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Abstract
A novel pressure vector sensor based on a short section of PANDA fiber with an orthogonal optical path Sagnac interferometer structure is proposed and experimentally demonstrated. The sensor structure was realized using a gold film, coated on the end of the fiber tip through the magnetron sputtering method. The birefringence-dependent interference dip is sensitive to external force. Therefore, pressure can be monitored by this sensor. The relationship between the force direction and the pressure sensitivity was studied. We embedded the sensor in aluminum, using ultrasonic consolidation technology, to investigate the application of its sensing properties in metal. Based on this, the influence of the embedding direction on the polarization characteristics of the fiber was analyzed. The experimental results showed that the sensor offered a high sensitivity of 2330 pm/(N·m) in its freeform and 780 pm/(N·m) after being embedded in aluminum. Due to its simple fabrication process, low cost, and high sensitivity, the pressure sensor described in this paper could be a competitive candidate in several pressure sensing applications.
© 2020 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
Stress-induced polarization-maintaining optical fibers (PMF) have been widely used in many fiber-based sensing applications, such as pressure sensors, and temperature sensors. [1–3]. Real-time measurement of pressure becomes more significant in bridge monitoring, aircraft aerial compression detection, construction life detection, and oil well pressure monitoring.
Recently, more research has been done on pressure sensors based on PMF [4–7]. A hybrid fiber optic sensing system for down-hole pressure measurement was presented in [4]. A hybrid fiber optic sensing technique was combined with a Fabry-Perot interferometer for down-hole measurement. A side-hole birefringent photonic crystal fiber, with a polycarbonate-filled ellipse core, and other photonic crystal fibers were realized for a pressure sensing measurement [5–6]. However, the hybrid fiber configuration is not only complicated, but also unsuitable for embedding in a solid matrix structure because the F-P cavity is prone to collapse. Additionally, the side-hole birefringent photonic crystal fiber is known to be inappropriate for implanting in solid structures for measurements, owing to the air-holes in the fiber cladding. The spectral shift of the Brillouin dynamic grating in four different types of PMFs were investigated under hydrostatic pressure, based on optical time-domain analysis [7]. However, such measurements require complex signal demodulation systems, creating a bottleneck for wide applications. In order to force measurements, other types of optical fibers have also been used, such as single mode fibers [8] and side hole fibers [9]. Although pressure sensor measurements have been realized, the problem that needs to be addressed is the study of pressure sensors in practical applications. Furthermore, in previously proposed configurations, some drawbacks were experienced. For example, the PMF ring loop [2–3] structure was used for sensing. Although it can constitute Sagnac interferometer, the configuration of optical path construction of this ring structure is more complicated. The layout is inconvenient in practice because two fibers are needed and the sensing zone makes it unsuitable for embedded health monitoring in engineering structures.
In this paper, a Sagnac interferometer, based on a short section PANDA fiber, for high sensitivity pressure measurements is proposed and experimentally demonstrated. An analytical expression of the birefringence function was derived, by which the birefringence could be easily calculated under external forces. The pressure sensor was systematically studied and applied in a metallic structure. The optimal embedding direction of the pressure sensor, based on PMF, was analyzed. A gold film coated the end of the fiber tip, through a magnetron sputtering method. The pressure sensor worked on reflection with a compact size, making it suitable for embedded pressure monitoring in metallic structures.
2. Stress distribution inherent in PANDA fiber
As shown in Fig. 1, the PANDA fiber consists of a fiber core (quartz glass doped with GeO2), cladding (pure SiO2), and the stress applying parts (high concentration doping B2O3). During the fabrication process, the optical fiber is cooled from a high temperature to the room temperature and thermal stress is generated inside the optical fiber as a result of the different thermal expansion coefficients of the three parts [10]. Owing to the non-axisymmetric distribution in the stress regions, the thermal stress distribution is also non-axisymmetric, which results in stress birefringence. To investigate the stress distribution inherent in PANDA fiber and its response to external stress, numerical simulations based on the finite element analysis (FEA) method have been performed. The values of the parameters in the FEA were based on YOFC. Co. China PANDA fiber (PM1550-18/150), as given in Table 1. The other parameters were obtained from Refs. [9,11].
Table 1. The parameters used in the FEA
For convenience of expression, we marked the angle of the fiber section (shown in Fig. 1). The results of the FEA are presented in Fig. 2. It is clear that in the stress applying parts, intrinsic stress components, X-stress and Y-stress, are both positive, indicating that the stress-applying zone presents tensile stress on the fiber core in the horizontal direction. While both X-stress and Y-stress are negative in the non-stress applied region, which indicates that the cladding presents compressive stress to the fiber core. The force on the core comes from the superposition of these two parts. Its equivalent schematic diagram is shown in Fig. 1 (marked by a white arrow).
Fig. 2. Stress distribution of the PANDA fiber. (a) X-stress distribution of fiber cross section. (b) Y-stress distribution of fiber cross section.
3. Stress-induced birefringence vector with relation to lateral pressure
A schematic diagram of the PANDA fiber under lateral pressure is shown in Fig. 3. The radius of the PANDA fiber is denoted by r (m) and the force per unit length is f (N/m). The coordinate system (X,Y) is established according to the fast and slow axes of the PMF (when no transverse stress is applied), where the X-axis and Y-axis are the slow and fast axes, respectively. The coordinate system (ξ,η) is established based on the direction of the force; the forces are applied along the η axis. The origin of the two coordinate systems are both located in the center of the core and the angle between the Y-axis and η-axis is set as α. The light spreads in the Z direction, i.e., along the direction perpendicular to the plane (X,Y). Suppose that the fiber is not subjected to external forces, the fast axis and slow axis refractive index are $n$ and $n + \Delta {n_0}$, respectively. The beat length ${L_{b0}}$ can be expressed as:
Because the force F is perpendicular to the Z-axis, the stress and strain in the Z direction can be ignored. The transverse stress applied on the optical fiber can be regarded as a “plane strain problem,” with respect to the theory of mechanics of elasticity. The stress components in each direction of the cross section of the polarized fiber core can be approximately expressed as [12,13]Fig. 3. Schematic diagram of external pressure on PANDA fiber. (a) Cross section diagram of applied external forces (b) Overall diagram of applied external forces
According to the elastic-optical effect, the dielectric tensor of the material is changed by the external force. The dielectric tensor can then be expressed as
In order to further analyze the influence of the force and its direction on the fiber birefringence, we selected some special angles, such as 0, π/8, π/6, π/4, 5π/12, 3π/8, π/2, and so on, and simulated the birefringence change resulting from the external force under each angle. The results are shown in Fig. 5. When the angle is fixed, the birefringence value can be observed to have an approximately linear relationship with pressure. When the angle is within the range of α${\in}$ 0 – π/4, the birefringence value shows a gradually increasing trend as the pressure increases. However, when the angle is within the range of α${\in}$π/4 – π/2, the birefringence value shows a gradually decreasing trend as the pressure increases. The opposing linear relationship is primarily due to the direction of the force. As can be observed from the figure, the change of birefringence presents a changing relationship of a sine curve with π as the period, along with the change of pressure action angle. The birefringence B reached its maximum and minimum values when the angle $\alpha = k\pi \;\;(k \in Z)$ and $\alpha = k\pi + \pi /2\;\;(k \in Z)$, respectively. It is important to note that when the angle $\alpha = \pi /4 + k\pi /2\;\;(k \in Z)$, external forces have minimal effect on birefringence, with a value of just 10−6. It can be concluded that when the PANDA fiber is used to measure the change of external pressure, angle α should be chosen, as far as possible, at the extreme point shown in Fig. 5, where the change is most sensitive, i.e., the pressure change is the largest at $\alpha = k\pi /2\;\;(k \in Z)$, which is conducive to the realization of a pressure sensor.
Fig. 5. (a) Relationship between external forces and birefringence when the angle is constant. (b) Magnification of the birefringence change when α is π/4.
4. Experimental principle and analysis for pressure vector sensing
4.1 Experimental principle and analysis
Based on the above analysis, we can realize the pressure vector sensing of PANDA fiber. An experimental verification was performed by designing and implementing a setup, shown schematically in Fig. 6(a). In this experiment, we used PANDA fiber with a length of 17 cm and a gold film with a thickness of ∼50 nm. The film was coated on the end of the fiber tip by the magnetron sputtering method, and can provide a reflectivity of 75% at 1550 nm. The fabricated sensor was placed on a lifting stage and two sides of the sensor were clamped by rotatable clamps, which had a rotation range of 0° – 360° and a division value of 2°. A pressure instrument was used to control the magnitude of the force and the real-time pressure value applied on the fiber was monitored by a pressure gauge. An amplified spontaneous emission, with a spectral range of 1510–1600 nm, was employed as the light source in this experiment. The interference spectrum was monitored by an optical spectrum analyzer with a 0.02 nm resolution. Because the end of the PANDA fiber was coated with a gold film, its transmission light path was equivalent to a Sagnac interferometer [1].
Fig. 6. Schematic diagram of experimental principle. (a) Diagram of experimental device. (b) Illustration of the polarization state of the propagated light in a Sagnac interferometer. (c) Interference signals produced by Sagnac interferometer.
The characteristics of the Sagnac interferometer is equivalent to the system schematically illustrated in Fig. 6(b). The reflection spectrum of the obtained sensor is shown in Fig. 6(c). Among these interference dips, one can choose a dip with a central wavelength to perform a measurement. The birefringence of the fiber was changed under the action of external forces, which resulted in a change of the phase difference between the fast and slow axes. Additionally, the dip of the interference will shift. Thus, the pressure vector sensing was realized. Before the pressure measurement, the position of the PANDA fiber needed to be carefully adjusted to make sure that the line between the stress regions of the fiber was located in, or perpendicular to, the force direction. Because the stress regions of the PANDA fiber could be observed with a microscope, the sensor was first rotated to a particular state, such that the two stress regions are parallel to the horizontal plane. Then, by slightly adjusting the rotatable clamp and monitoring the wavelength shift of the interferometer’s output spectrum with the pressure changes, a direction corresponding to the largest shift was found. This direction was defined as a force direction of 0°, as shown in Fig. 3(a). The pressure sensitivities of the sensor were measured in directions from 0° to 360° to show a clearer directional identification characteristic. Considering that the rotation error is ∼1°-2° for the rotatable clamp, the increment is set as 10°. The pressure sensitivity with respect to the force direction of the Sagnac interferometer is presented in Fig. 7. The sensitivities show a good sinusoidal distribution, which is consistent with the relationship between birefringence and the angle change analyzed above. The stress sensitivity varied with period as π, and the stress sensitivity values are 2330 pm/(N·m) at 0°; −2298.75 pm/(N·m) at 90°; 2233.75 pm/(N·m) at 180°; −2256.25 pm/(N·m) at 270°; and 2291.25 pm/(N·m) at 360°. The small sensitivity inconsistency between the opposing force directions is primarily due to the bending direction error, which is caused by the fiber rotators.
The wavelength shift against force, for the case of α = 0°, is plotted in Fig. 8(a) and the reflection spectrum evolution of the sensor, when subjected to a force range from 0 N to 100 N, with an increment of 10 N, is depicted in Fig. 8(b).
Fig. 8. (a) Linear fitted curves of wavelength shift versus force variation (b) The spectral response variations with an increase of force when the angle is 0°.
As observed in the figures, the interference spectrum shifted towards a longer wavelength with an increase of force. The fitted curve shows good linearity, and the reflection spectrum evolution presents small differences. It is demonstrated that the pressure sensor presented in this investigation offers good repeatability. In addition, the wavelength shift versus pressure variation for the case of α = 45° was plotted and fitted with a polynomial fitting function, as depicted in Fig. 9. The fitted results indicate that the pressure sensitivity is as high as 49.87 pm/(N·m), with an R2 value of 0.9915. It is important to note that when α is 45°, the fitted curve of the pressure sensitivity is consistent with the curve trend of the above birefringence simulation (shown in Fig. 5).
4.2 Pressure vector sensing application
In order to realize sensing application of the pressure vector sensor, the sensing properties of metal aluminum matrix sensor with embedded PANDA fiber by ultrasonic consolidation (UC) technology were studied [14]. A schematic of the embedding process of the optical fiber for the sensor is shown in Fig. 10(a). Before embedding, we used a microscope to look for α = 0° (in Fig. 10(b)) and marked it, gently rotated the fiber to 90° and marked it again. Then, the fiber was embedded in the metal aluminum foil using UC technology. During the UC process, there were three control parameters: vibration amplitude, consolidation contact pressure (CP), and weld speed. In this experiment, embedded optical fiber samples were prepared using process parameters that were in the previously identified process window for aluminum 1100 [15]. Bonding of the foil layers occurred through the action of ultrasonic vibration, causing highly localized interfacial slip between the mating surfaces, which breaks up the surface oxide layer and other contaminants. Internal stresses result in elastic-plastic deformation across the interface, ensuring intimate contact and atomic diffusion between the metal foils, which leads to real metallurgical bonds [16]. The welded sample is shown in the Fig. 10(c); the cross-section image of the sample is shown in Figs. 10(d) and 10(e). From the microscopic observations, the intimate contact between the Al matrix and PANDA fiber was obtained. Although there is a slight change in the angle after the fiber embedding, it does not significantly affect pressure sensing measurements.
Fig. 10. (a) Schematic showing embedded fibers by UC technology. (b) Micrograph of the PANDA fiber rotated to an angle of 0° with respect to the Y-axis. (b) The sample was welded by ultrasonic consolidation (c) Cross-section image of sample. (d) Enlarged view of the end face of (c).
Figure 11 shows the comparison of the characteristics of the sensors before and after embedding, at 0° and 90°. It can be observed from the figure that there were four dips, in the range from 1530 nm to 1600 nm, and the free spectral range (FSR) was 16.45 nm before the fiber was embedded. When the fiber was embedded at 0°, the dip of the interferometer increased to 8 and the FSR was 8.66 nm. With Ref. to [17], the birefringence values before and after the fiber embedding were calculated to be 5.08×10−4 and 9.632×10−4, respectively. The change in birefringence was primarily owing to CP during the ultrasonic welding. It is worth noting that when α = 90° for the embedded fiber, there was no interference spectrum, indicating that the fiber lost its polarization-maintaining characteristics. As shown in Fig. 2, the tensile and compressive stresses are along the slow and fast axes, respectively. Thus, when the fiber was embedded a 90°, the external force applied is opposite to the internal stress, which weakens the fiber's polarization-maintaining properties. We should, therefore, be mindful of the direction of the stresses applied externally and the stresses inherent when using the polarization-maintaining fiber, so as to choose the most suitable sensing direction.
The wavelength shift against force when embedding at α = 0° is plotted in Fig. 12(a) and the reflection spectrum evolution of the sample, when subjected to a force range from 0 N to 100 N, with an increment of 10 N, is depicted in Fig. 12(b). From the figures, the pressure sensitivity was observed to be 780 pm/(N · m). The sensitivity difference before and after embedding is primarily due to the plastic flow of metal caused by ultrasonic welding. The metal was tightly wrapped around the fiber, resulting in an extrusion pressure between the fiber and the metal, and the birefringence change was due to the superposition of internal and external stresses. Based on good linearity and stability of the presented results, this study lays a foundation for the future application of pressure sensors.
Fig. 12. (a) Linear fitted curves of wavelength shift versus force variation and (b) the spectral response variations with the increase of force when the embedding angle was 0°.
5. Conclusions
A novel fiber optic sensor, based on a short section of PANDA fiber, for pressure measurements was described. The sensor was simply realized by coating the end of the fiber tip with a gold film with a magnetron sputtering method. Because the interference dip, dependent on the birefringence, is sensitive to external force, pressure can be measured by this sensor. The experimental results show that this sensor provides a high pressure sensitivity of 2330pm/(N·m) in its freedom and a pressure sensitivity of 780 pm/(N·m) after being embedded in aluminum over the force range of 0–100N. The optimal embedding direction of the pressure sensor, based on polarization-maintaining fiber, was analyzed. Based on its simple fabrication process, low cost, and high measurement sensitivity, the sensor presented in this study could be a realistic candidate in the high-accuracy pressure measurement field.
Funding
National Key Research and Development Program of China (2019YFB2203903); National Natural Science Foundation of China (61535004, 61735009, 61827819); Special Fund For Guangxi Bagui Scholars (AD17195074, AA18242043); Fundamental Research Funds for the Central Universities (3072019GIP2519).
Disclosures
The authors declare that there are no conflicts of interest related to this article.
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