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In this article, we propose and demonstrate a cascaded interferometers structure based on a dual-pass Mach–Zehnder interferometer (DP-MZI) and a Sagnac interferometer (SI) for simultaneous measurement of strain and lateral stress. The cascaded interferometers configuration consists of a SI structure following with a MZI setup. By inserting a section of polarization-maintaining photonic crystal fiber (PM-PCF) in the sensing loop of the SI structure, an inline interference between the two orthogonal polarization modes of PM-PCF, as well as the interference between the sensing arm and the reference arm of the DP-MZI, i.e., the cascaded interferometers with dual interference, are realized. Theoretical study shows that the reflection spectrum of such cascaded interferometers is consisted of two parts: the big spectrum envelope owing to the SI and the fine interference fringes as a result of the DP-MZI. Experimental results show that the SI achieves the sensitivity of lateral stress and strain 1.28 nm/kPa, 0.78 pm/µε, respectively, while the DP-MZI achieves −0.009 nm/kPa and 5.65 pm/µε, demonstrating the ability for dual parameters measurement with high accuracy.
© 2015 Optical Society of America
1. Introduction
Optical fiber sensor devices have been successfully used in a range of applications, including refractive index [1], strain [2], temperature [3], acoustic [4], and so on, revealing their superiorities of high sensitivity, low power consumption, immunity to electromagnetic interference, and multiplexing capability. Strain and stress are two important measurement parameters reflecting deformation and force circumstances of the objects, and then revealing useful life and safety performance of these objects [5]. In recent years, a lot of schemes and techniques in terms of fiber Bragg gratings (FBGs) [6], photonic crystal fiber (PCF)-based Mach–Zehnder interferometers (MZI) [7], polarization-maintaining fiber (PMF)-based Sagnac interferometers (SI) [8], and Fabry-Perot interferometers (FPI) with air bubble [9], have been proposed and studied for strain sensing. These configurations have shown good performance and practicality, while their sensing sensitivity needs to be further improved for high-precision measurement. In order to obtain higher accuracy, some improvements of the traditional structures and methods have been researched, such as hollow-core ring photonic crystal fiber (HCRPCF)-based FPI [10], frequency comb Vernier spectroscopy [11], and Microfiber in-line Mach–Zehnder interferometer [12]. Besides, a variety of fiber-optic sensors, including FBG-based in butterfly microstructured optical fibers (MOF) [13], fiber laser hydrophone [14], and FBG in two-hole microstructured optical fibers (TH-MOF) [15], have been reported recently for stress sensing.
However, under some circumstances, strain and stress which act on fiber sensors may affect each other. This kind of considerable cross-sensitivity makes them difficult for practical applications. To solve this problem, dual-parameter sensors, which can distinguish different responses of the sensor to two measurands, can be a good choice. This method is widely used in many fields of dual parameters measurement, such as temperature and refractive index [22], curvature and temperature [23], force and temperature [24]. The condition numbers of the matrix results of this mentioned dual-parameter sensors can be calculated as 3.6 × 103, 2.31 × 103, and 4.62 × 103, respectively, implying that the performance discriminating the dual parameters of the sensor can be greater improved.
In this paper, we introduce and investigate a dual-pass Mach–Zehnder interferometer (DP-MZI) and Sagnac interferometer (SI) based cascaded interferometers mechanism for constructing dual-parameter sensing. The DP-MZI is formed by connecting a two-path MZI and a Sagnac loop, the SI is composed by inserting a section of PM-PCF supporting two orthogonal polarization modes in the sensing loop. Owing to different interferometric mechanisms, the proposed cascaded interferometers configuration can be used for realizing simultaneous measurement of strain and lateral stress. Both principle study and experiments are conducted to verify the sensing mechanism and test the operating performance of our sensor. Experimental results demonstrate that the proposed sensor is a good candidate for simultaneous measurement of strain and lateral stress with high accuracy. Due to its advantages of high sensitivity, low cost, simplicity for manufacturing and ability for dual-parameter sensing, the proposed sensor may have great potential applications in fields of structural health monitoring (SHM), product quality monitoring, geological disaster warning, etc.
2. Experimental setup and principle
The schematic configuration of our proposed dual-parameter sensor based on cascaded interferometers is shown in Fig. 1. The beam from an amplified spontaneous emission (ASE) broadband source (BBS) passes through the MZI and SI cascaded interferometers configuration. Two 3 dB optical fiber couplers (OC1 and OC2) are connected to form a MZI structure, and the two output ports of OC2 are fused into a loop, i.e. a DP-MZI is realized [16,17]. Besides, a section of PM-PCF (0.7 m in our experiment, YOFC, Inc.), whose cross-sectional view can be seen in the inset, is inserted in the loop to generate a SI. Two big holes surrounded by many small holes can be seen in the inset view, which makes the PM-PCF orthogonal asymmetric and two orthogonal polarization modes can be supported. A polarization controller (PC) is also inserted in the loop for adjusting the polarization state. Overall, the sensing mechanism of our cascaded interferometers can be considered as composed of two parts: the DP-MZI and the SI. Besides, the transmission spectrum of our sensor is monitored by an optical spectrum analyzer (Yokogawa, Inc., AQ6370, resolution 20 pm) and a signal processing system is employed to analyze and demodulate the transmission spectrum to get the required measurands. The measured insertion loss of the entire sensor is 10.89 dB.
Fig. 1 Schematic diagram of the experiment setup. Inset: Cross-sectional view of the PM-PCF. BBS: broadband source; OC: optic fiber coupler; PC: polarization controller; OSA: optical spectrum analyzer.
When it comes to the PM-PCF based SI, due to the effective refractive index difference of the two orthogonal polarization guided modes mainly in the PM-PCF, the output spectrum is a periodic function of the wavelength [18]. Therefore, the phase difference over the length L0 of the PM-PCF can be given by
and the free spectral range (FSR) of the interference spectrum as a result of the PM-PCF based SIwhere is the wave number, (in this paper) is the birefringence of the PM-PCF; and are effective refractive indices of the PM-PCF at the slow and fast axes, respectively.As for the DP-MZI, whose phase difference is doubled, and FSR is half that of the corresponding single-pass MZI [16]. They can be expressed as
where is the effective refractive index of the optical fiber and (about 3.8 mm in our experiment) is the path difference of the MZI.3. Experiment results and discussion
Figure 2 gives the transmission spectrum of our cascaded interferometers structure, which is composed of a big spectrum envelope owing to the SI and fine interference fringes caused by the DP-MZI. Both the FSRs of the big spectrum envelopes and fine interference fringes can be read from Fig. 2, which are 2.63 nm and 0.217 nm, respectively. The former value is consistent with the theoretical calculation from Eq. (2) and the later one is almost equal to the theoretical calculation from Eq. (4). Hence the overall transmission spectrum can be regarded as superposition of spectrums formed by the SI and the DP-MZI.
Experiments are carried out to examine different variations of the spectrum under the strain and lateral stress. As can be seen in Fig. 1, measurement system (a) in the blue dashed box is a strain measurement system, which contains a fixed stage, a moved stage, and a section of SMF with length of L = 0.5 m clamped between the two stages. And what’s in the pink dashed box is a lateral stress measurement system (measurement system (b)), where the PM-PCF is sandwiched between two square metal blocks with side length of 9 cm. Counterpoises with different weights are placed on the top metal block to apply lateral stress. As shown in Fig. 3(a), the green line and the purple line are Gauss fits of the transmission spectrums under ambient lateral stress of 0.76 kPa and 1.14 kPa without strain applied. It indicates that the dip of the big spectrum envelope (dip1 in Fig. 3(a)) will experience a “redshift” with the lateral stress increased, while that of the fine interference fringes experiences relatively small shift. Similarly, employing the Guass fitting method, the shifts of the transmission spectrums in ambient strain of 0 µε and 20 µε can be clearly observed by fringe-tracking method [19]. As displayed in Fig. 3(b), the dip of the fine interference fringe experiences “redshift” with the strain increased while the dip of the big spectrum envelope stays almost unchanged.
Fig. 3 (a) Transmission spectrums in ambient lateral stress of 0.76 kPa and 1.14 kPa without strain applied. (b) Transmission spectrums under ambient strain of 0 µε and 20 µε.
In order to investigate the sensing performance of our dual-parameter sensor, we track and record the wavelength shifts of dip1 and dip2 along with the lateral stress and strain variations. Lateral stress measurement is implemented by loading counterpoises with different weights as illustrated in Fig. 1. Figure 4 shows that both dip1 and dip2 experience a shift when the lateral stress increases from 0 kPa to 1.77 kPa, with the lateral stress sensitivities of 1.28 nm/kPa (or another expression 111 pm/(N/m)) and −0.009 nm/kPa, respectively. It is worth to mention that we need to move the measurement system (b) to replace the measurement system (a) for recording the shift of dip 2 under ambient lateral stress.
By moving the moveable stage in the measurement system (a) in a step value of 10 µm (20 µε), strain measurement can be realized. As presented in Fig. 5, both dip1 and dip2 shift to longer wavelength when the strain is increasing from 0 to 200 µε, demonstrating strain sensitivities of 0.78 pm/µε and 5.65 pm/µε, respectively. It is also need to note that the measurement system (b) should be replaced by the measurement system (a) when recording the shift of dip 1 under ambient strain.
It is worth to mention that the dips (dip1 and dip2) can shift back to the original positions after each original condition recovery, indicating that the system has good repeatability. In view of the lateral stress and strain measurement results obtained in the above experiments, the dual-parameter simultaneous measurement can be achieved by calculating the following function:
here and are the variations of the lateral stress and strain, respectively. and represent wavelength shifts of dip1 and dip2, respectively. Above experimental results indicate that A = 1.28 nm/kPa or 111 pm/(N/m), B = 0.78 pm/µε, C = −0.009 nm/kPa, and D = 5.65 pm/µε. Comparing the sensing performance of our cascaded interferometers structure with other recently reported schemes, sensing sensitivity values are listed in Table 1. It is obvious that the sensing structure proposed in this article has a significant improvement in both lateral stress and strain sensitivities.
Table 1. Comparison of Experimental Sensitivities of Typical Schemes for Lateral Stress and Strain Measurement
Here we use M to represent our parameters matrix. As we know, the inverse of the determinant of the matrix can be used for quantifying the discrimination between the dual parameters of the sensor [20]. So our result (1/|M| = ~0.138) reveals the good discrimination between lateral stress and strain of the proposed sensor. As reported, the condition number of the matrix is also applied to assess the performance, which provides an indication of the sensitivity of the matrix operation to uncertainties in the matrix elements [21]. In light of this, our result (cond(M) = 4.50) have a very low condition number, which is far less than [20,22–24], hence inverting it permits the recovery of lateral stress and strain measurements from the response data. Overall, the data implies that our sensor is a good candidate for dual parameters measurement.
With respect to the stability of our sensor, according to our experimental observations, the polarization state changes induced by the temperature fluctuation can only lead to small changes of the interference fringe contrast, while almost no drift of the interference spectrum. So the environmental disturbance to the SI structure has minor impact on our measurement results. However, the MZI structure is sensitive to the polarization and temperature variations. As we know, the longer the fiber length or the farther the distance of the arms, the sensor will be more susceptible to temperature disturbance. So we need to both keep the two arms close and keep the ambient temperature small fluctuation during our experiment. To overcome this problem, we are considering replace the MZI with a Michelson interferometer whose arms can be short as design. Or we can also redesign the scheme as a inline structure, it is a work in the next step.
4. Conclusions
In summary, a scheme for realizing simultaneous measurement of lateral stress and strain based on DP-MZI and SI have been proposed and experimentally demonstrated. Theoretical analysis and experimental results indicate that the transmission spectrum of the cascaded interferometers configuration can be considered as the superposition of the fine interference fringes of DP-MZI and the big envelopes of the SI. Adopting Gauss fitting and fringe-tracking method to the transmission spectrum, simultaneous measurement of lateral stress and strain can be realized by tracking the wavelength shifts of certain resonant dips of the DP-MZI and SI. Experimental results of the two different interference mechanisms indicate lateral stress sensitivities of 1.28 nm/kPa and −0.009 nm/kPa, as well as strain sensitivities of 0.78 pm/µε and 5.65 pm/µε. Owing to its advantages of high sensitivity, low cost, simplicity for manufacturing and dual-parameter sensing, the proposed sensor may have great potential applications in fields of structural health monitoring (SHM), product quality monitoring, geological disaster warning, etc.
Acknowledgments
This work is supported by a grant from the National Natural Science Foundation of China (No. 61275083, 61290315) and the Fundamental Research Funds for the Central Universities (HUST: No. 2014CG002). The authors thank Hao Liao, Li Liu, Wei Yang, Wenjun Ni, Chao Luo, shafi, Jing Chen, Dafeng Chen and Enci Chen for their kindly help.
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