Robust in-fiber spatial interferometer using multicore fiber for vibration detection.

We report the demonstration of a novel in-fiber spatially integrated Michelson interferometer based on weakly coupled multicore fiber (MCF) for vibration sensing. The compact interferometer is constructed by using two separate cores of the MCF, where the fiber end is cleaved in order to generate strong Fresnel reflection, and independent light coupling between the cores of MCF and the single mode fibers (SMFs) is enabled by the fan-in coupler. Vibration gives rise to differential strain variation between cores which results in the modification of phase difference of the interferometer. A narrow linewidth laser is employed, in order to interrogate the phase change induced reflection power variation. Vibration event can be identified and the vibration frequency can be retrieved by processing the measured reflection power with fast Fourier transform (FFT). Broad vibration frequency response range up to 12 kHz (limited by the cut-off frequency of the voltage driver of the vibration source) has been achieved. Performance of the sensor has been shown to be independent of the selection of different core pairs, where the MCF is wound to a piezoelectric transducer (PZT). The proposed in-fiber integrated spatial interferometer does not require any special processing of the fiber (e.g., tapering, splicing, and so forth). The unique sensor structure provides some extraordinary merits, including ultra-compact size, high mechanical strength, high sensitivity and temperature insensitivity.


Introduction
Vibration detection is a widely used diagnosis and/or assessment method in many application fields, such as structure health monitoring, seismic monitoring and security monitoring. It helps to predict the potential threat of structural failure through real-time monitoring the characteristic frequency of vibration of the structure. By monitoring the underground vibration, the in-field seismic wave measurement provides useful information for oil and gas exploration, as well as for early prediction of earthquakes. In addition, it has also been used for security monitoring by extracting the vibration information on the ground or walls. The traditional piezoelectric vibration sensors suffer from a number of drawbacks, including sensitive to electromagnetic fields, not adaptable for harsh environments (e.g. high temperature, corrosive environment, etc.), difficult to carry out multiplexing. Optical fiber vibration sensor (OFVS) has shown great potential in these application fields, and it has undergone a rapid development in the past two decades, owning to its unique advantages, including intrinsic electrical passivity, immunity to electromagnetic interference, chemical resistance, light weight, small size and remote access ability. So far, various configurations of OFVS have been developed. One of the most widely used schemes is the tapered fiber based vibration sensors [1][2][3][4], where either the tapered fiber is used as the sensing arm of the Mach-Zehnder interferometers or the microbending loss of the tapered fiber is utilized to detect vibration. However, the tapered fibers are fragile, which results in poor mechanical strength of the sensor head. Fiber Bragg gratings have also been extensively used for vibration sensing [5][6][7][8]. It normally requires a wavelength scanning light source to demodulate the Bragg reflection wavelength, so the detectable frequency range is usually quite limited. In addition, modal interferometers which are fabricated by splicing different kinds of fibers have also been demonstrated [9][10][11][12]. However, the concern is that this kind of sensors has bad mechanical strength due to splicing.
In this work, we propose and experimentally demonstrate a novel in-fiber spatially integrated Michelson interferometer (MI) by employing weakly coupled multicore fiber and a fan-in coupler, where the fiber end is cleaved to generate sufficient Fresnel reflection, and two separate spatial cores of the MCF is employed to construct the single fiber embedded MI configuration. The proposed compact MI has been used for vibration sensing, and broad vibration frequency response range up to 12 kHz (limited by the cut-off frequency of the voltage driver of the PZT) has been achieved. The vibration responses of MIs constructed using different core pairs have been experimentally compared. The results show that the selection of fiber core pairs has no effect on the determination of vibration frequency. Thanks to the unique in-fiber integrated spatial interferometer configuration with independent light coupling enabled by the fan-in coupler, the proposed sensor does not require any special processing of the fiber (e.g. tapering, splicing, etc.). This gives it the advantages of compact size, high mechanical strength, high sensitivity and temperature-insensitivity. Figure 1 shows the cross sectional view of the MCF (YOFC, China) used in our experiments. It contains seven cores with the outer six cores arranged hexagonally. The cladding diameter of the MCF is 150 μm and the core-core pitch is 42 μm. The cores are surrounded by deep trench in order to suppress crosstalk, where −45dB/100km crosstalk between adjacent cores has been achieved [13]. In the proposed MCF based spatially integrated Michelson interferometer, sufficient Fresnel reflection is enabled by cleaving the fiber end, and two independent cores of the MCF constitute the arms of the MI. The output electric fields of light from the two cores are given by 1

Working principle of in-fiber spatially integrated MI vibration sensor using MCF
, then the output reflection power ( ) I t of the MI is governed by [14]: where n is the effective refractive index of the fiber core, l  is the length difference between the two arms, and λ is the wavelength of the input light.
Vibration induced displacement will lead to the change of curvature of the MCF. When the MCF is bent, the cores at off-center positions (i.e. the six outer cores) will be either stretched or compressed, as shown in Fig. 2. This will cause local tangential strain at the bending point, and the generated strain i ε in a specific core i is angular position dependent, as given by [15]: where d is the distance of core i to the fiber center, R is the bending radius, b θ is the bending angle and i θ is the angular position of core i [15]. Specifically, as shown in Fig. 2, the cores on the outer side of the neutral plane will be elongated [e.g. core A in Fig. 2], while the cores on the inner side of the neutral plane will be compressed [e.g. core B in Fig. 2]. So if the curvature of the MCF changes, the length difference l  between the two cores of the MI will vary as well. Meanwhile the effective refractive index n of the fiber cores will also change due to the bending induced tangential strain. As a result, the optical phase difference ( ) t ϕ  between the two cores of the MI will be changed, and the interfered output of the MI will vary with vibration. Therefore, by monitoring the variation of output power of the MI over time, the vibration frequency can be obtained. It must be pointed out that the other reported interferometric vibrations sensors that are fabricated by either splicing or tapering are essentially based on the principle of light interference between different optical modes (including super-modes) within a single optical path in the fiber [3,[9][10][11][12]. However, different from previously reported interferometric vibrations sensors, the proposed MCF based in-fiber spatially integrated MI is fabricated by using two independent cores of a single fiber, where two completely separate optical paths are employed to construct the interferometer, and independent light coupling between the cores of MCF and the SMFs is enabled by the fan-in coupler. The vibration-sensitivity is essentially caused by the differential strains between the cores that result from the vibration induced structural deformation of the MCF. So the fundamental working principle of the proposed MI sensor is different from the other reported interferometric sensors, and the work presented in this paper reveals a novel approach to fabricate optical fiber interferometers based on spatially integrated configuration within a single fiber, which will find various applications in bending measurement, and many other parameters that are related to bending, such as vibration, acc the unique ad fabricated by sensors.

Experime
The  Fig. 4(c). The dominant peak in the figure appears at 7 kHz, which agrees well with the applied frequency value. In addition, 37 dB signal-to-noise ratio (SNR) has been achieved, which indicates that the proposed sensor possesses enough SNR budget to enable the measurement of higher vibration frequency. In order to further evaluate the performance of the proposed MI sensor for vibration sensing, experiments have been carried out by applying different vibration frequency to the PZT from 1 kHz to 12 kHz at 1 kHz interval. The load voltage of PZT is fixed at the same value when different vibration frequency is applied. The output time-domain power signals of the MI at different vibration frequencies are sampled and processed by FFT, respectively. The retrieved FFT spectra are shown in Fig. 5. The result verifies the excellent measurement accuracy of the proposed MI sensor in terms of the determination of vibration frequency. It also indicates that high SNR can be obtained by the sensor, even when the vibration frequency is very high (e.g. 12 kHz in the figure). In addition, it should be pointed out that the electric cut-off frequency of the high voltage driver of the PZT is less than 13 kHz, which determines the maximum available vibration frequency in the lab. Due to sufficient SNR offered by the MCF spatially integrated MI configuration, it is believed that the proposed sensor is able to measure vibrations at much higher frequencies. In order to investigate the vibration response characteristics of the spatially integrated MI configurations using different core pairs, experiments have been conducted by selecting distinct combinations of two cores to construct the MIs, and then use them to measure vibration respectively. Due to the symmetrical distribution of cores of the MCF, we choose the core pairs with 60° angular offset (i.e. core 2 and core 7), 120° angular offset (i.e. core 2 and core 6), 180° angular offset (i.e. core 2 and core 5), as well as the combination of one outer core and the center core (i.e. core 2 and core 1) in the experiment to investigate the dependence of performance on core pairs. The MIs that consist of different core pairs have been used to measure a 2 kHz vibration, respectively. In the experiment, the output signals of the MIs are recorded and processed by FFT, respectively. The obtained FFT spectra are presented in Fig. 6. The SNRs of the FFT spectra are 23.1 dB, 23.49 dB, 22.75 dB and 20.4 dB for core2-core1, core2-core5, core2-core6 and core2-core7, respectively. It is founded that all MIs using different core pairs are able to retrieve the correct vibration frequency, thus it indicates that the determination of vibration frequency of the MI sensor is independent of the selection of different core pairs. It is worth noting that the vibration amplitude is small here, since the amount of diameter change caused by PZT is actually very small in the experiments. However, owing to the fact that the strong Fresnel reflection brings in sufficient optical power to the photodetector, which ensures high SNR for the measured time-domain waveforms of the interferometer. Additionally, since about seven rings of MCF have been wound to the PZT, the vibration induced accumulated phase change is actually large for all the cores, and this has resulted in high fringe contrast of the measured interference waveforms. That's why high SNRs have been obtained for all the measurements using different core pairs. Since the MI structure is very sensitive to optical phase change, the wavelength drift induced phase fluctuation of the laser source might be a factor that degrades the performance of the proposed vibration sensor. In order to investigate the impact of laser phase noise on the reliability of system, experiment has been carried out for comparison by monitoring the output signal of the sensor when there is no vibration applied to the sensing fiber. Figure 7(a) shows the measured output power of the MI without vibration applied, where two separate measurements have been presented. It is found that due to random wavelength drift of the laser, the output power of the MI shows slight change over time when there is no vibration applied to the MCF. The frequency spectra of the two measurements are then obtained by calculating the FFT, as shown in Fig. 7(b). The result indicates that the laser phase fluctuation induced frequency noise of the sensor has very weak power spectrum amplitude, and the noise floor is less than −40 dB in the frequency region that is higher than 200 Hz. Therefore, the laser wavelength drift induced phase noise will not cause severely detrimental impact on the measurement. It is worth mentioning that the in-fiber spatially integrated MI configuration also provides another advantage of temperature insensitivity. Because the MCF used here is a homogeneous MCF, whose fiber cores are made from the same preform. So they have the same thermal expansion coefficients and thermo-optic coefficients. Since the two arms of the proposed MI are embedded in the same fiber cladding. So they will undergo the same environmental temperature change, and this will lead to identical phase change of light in the two arms. As a result, the sensor response is immune to the temperature variation, and this will help to enhance the reliability of the sensing system. In addition, it should be mentioned that linear response of the output power of MI on the vibration amplitude will be ensured if vibration induced phase change locates in the linear region of a monotonic interval of the cosine transmission spectrum of MI, as indicated by Eq. (1), then it is able to measure the vibration amplitude quantitatively by monitoring the output power of MI. Finally it should be pointed out that it is possible to achieve multiple-point detection by using the MCF. In the case of long sensing range, distributed fiber sensing technique such as phase-sensitive optical timedomain reflectometer (φ-OTDR) can be implemented in one core of the MCF, so that φ-OTDR can be used to locate different vibration points along the entire fiber, meanwhile the vibration frequencies can be measured by the interferometer.

Conclusions
In conclusion, we have proposed and demonstrated a simple and efficient optical fiber vibration sensor based on in-fiber spatially integrated Michelson interferometer using weakly coupled MCF. Vibration sensing with high sensitivity, high SNR and large frequency response range up to 12 kHz has been achieved, which is much higher than the values that are measured by the sensors that are made of strongly coupled MCF [10,11]. The dependence of MI performance on the selection of core pairs has been experimentally compared, and it turns out that MIs constructed using any two cores are able to retrieve the correct vibration frequency in the case of small vibration amplitude. Thanks to the unique structure of multiple separate cores embedded in the MCF, the proposed in-fiber integrated MI configuration possesses the advantages of temperature-insensitivity. Moreover, it does not need any special processing of the sensing fiber (e.g., tapering, splicing, etc.), therefore it possesses the advantages of compact and high mechanical strength. These advantages make the proposed fiber sensor more applicable in field installation than other alternative proposals. So it is believed that it will find many applications in vibration measurement.