-bending of 0° and 180° bending orientations, respectively. Moreover, this device is immune to SRI and exhibits low temperature sensitivity, which presents an advantage of low crosstalk of SRI and temperature in one-dimensional micro-bending sensing application.

## 2. Operation principle and device fabrication

The optical micrograph of GMF is shown in the inset of Fig. 1. Diameter of the germanium (Ge) doped core is 14.8 μm, and there are six air holes surrounding the core. The diameter of each air hole, the space of adjacent air holes, and the outer cladding are 17.5 μm, 23 μm, and 125 μm, respectively. Usually, the core diameter of SMF is 8.2 μm, so the core diameter of GMF is larger than SMF. Furthermore, when splicing GMF with SMF, high order mode can be easily excited because the mismatch of mode field. A finite element method (FEM) was applied to analyze the dispersion of GMF, and simulated effective mode indices against wavelength are plotted in Fig. 1(a). Black line represents the effective mode index of LP_{01} while blue line is the effective mode index of LP_{11}. Mode fields of LP_{01} and LP_{11} at the wavelength of 1550 nm are shown in Figs. 1(b) and 1(c), respectively. And effective mode index difference of LP_{01} and LP_{11} is calculated to be 0.00186.

Schematic diagram of this device is depicted in Fig. 2. To fabricate this device, a piece of GMF is lateral offset spliced with SMF. When light transmits from SMF to GMF at the 1st offset point, LP_{11} mode is excited [16, 23], transmitting together with LP_{01} mode in the core with different refractive indices, and then coupled back to SMF at the 2nd offset point, generating interferential pattern [16]. So, the 2nd offset point is applied to enhance the visibility of fringe pattern. Distribution of energy and the visibility of fringe pattern depend on the ratio of the intensity of ${I}_{L{P}_{01}}$and ${I}_{L{P}_{11}}$ [24]. And the transmitted intensity of GMF-based sensing device can be expressed as:

_{01}and LP

_{11}modes can be expressed as:here, ${n}_{eff}^{L{P}_{01}}$ and ${n}_{eff}^{L{P}_{11}}$ are the effective mode indices of LP

_{01}and LP

_{11}, respectively. L is the length of the GMF and λ is the operation wavelength. According to the Eq. (1), when the accumulated phase difference $\Delta \phi $ of LP

_{01}and LP

_{11}modes is satisfied:the interference dip wavelength can be expressed as:

Figure 3(a) shows the transmission spectra evolution of this device with a lateral offset alignment of the 1st point from 0 to 6 μm while the 2nd point was manually spliced without lateral offset, and the total length of GMF is 43 cm. Interferential dips occur with 0 μm offset due to the mismatch of mode field, but the visibility of fringe pattern is small, and the total insertion loss is only ~1.5 dB. The visibility of fringe becomes bigger as the offset value increases; meanwhile the insertion loss is also enlarged. Figure 3(b) shows another process, the 2nd point was lateral offset alignment while the 1st point was manually spliced without lateral offset. Visibility of fringe pattern also becomes bigger with offset value increases, but the insertion loss is greatly increasing as well. Therefore, to compromise, the 2nd point with a lateral offset of 4 μm is optimized to achieve fringe pattern with high quality. At last, this device with a length of 4.2 cm GMF was fabricated. The evolution of transmission spectra with different offset value of the 1st point is shown in Fig. 4(a), while the 2nd point was spliced with 4 μm offset value in advance. As studied from Fig. 4(a), when the offset value is larger than 4 μm, the insertion loss is further increasing. So, we applied the lateral offset of 4 μm to do the sensing character in our experiment. Figure 4(b) shows that the transmission spectra of this device with 4 μm lateral offset of both splicing points. The average insertion loss is 1.73 dB and the visibility of fringe pattern reaches 12.61 dB. Although the structure of six-air-hole GMF is symmetrical, both splicing points with a lateral offset of 4 μm in the same way will result in the asymmetric sensing structure. Hence this device exhibits red shift (0° bending orientation) and blue shift (180° bending orientation) of dip wavelength for the micro-bending and presents a one-dimensional micro-bending vector sensing character which will be discussed in detail latter in section 3.

In addition, this device was fabricated with several lengths of GMF to measure the fringe separation △λ; experimental data is shown in Fig. 5(a). According to the Eq. (4), the relationship of △λ and △n can be the simplified expression as:

where$\Delta \lambda ={\lambda}_{2}-{\lambda}_{1}$, ${\lambda}_{1}$and ${\lambda}_{2}$are the central wavelengths of adjacent interferential dips, $\Delta n={n}_{eff}^{L{P}_{01}}-{n}_{eff}^{L{P}_{11}}$. According to the Eq. (5), theoretical curve (solid line) of ∆λ with different lengths of GMF is plotted in Fig. 5(a), which shows that the experimental data is in good agreement with theoretical calculation. Figure 5(b) plots the different experimental effective mode indices under several tested numbers, and the average value is 0.00183. The deviation of experimental average value and theoretical calculation is 3 × 10^{−4}, which has proved that fringe pattern was generated by LP

_{01}and LP

_{11}modes, and this deviation is smaller than the report of collapsed PCF [16].

## 3. Experiments and discussion

Experimental setup for investigating the micro-bending of this device is shown in Fig. 6(a). The light from the SLED (ranging from 1250nm to 1650nm) is transmitted through this device, and the transmission spectra are recorded by an optical spectrum analyzer (OSA, YOKOGAWA AQ6370B) with the resolution of 0.05 nm as the curvature varies. This device is attached to two graduated coaxial rotational fiber holders, which are fixed on the top of two heavy translation stages, respectively. So the fiber can be rotated arbitrarily along the fiber axis for full 360° rotation. Two plastic plates are placed to abut the both sides of fiber and guide the fiber bending in the vertical direction when one of the translation stage moves inward inducing the bending of fiber toward the –Y axis direction. At the same bending curvature, we rotate the fiber to detect the response of dip wavelength shift. The fiber at 0° orientation is defined when the wavelength presents a maximum red shift, which is consistent with the direction of the offset splicing. On the contrast, for the 180° orientation, a maximum blue shift occurs. After the confirmation of 0° and 180° orientations, the other vertical orientations are corresponding to the fiber fixed at 90° and 270° orientations. For the top view of sensing fiber structure at 90° and 270° orientations, it looks like the same. So we use one draft to show both 90° and 270°orientations. Figure 6(b) shows the four orientations of the bending. When this device is rotated to 0°orientation, we fix it to a stainless steel sheet, and then record the bending response of the dip wavelength in 0° and 180° directions, corresponding to concave and convex of the steel sheet, as shown in Fig. 6(a). And the resulting curvature (C) can be expressed as [1, 25]:

where d is bending displacement at the center of this device and R is radius of the bending. D and D_{0}are the half of the reduced and initial distance of the two fiber holders, respectively. By adopting the approximation of the ${\mathrm{cos}}^{2}(\frac{{D}_{0}}{R})$ to the fourth order of binomial of Eq. (7), the relationship of curvature C and D, D

_{0}is carried out in Eq. (8) [25].

Figure 7 shows the refractive index profile of curved GMF with curvature of 0.986 m^{−1}. The effective index profile of curved GMF along –Y direction can be modified through the method of conformal transformation [1]. Variation of material effective index ${n}^{\prime}(y)$ can be approximately expressed as the equation following when the fiber radius (y) is much less than the radius (R) of bending [1, 6]:

_{0}is the initial effective index of GMF, and curvature C is positive.

Variation of effective mode indices and distribution of energy are induced by material effective indices with curvature of 0.986 m^{−1}, and effective mode indices of LP_{01} and LP_{11} are respectively achieved to be 1.447416 and 1.445549, so their refractive index difference ∆n is 0.001867, which is performed by COMSOL FEM shown in Fig. 8. Comparing with the initial effective mode indices of LP_{01} (n = 1.447405) and LP_{11} (n = 1.445545), as well as ∆ = 0.00186, when applying bending on the fiber at 0° orientation, material effective index increases because the compression of the core material at the side of Y direction [6, 26, 27], which is shown in Eq. (9) in the case of y<0 [1]. In addition, the modes of bent fiber are asymmetrical and shifted toward high refractive index area [27, 28] that results in the variation of propagation constant [7, 17], and the increase of the effective mode index difference affects the change of the optical path difference [4, 5]. So, the central wavelength of dip exhibits red shift according to the Eq. (4) as effective mode indices increase.

Experimental results were also carried out and verified by respectively calculating effective mode index difference of LP_{01} and LP_{11} in Figs. 9(a) and 9(b) according to the Eq. (4) and Eq. (5), which is reasonably agreed with the simulation results. It is in the opposite case that y>0 when the fiber bends at 180° orientation. The results demonstrated that a blue shift occurs and effective mode index difference of LP_{01} and LP_{11} decreases in the mode overlap region at the splicing points, as shown in Figs. 9(c) and 9(d). Moreover, the asymmetric structure of this device will lead to different shifting values of central wavelength at 0° and 180° bending orientations because their effective mode index difference of the same curvature is different. Relative research of the asymmetric structure of LPFGs inducing different linear spectral responses in micro-bending was reported [2]. From the above, variation of mode effective indices will induce the central wavelength shift of dip, which makes this device available to recognize the bending degree and direction in one dimension and a small bending range.

The curvature ranged from 0 to 0.986 m^{−1} in the experimental investigation. Transmission spectra responding to the bending variation of the different axial rotation angle were recorded by OSA using the 3 dB central wavelength method and all data were measured in room temperature. Two typical results at fiber bending orientations of 0° and 180° are respectively shown in Figs. 10(a) and 10(b) by changing curvature and the inserts are the magnifying area of transmission spectra. Either the interference dips have red shift or blue shift is depended on the bending orientation. Figure 10(c) shows different linear spectral responses of the interference dip at the wavelength of 1513.67 nm against the applied bending for the fiber orientations of 0° and 180°. Bending sensitivities of 0.441 nm/m^{−1} and −0.754 nm/m^{−1} in the micro-bending range [0-0.986 m^{−1}] are achieved for the bending of 0° and 180° orientations, respectively. Because of the asymmetric structure of this device as previously analyzed [2], effective mode index difference of LP_{01} and LP_{11} is different when applied different bending orientations. Besides, the central wavelength exhibits small response at 90° and 270° bending orientations for the symmetric structure and optical path difference induced by the bending approximately keeps as a constant, which is shown in Fig. 10(d).

The temperature and SRI sensitivities of this device were also investigated. In temperature measurement, this device with different lengths of 4.2 cm and 3.4 cm were placed in a heater with heating temperature ranging from 30 to 90 °C, temperature sensitivities of −6.5 pm/°C and −8.9 pm/°C at the wavelength of 1523.76 nm and 1513.67 nm were respectively achieved, which is shown in Fig. 11(a). Crosstalk of temperature for bending measurements with the device length of 3.4 cm are 2.02 × 10^{−2} m^{−1}/°C and 1.18 × 10^{−2} m^{−1}/°C at 0° and 180° bending orientations, respectively. We think the crosstalk of temperature is so small that they can be neglected in room temperature measurement. Another merit of this device is insensitive to SRI, as the experimental result shown in Fig. 11(b). Because both LP_{01} and LP_{11} modes transmit in the core that surrounded by six air holes in GMF, the central wavelength of interference dip is hardly shifting when the SRI changed in a range of 1 to 1.4729. Thus, this device is immune to SRI and presents an advantage of low temperature crosstalk in micro-bending sensing.

## 4. Conclusion

We have reported a micro-bending sensing device by lateral offset splicing a piece of GMF with SMF. The effective indices of two modes in the central core generating interferential pattern are further studied and investigated in simulation and experiment when applied bending. The bending sensitivities are 0.441 nm/m^{−1} and −0.754 nm/m^{−1} for the curvature of 0° and 180° bending orientations in a micro-bending range [0-0.986 m^{−1}], respectively. This device is immune to SRI and the crosstalk of temperature is relatively low, which can be a good candidate for one-dimensional micro-bending sensing application.

## Acknowledgments

This work was supported by the National Natural Science Foundation of China (NSFC) under Grants No. 61275125, 61007054, 61308055, National High Technology Research and Development Program of China under Grant No. 2013AA031501 & 2012AA041203. Shenzhen Science and Technology Project (NO. JC201104210019A, ZDSY20120612094753264, JCYJ20130326113421781) and Specialized Research Fund for the Doctoral Program of Higher Education (SRFDP, 20124408120004).

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