### Distributed curvature sensing based on a bending loss-resistant ring-core fiber Download： 739次

## 1. INTRODUCTION

In the past few decades, distributed optical fiber sensing has been extensively investigated due to advantages like compactness, low cost, and long sensing range. Importantly, it offers the possibility that one optical fiber can replace a large number of closely spaced point sensors [1–

Compared with conventional SMFs, the specialty optical-fiber-based BOTDA systems show unique advantages in measuring physical quantities besides temperature and strain, one of which is the distributed curvature. Distributed curvature sensing is now widely demanded in a variety of applications, such as surgical instruments [23], microelectronic systems [24], and structural health monitoring [25]. As is known, the Brillouin frequency shift (BFS) of SMFs shows weak dependence on fiber bending [26]. In addition, the fiber macrobending loss of SMFs will increase sharply as the curvature radius decreases. Thus, the bending loss of SMFs is widely utilized for point microbend sensors, which can achieve a minimum detectable curvature radius of 0.3 cm [27], but it suffers from the signal-to-noise ratio (SNR) reduction, especially for multipoint or distributed curvature measurement. It has been reported that bending-induced BFS variation is much larger in FMF compared with SMF. And the FMF-based BOTDA has achieved distributed curvature measurement with bending radii ranging from 0.9 to 2.7 cm [17]. It has also been demonstrated that for BOTDA systems based on the MCF, both the bending angle and radius can be retrieved by using signals from multiple cores in the same cladding, which establishes a foundation to perform distributed three-dimensional shape determination [21]. However, for the fibers mentioned above, the minimum measurable bending radius is severely limited by fiber macrobending loss. In this case, a kind of specialty optical fiber with an excellent bending loss resistance is essential for distributed curvature measurement.

The ring-core fiber (RCF) is another kind of specialty optical fiber that has been studied primarily in mode-division multiplexing (MDM) transmission systems [28

In this work, BOTDA-based distributed curvature sensing by exploiting the RCF is investigated. First, the BFS dependence on temperature and strain for the RCF is measured, which is slightly smaller than that of the SMF. For the bent RCF, the optical mode deformation within the bending fiber is quantitatively analyzed with a numerical simulation method. Simulation results demonstrate that the optical mode field will shift away from the fiber neutral axis and undergo a tensile strain. More particularly, the peak Brillouin gain is found to increase in the bent RCF region due to the decreased optical mode effective area, which may provide another measurement parameter for curvature determination. After that, the distributed curvature measurement based on the RCF is conducted with a bending radius range from 0.5 to 1.5 cm. The maximum bending loss is measured to be less than 0.01 dB/turn. In the experiment, both BFS and peak Brillouin gain change significantly with varying curvature radii, as the simulation implies. The maximum BFS variation at a bending radius of 0.5 cm is about 32.9 MHz. At the same time, the peak Brillouin gain is almost doubled compared to that in the straight RCF. Experimental results indicate that the RCF has a much higher bending response compared with the SMF, in addition to its excellent macrobending loss resistance. These features enable the RCF to be an appropriate candidate for distributed curvature sensing with extreme bending conditions.

## 2. FIBER PARAMETERS AND THE PRINCIPLE OF CURVATURE SENSING

In a BOTDA system, usually a low-frequency probe light and a high-frequency counterpropagating pump pulsed light are launched into the sensing fiber, and optical power will transfer from the pump light to the probe light through the stimulated Brillouin scattering (SBS) process. When the frequency offset between the pump and probe light approaches the local BFS of the fiber, the transferred power reaches a maximum that corresponds to a peak Brillouin gain. At location

The fiber we used for the BOTDA is an RCF (manufactured by YOFC). Figure

#### Fig. 1. (a) Optical microscope image of cross section of the RCF; (b) measured refractive index profile of the RCF; (c) simulated ${\mathrm{LP}}_{01}$ , ${\mathrm{LP}}_{11}$ , ${\mathrm{LP}}_{21}$ , and ${\mathrm{LP}}_{31}$ mode groups supported by the RCF.

The mechanism of distributed curvature sensing using the RCF is theoretically analyzed as follows. As shown in Fig.

#### Fig. 2. (a) Position-dependent strain induced by fiber bending; (b) strain distribution on the fiber cross section; (c) simulated optical mode field of the bent RCF.

Fiber bending will also induce a perturbation on the refractive index profile over the RCF cross section, thus leading to mode-field deformation [36]. Based on the method of conformal mapping [37] and FEM simulation, the mode field for the bent RCF with a curvature radius of 0.5125 cm is analyzed, and the simulated ERI is 1.4691. As shown in Fig.

## 3. EXPERIMENTAL SETUP AND RESULTS

The experimental setup employed in this work is illustrated in Fig.

#### Fig. 3. Experimental setup for the BOTDA system based on the RCF. PC, polarization controller; EOM, electro-optic modulator; MS, microwave synthesizer; SOA, semiconductor optical amplifier; AFG, arbitrary function generator; PS, polarization scrambler; EDFA, erbium-doped fiber amplifier; CIR, circulator; FBG, fiber Bragg grating; PD, photodetector; inset, measured far-field profile at the output end of the RCF when excited through an SMF.

In the experiment, to selectively excite the fundamental

First, the Brillouin gain spectrum (BGS) distribution of the RCF is measured, and its response to temperature and strain is characterized. To study the temperature sensitivity of the RCF, a 14 m segment at the far end is immersed in a temperature-controlled water-bath pot. Distributed measurement is performed with a pulse width of 50 ns, which corresponds to a spatial resolution of 5 m. Figure

#### Fig. 4. (a) Measured BGS distribution along the RCF with a heated segment; (b) experimentally measured BGS and Lorentz fitting curve at the output end of the RCF.

The BFS change of the RCF with temperature from 40.5°C to 61°C is shown in Fig.

#### Fig. 5. BFS as a function of (a) temperature and (b) strain for the RCF and the linear fitting results.

Next, the distributed curvature measurement of the RCF is performed. As shown in Fig.

#### Fig. 6. (a) Schematic diagram of distributed curvature measurement by winding the RCF around plastic cylinders with different diameters; (b) measured BGS distribution along the bent RCF.

To comprehensively characterize the BGS response in bent RCF, the BFS and peak Brillouin gain are analyzed separately. The measured distributed BFS along the bent RCF is shown in Fig.

#### Fig. 7. Measured fiber bending-induced (a) BFS and (b) peak Brillouin gain variation along the RCF.

To further investigate the macrobending loss characteristics, we wind the RCF and a standard G.652.D SMF onto cylinders with different diameters and measure the loss. As shown in Fig.

## 4. SIMULATION RESULTS

In order to quantify the BFS and peak Brillouin gain variation resulting from fiber bending, the mode field in the bent RCF is numerically analyzed using the FEM. The simulated mode-field distributions with increased curvature radius are shown in Fig.

#### Fig. 9. Simulated mode-field distributions of the bent RCF with different curvature radii.

#### Fig. 10. Calculated power center shift and normalized effective area as functions of curvature radius.

With simulation results of the power center shift and effective area change, we can further study the BFS and peak Brillouin gain variation accordingly. The bending-induced strain is approximated by the strain at the power-averaged center. By combining Eqs. (

Using the measured strain coefficient

#### Fig. 11. (a) Simulated bending-induced BFS change and experimental results; (b) simulated bending-induced peak Brillouin gain variation and experimental results.

According to Eq. (

The measurement range and sensitivity of the RCF are compared with other FMFs. Step-index four-mode FMFs with core diameters of 20.6 and 18 μm have been demonstrated for distributed curvature measurement [17,18]. In Fig.

#### Fig. 12. (a) Comparison of BFS variation and measurement range for the RCF and FMFs; (b) comparison of measurement sensitivity for the RCF and FMFs.

It should be noted that birefringence can result from extreme bending conditions; thus, its effect on BFS variation should be carefully studied. Birefringence is known as the ERI difference in the

Based on the phase-matching condition of SBS, the variation of BFS

## 5. DISCUSSION

The insensitivity of the Brillouin gain to temperature variance can improve the curvature measurement accuracy under a temperature-changing environment. To quantitatively analyze the influence of temperature on curvature measurement, a segment of the RCF around a plastic cylinder with a diameter of 1.5 cm is immersed in a temperature-controlled water-bath pot, with the rest of the RCF kept at a room temperature of 23°C. Using the straight loose RCF at room temperature as a reference, the BFS change and normalized peak Brillouin gain of the heated curved segment are observed; see Figs.

#### Fig. 14. (a) BFS change of the heated curved RCF with temperature; (b) Brillouin gain change of the heated curved RCF with temperature.

Figure

## 6. CONCLUSION

We have proposed and demonstrated a BOTDA system based on the RCF for the distributed curvature sensing for what we believe is the first time. First, a thorough experimental investigation on temperature and strain coefficients of the RCF has been reported. More importantly, a distributed curvature sensing has been demonstrated, with a radius ranging from 0.5 to 1.5 cm. The maximum BFS variation at a bending radius of 0.5 cm is about 32.9 MHz. In addition, the peak Brillouin gain of the RCF also presents a high response to fiber bending, which is about 2 times larger at a bending radius of 0.5 cm than that in straight RCFs. For a quantitative study, we propose a numerical method to evaluate the BFS and peak Brillouin gain variation caused by fiber bending. The simulation results are in good agreement with those in experiments.

The proposed RCF-based BOTDA system exhibits some unique advantages in distributed curvature measurement. First of all, the BFS of the RCF has a much higher sensitivity to curvature variation compared with SMFs. Moreover, the peak Brillouin gain shows a distinctive characteristic of curvature sensing, whose insensitivity to temperature and axial strain variance can eliminate the environmental influence on measurement accuracy. At last, the RCF is of excellent bending loss resistance, which enables it to carry out distributed curvature sensing with extreme bending radius. Overall, we believe that RCF can be widely deployed in fields for highly sensitive curvature monitoring applications.

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##### Article Outline

Li Shen, Hao Wu, Can Zhao, Lei Shen, Rui Zhang, Weijun Tong, Songnian Fu, Ming Tang. Distributed curvature sensing based on a bending loss-resistant ring-core fiber[J]. Photonics Research, 2020, 8(2): 02000165.