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Abstract
Polarization-maintaining few-mode fibers (PM-FMFs) have found applications in sensors with attractive features that traditional single-mode fibers do not possess. We propose a measurement method for multi-parameter sensing based on PM-FMFs. This method is mainly based on the polarized interference effect of PM-FMF. We experimentally demonstrate the principle of the simultaneous sensing of temperature, strain and transverse force. The sensor has been verified by three groups of multi-parameter measurement experiments showing that the changes of multi-parameter derived from the wavelength shift of the polarized interference spectrum are consistent with the multi-parameter changes set in the experiments. The proposed PM-FMF based sensor has a temperature sensitivity of 0.3 nm/°C, a strain sensitivity of 0.01 nm/µε and a transverse force sensitivity of 0.0065 nm/(N/m).
© 2020 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
Recently, few-mode fiber (FMF) has attracted significant attention due to its potential to solve the capacity crunch problem through mode-division multiplexing (MDM) [1–6]. It is important to mention that FMF also becomes a research focus in the field of fiber sensing [7–10]. Employing the spatial dimension, sensors based on FMF has the ability to measure a variety of physical disturbances (temperature, stain and transverse force, etc.) with high sensitivity and insulation. The existing FMF sensing systems based on Brillouin frequency shift (BFS) in each mode have achieved distributed temperature and strain discrimination [11,12]. It has solved the problem in single-mode fiber (SMF) sensors that the sensor performance can be jointly affected by parameters. However, the FMF sensing systems are quite complicated and the DSP algorithms are indispensable. Besides, the FMF sensors can not be applied for simultaneous measurement of multiple parameters. In this case, researchers turn their attention to special FMFs [13–17]. The application of PM-FMF in sensing fields is an interesting area, which is only briefly investigated at best. It’s both the polarization-maintaining and few-mode property of PM-FMF that make it more suitable for multi-parameter sensing. PM-FMF sensor is simpler than FMF-based Brillouin sensor and it can achieve simultaneous multi-parameter sensing.
In this work, we first propose a multi-parameter sensor based on the polarized interference of the PM-FMF, which can achieve the high-precision sensing of temperature, strain and transverse force simultaneously. Because of the linearly independence, the temperature, strain and transverse force sensing coefficients of the LP01, LP11a and LP11b modes can be measured respectively. We experimentally demonstrate the effectiveness with a high temperature sensitivity of 0.3 nm/°C, strain sensitivity of 0.01 nm/µε and transverse force sensitivity of 0.0065 nm/(N/m), respectively.
2. Principle and experimental setup
The basic principle supporting the multi-parameter sensing measurement method is that the LP modes in PM-FMF have different beat lengths [18], due to the refractive index difference of two orthogonal polarization modes is different. The changes of external parameters cause the wavelength shift of polarized interference spectrum. The sensing coefficients of the single parameters in each mode can be measured in the single parameter sensing experiment, and the variation of the parameters in the multi-parameter sensing experiment can be calculated by the wavelength shift of the spectrum of each mode. The effect of the external parameter fields on the polarized interference spectrum can be expressed by the following equation:
where $A = {[{\Delta {\lambda_{\textrm{01}}}{\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} \Delta {\lambda_{\textrm{11a}}}{\kern 1pt} {\kern 1pt} {\kern 1pt} \Delta {\lambda_{11b}}} ]^T}$ , $B = {[{\Delta T{\kern 1pt} {\kern 1pt} {\kern 1pt} \Delta S{\kern 1pt} {\kern 1pt} {\kern 1pt} \Delta F} ]^T}$ and $k = \left[ \begin{array}{l} {k_{T01}}{\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {k_{S01}}{\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {k_{F01}}\\ {k_{T11a{\kern 1pt} {\kern 1pt} {\kern 1pt} }}{k_{S11a}}{\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {k_{F11a}}\\ {k_{T11b}}{\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {k_{S11b}}{\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {k_{F11b}} \end{array} \right]$. A is the wavelength shifts in the polarized interference spectrum of each mode. B is the changes of the external parameter fields. ${k_{T01}}$, ${k_{T11a}}$ and ${k_{T11b}}$ are the temperature sensing coefficients, ${k_{S01}}$, ${k_{S11a}}$ and ${k_{S11b}}$ are the strain sensing coefficients, ${k_{F01}}$, ${k_{F11a}}$ and ${k_{F11b}}$ are the transverse force sensing coefficients of the LP01, LP11a and LP11b mode respectively.For PM-FMF, the beat length of each LP mode is different, and the effects of the external parameters are independent of each other, so the row vector or column vector of the matrix k acting as multi-parameter coefficients obtained by the polarized interference spectrum is linearly independent. In other words, the multi-parameter coefficients matrix k is invertible. By measuring the wavelength shift of the polarized interference spectrum of each mode, the variation of the multi-parameters can be calculated according to the following equation:
Figure 1 shows the experimental setup of multi-parameter sensing system. In this PM-FMF sensing system, an amplified spontaneous emission (ASE) broadband light source is coupled into one end of the PM-FMF which is called free-space fiber coupling. The phase plate converts the LP01 mode into a higher-order mode, and the linear polarizer 1 is inserted to generate linearly polarized light. After coupling into the PM-FMF, linear polarizer 2 is inserted to generate polarized interference effect between two orthogonal polarizing modes in the same LP mode. The same phase plate can be used to convert back the excited higher-order mode into the LP01 mode, then the free-space light is coupled into the single-mode fiber through a collimator, and the polarized interference spectrum is obtained by an optical spectrum analyzer (OSA). The heater in Fig. 1 plays the role of heating the PM-FMF. The fiber rotators are used for holding the PM-FMF, and at the same time, they can rotate the angle to change the force direction on the PM-FMF. Each fiber rotator is placed on a 3-axis flexure stage, we can tune the fine-threaded drives on the stage to stretch the PM-FMF.
Fig. 1. Experimental setup for multi-parameter sensing measurement. a: amplified spontaneous emission (ASE) light source; b: collimator; c: polarizer 1; d: phase plate; f: collimator; g: fiber rotator; h: heating panel; n: optical spectrum analyzer (OSA).
The polarized interference intensity of each mode i can be written as
where ${A_i}$ is the optical field amplitude, $R = \cos (\alpha )\cos (\gamma )$, $S = \sin (\alpha )\sin (\gamma )$, $\alpha$ is the angle between the principal axis of the polarizer 1 and the principal axis of the PM-FMF, $\gamma$ is the angle between the principal axis of the polarizer 2 and the principal axis of the PM-FMF, the phase difference ${\phi _i}$ accumulated by sensing of two polarization modes of mode i is given asThe temperature T and phase ${\phi _i}$ satisfies the following relationship
Fig. 2. The polarized interference spectrum of the PM-FMF and the wavelength shift as the temperature increases.
The strain S and the phase ${\phi _i}$ satisfies the following relationship
The transverse force W and the phase ${\phi _i}$ satisfies the following relationship
3. Experimental results and discussions
The fiber used in this experiment is a 3-mode (LP01, LP11a and LP11b) PANDA PM-FMF fabricated by Fiberhome. Figures 3(a), 4(a) and 5(a) show the shift of the inference spectrum with the parameter changes. We first conducted the sensing experiments with temperature as a single variable. Figure 3(b) shows the wavelength shift fitting curves of LP01 mode, LP11a mode and LP11b mode versus temperature, the spheres, stars and up triangles are the scatter points of the experimental results. These scatter points are linear fitted and three wavelength-temperature relationship curves of LP01 mode, LP11a mode and LP11b mode are formed respectively. We can see that the wavelength shift of each mode changes linearly with temperature, and the corresponding temperature sensing coefficients of each mode are ${k_{T01}} ={-} 0.\textrm{28693}$, ${k_{T11\textrm{a}}} ={-} 0.\textrm{28534}$, ${k_{T11\textrm{b}}} ={-} 0.\textrm{30364}$.
Fig. 3. (a) The transmission spectrum around the same transmission minimum of the LP01 mode at different temperatures; (b) Wavelength versus temperature.
Fig. 4. (a) The transmission spectrum around the same transmission minimum of the LP01 mode at different strains; (b) Wavelength versus strain.
We then conducted the sensing experiments with strain as a single variable, the corresponding strain sensing coefficients of each mode showed in Fig. 4(b) are ${k_{S01}} = 0.01001$, ${k_{S11a}} = 0.00830$ and ${k_{S11b}} = 0.01057$. Then we conducted the sensing experiments with transverse force as a single variable, and the slow and fast axis of the PM-FMF were aligned to the direction of force respectively. After testing we found that the fast axis is more sensitive than the slow axis, so in the multi-parameter sensing experiment the fast axis were chosen to be the direction of the force. Figure 5(b) shows the wavelength shift fitting curves of LP01 mode, LP11a mode and LP11b mode versus transverse force per unit length. The wavelength shift of each mode also changes linearly with transverse pressure, and the corresponding force sensing coefficients of each mode are ${k_{F01}} = 0.00\textrm{658}$, ${k_{F11a}} = 0.00629$ and ${k_{F11b}} = 0.00\textrm{603}$.
Fig. 5. (a) The transmission spectrum around the same transmission minimum of the LP01 mode at different transverse forces per unit length; (b) Wavelength versus transverse force per unit length.
After measuring the sensing coefficients of three single parameter fields of each mode, we can write out the multi-parameter coefficients matrix $k = \left[ \begin{array}{l} - 0.2896\textrm{3}{\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} 0.01001{\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} 0.00\textrm{658}{\kern 1pt} {\kern 1pt} \\ - 0.2853\textrm{4}{\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} 0.00830{\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} 0.00\textrm{629}{\kern 1pt} {\kern 1pt} \\ - 0.3036\textrm{4}{\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} 0.01057{\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} 0.00\textrm{603} \end{array} \right]$, and the changes of the three parameter ΔT, ΔS and ΔF can be calculated according to Eq. (2).
We conducted the sensing experiment of simultaneous changes in temperature, strain, and force to verify the accuracy of the multi-parameter sensor. Figure 6 shows the wavelength shift under different temperature, strain and transverse force combinations in the multi-parameter sensing experiment. The wavelength shifts of the three LP modes are $\Delta {\lambda _{\textrm{01}}} = \textrm{0}\textrm{.52}nm$, $\Delta {\lambda _{\textrm{11}a}} = 0.32nm$, $\Delta {\lambda _{\textrm{11}b}} = \textrm{0}\textrm{.24}nm$. According to the equation we can calculate that $\mathrm{\Delta }T = \textrm{4}.75{\kern 1pt} {\kern 1pt} ^\circ C$, $\mathrm{\Delta }S = \textrm{107}\textrm{.88}{\kern 1pt} {\kern 1pt} \mu \varepsilon$, $\mathrm{\Delta }F = \textrm{123}\textrm{.95}{\kern 1pt} {\kern 1pt} N/m$ respectively. The data obtained in the experiment and the results obtained according to the equation are roughly consistent, the deviation is caused by the resolution and accuracy of the experimental instrument. Table 1 shows the other two groups of multi-parameters sensing data, where ΔTS, ΔSS and ΔFS represent the parameter changes we set in the experiment. It can be seen from the table that the calculated changes of the temperature differ from the changes set in the experiment by -0.36 °C to -0.06 °C, the calculated changes of the strain differ from the changes set in the experiment by -0.11 µε to 2.24 µε and the calculated changes of the transverse force differ from the changes set in the experiment by -1.67 N/m to -1.05 N/m.
Fig. 6. The wavelength shift of LP01, LP11a and LP11b mode under different temperature, strain and transverse force.
Table 1. Experiment data of multi-parameter sensing
4. Conclusion
We propose a multi-parameter sensor using PM-FMF based on polarized interference and deduce the equation to inversely solve the change of external parameters according to the wavelength shift of the interference spectrum by using a 3-mode PANDA PM-FMF to measure the simultaneous changes of temperature, strain and transverse, we experimentally demonstrated the effectiveness of the measurement method. The multi-parameter sensing system we used in this paper is economical and practical, which requires less system operation, and the sensor has a temperature sensitivity of 0.3 nm/°C, a strain sensitivity of 0.01 nm/µε and a transverse force sensitivity of 0.0065 nm/(N/m).
Disclosures
The authors declare that there are no conflicts of interest related to this article.
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