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Abstract
The orbital angular momentum (OAM) guiding fiber is used as a sensing element to measure strain and ambient temperature, sensing information simultaneously in a classical BOTDR configuration, due to its higher-order acoustic modes and high stimulated Brillouin threshold. The Brillouin threshold, the Brillouin gain coefficient and the Brillouin gain spectrum (BGS) of OAM fiber at 1.5 µm are characterized and demonstrated theoretically and experimentally. Taking advantage of the special acoustic properties of the peaks caused by the hard cladding-core interface in the Brillouin scattering process, the distributed multi-parameter sensing (e.g., strain and/or ambient temperature) is verified over a 1-km OAM guiding fiber, with the respective errors of strain and temperature of 18.2 µɛ and 0.93 °C, respectively.
© 2022 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement
1. Introduction
Brillouin scattering, a fundamental nonlinear light-matter interaction between photons and acoustic phonons occurring in any optical fiber material, has been extensively investigated and studied in the past several decades. More recently, it has opened many new engineering application possibilities in beam shaping (frequency/time domain) [1–4], imaging enhancement [5], temperature and/or strain distributed sensing [6–8], small-signal amplification [9], etc. For the Brillouin-based distributed fiber sensing configuration case, due to its excellent characteristics in terms of smallness in size, durability, low fabrication cost, and high stability, it can be currently acted as a remarkable candidate for the distributed fiberoptic sensing applications in the non-destructive structural health monitoring (SHM) of civil infrastructures [10–13] and human body motion detection [14]. Conventional Brillouin-based distributed fiberoptic sensors, including the Brillouin analyzer (optical time domain – BOTDA) and Brillouin reflectometer (optical time domain – BOTDR), generally employ standard single mode fibers (SMFs) such as G652, G655 and G657 fibers with one Brillouin gain peak as the sensing elements. Most of BOTDR and BOTDA presented so far have been demonstrated to base on the temperature and strain dependence of the Brillouin frequency shift (BFS). Then, the BFS, which is the center frequency of the Brillouin scattering spectrum, can be achieved by fitting the Brillouin gain spectrum (BGS) with a novel and simple analytical expression [15]. However, since the BFS is jointly affected by multi-parameter cross-sensitivity effects [16], particularly the combination of strain and ambient temperature, has been a great challenge. Since then, many studies have been carried out to address the joint effects of several environmental factors and explicitly quantify each response. Bao et al. [17] employed a specially developed fiber containing a reference fiber (namely temperature compensation) and a sensing fiber to remove the joint effects of temperature and strain external disturbances. The main drawback of the proposed method is no guarantee of strain decoupling in the real ambient conditions. Meanwhile, some groups focused on studying the sensing performance of Brillouin-based sensor with different hybrid methods. Zou et al. [18] successfully demonstrated a hybrid method to discriminate ambient crosstalk information, which was to utilize additional parameters instead of the BFS alone, in both the SMF and polarization maintaining fiber (PMF). Taki et al. [19] did the research to investigate the Raman-Brillouin hybrid sensing system to eliminate the crosstalk caused by ambient environment. Obviously, the proposed methods mentioned above require rather complicated monitoring systems.
The sensors using multiple Brillouin peaks optical fibers as sensing elements have also been considered as possible solutions. The photonic crystal fiber (PCF), the large effective area non-zero dispersion-shifted fiber (LEAF), and the specially designed fibers (e.g., M-shaped, G.652.D) were designed to obtain simultaneous strain and temperature information recovery through measuring the BFSs of multiple Brillouin peaks [20–22]. However, the shortage is that the small sensitivity coefficient differences in the strain or temperature dependence for different Brillouin peaks result in a large amplification factor of measurement error. Recently, an effective technique for the multi-parameter discriminative sensing measurements using multiple optical modes in the few-mode fiber (FMF) has attracted much attention in FMF-based Brillouin sensing configurations [23,24]. In the proposed schemes, the mode conversion elements are needed to excite different optical modes, each excited optical mode is monitored by another mode launcher. It is evident that the complexity of the entire Brillouin-based sensing scheme is difficult to reduce. Thanks to the sharp rise and fall of the index profile of the orbital angular momentum (OAM) guiding fiber between the edge of the core and the cladding region as well as the center and edge of the core results in a significant differences in the acoustic properties. Coupling between the longitudinal and shear acoustic waves is largely enhanced, leading to the generation of higher-order acoustic modes. The OAM guiding fiber with higher order acoustic modes, which is also a kind of FMF, is considered as ideal alternative for distributed long-range sensing, since it can obtain higher measurement accuracy [25,26]. The corresponding studies indicated that the OAM guiding fiber can be used not only as sensing medium in BOTDA but also for the optical deep learning [26,27]. However, to our knowledge so far no multi-parameter sensor based on spontaneous Brillouin scattering (SpBS), and its Brillouin characterization in OAM guiding fiber was reported.
Here, a simplified novel Brillouin-based distributed sensor is proposed and experimentally demonstrated, based on the SpBS effect in an OAM guiding fiber. Different from the existing FMF-based sensing methods [28,29], our proposed sensor uses both linearly polarized (LP01) mode and higher-order acoustic modes, resulting in multiple Brillouin peaks in responding to multiple sensing parameters measurements. The BFSs of the multiple Brillouin peaks in the measured BGS are retrieved to evaluate the strain and temperature coefficients, respectively. The corresponding results demonstrate that the presented sensing method is suitable to discriminate simultaneously temperature and strain information in a relatively uncomplicated single-end scheme. The unequal Brillouin gain coefficients of the first two Brillouin peaks enable the discrimination measurement over a 1-km OAM guiding fiber, with the measurement accuracy of 18.2 µɛ and 0.93 °C for strain and temperature, respectively. Besides, this paper reports the first measurement of Brillouin characterization in the OAM guiding fiber operating at the 1.55 µm wavelength region. Stimulated Brillouin scattering (SBS) is observed from a fiber under test (FUT) merely 1-km in length when a continuous wave (CW) light power of 307.1 mW is launched into the FUT. From the measured Brillouin threshold value we estimate its Brillouin gain coefficient. The Brillouin gain coefficient of the OAM guiding fiber of 5.54 × 10−12 m/W, as much as 7.9 times lower than fused silica fiber (about 4.4 × 10−11 m/W) is monitored.
2. Theory
The change of BFS $\Delta {\nu _\textrm{B}}$ related to the change in strain $\Delta \varepsilon$ and ambient temperature $\Delta T$ can be given by:
where ${C_\mathrm{\varepsilon }}$ denotes the Brillouin coefficient for strain, and ${C_\textrm{T}}$ represents the Brillouin coefficient for temperature. In order to obtain the discrimination of strain and temperature information at the same time, the OAM guiding fiber should contribute two BFSs with different Brillouin coefficients at least. Assuming that $\Delta {\nu _{\textrm{B,}m}}$, $m \in \{{\textrm{1,2}, \ldots ,n} \}$ denotes the BFS of the m-order acoustic mode. In addition, we assume that at least two acoustic modes (m ≥ 2) are used for the discriminative measurement with the strain and temperature coefficients ${C_{\mathrm{\varepsilon ,}m}}$ and ${C_{\textrm{T,}m}}$. Therefore, the following matrices can be derived from Eq. (1), rewritten as: where ${\textbf v} = {[\Delta {\nu _{\textrm{B,1}}},\Delta {\nu _{\textrm{B,2}}}, \ldots ,\Delta {\nu _{\textrm{B,}n}}]^\textrm{T}}$, and ${\textbf B} = {[\Delta \varepsilon ,\Delta T]^\textrm{T}}$. ${\textbf C}$ represents an n × 2 coefficient matrix, can be described as:Consequently, the method with at least two acoustic modes in OAM guiding fiber based on SpBS effect has the ability to realize multi-parameter sensing over the whole fiber link through the demodulation of BFSs. Jin et al. [30] studied the principle and established an analysis model to evaluate strain and temperature measurement error. It is given by:
Meanwhile, based on the small-signal steady-state theory of SBS, the Brillouin gain coefficient can be estimated using the equation below [31]:
Although in our proposed method only the LP01 mode is used for the discrimination of temperature and strain sensing information, we should note the fact that the couplings of the several guided optical modes and the higher-order acoustic modes lead to the generation of the multiple Brillouin peaks in the OAM guiding fiber. For the sensing fiber, the radii of the fiber cladding and core are 62.5 µm and 3 µm, respectively. Figure 1(a) highlights the graded index profile of the OAM guiding fiber, which is measured using a commercial ellipsometer (FPINT-IFA100, Felles Photonic Instrument Ltd.). The monitored result is similar to the result in reference, and the refractive index profile exhibits an inverse-parabolic graded-index profile [26]. A finite-element method (FEM) is adopted to simulate the supported LP modes in the OAM guiding fiber. As depicted in Fig. 1(b), the OAM guiding fiber with the refractive index profile displayed in Fig. 1(a) is found to support three LP optical modes, LP01, LP11, and LP21. When the incident laser is launched from standard SMF to the OAM guiding fiber with perfect alignment, the coupling efficiency between the fundamental mode of the SMF and the higher-order LP modes in OAM guiding fiber will be minimized. Furthermore, most optical fiber components applied in sensing schemes only accommodate LP01. For most multi-parameter Brillouin-based sensing system, therefore, it is enough to study the optic-acoustic characteristics of the OAM fiber corresponding to the LP01 fundamental mode.
Fig. 1. The characteristics of the OAM guiding fiber. (a) Theoretical refractive index profile and experimental (relative to silica index) refractive index profile of the OAM guiding fiber. (b) Simulation results of electric fields of guided LP modes at 1.55 µm in the OAM guiding fiber.
3. Experimental setup
The experimental arrangement used to estimate the Brillouin characterization in OAM guiding fiber is built as shown in Fig. 2(a). A CW pump light from an external cavity tunable diode laser (ECDL) operating at 1.55 µm is amplified by an erbium-doped fiber amplifier (EDFA), and then is launched into the measured OAM guiding fiber through an optical circulator (CIR). The pump light that is backscattered from the FUT is captured at the third port of the CIR. After passing through the 50/50 coupler (OC2), the backward wave is split into two equal branches. The power of light backscattered from the 1-km FUT could be monitored using an optical power meter (P2: Thorlabs, PM100D). An optical spectrum analyzer (OSA: Yokogawa, AQ6370D) with a resolution of 20 pm is applied to monitor the spectral changes of the backscattered signal propagating through the OAM guiding fiber. Meanwhile, another identical optical power meter (P1) is used to measure the CW pump laser power. In order to reduce the influence of OAM fiber end reflection on Brillouin characteristic test, the OAM fiber end is immersed in matching solution (oil).
Fig. 2. Schematic diagram of experimental setup. (a) Experimental apparatus used for stimulated Brillouin scattering threshold measurement in the OAM guiding fiber. (b) Experimental setup of the OAM guiding fiber based on BOTDR configuration. ECDL: external cavity diode laser; OC: optical coupler; LO: local oscillator; FUT: fiber under test; BPF: band-pass filter; OSA: optical spectrum analyzer; ISO: isolator; PS: polarization scrambler; PD: photo-diode; VOA: variable optical attenuator; CIR: circulator; DAQ: data acquisition card; FBG: fiber Bragg grating; LNA: low-noise amplifier; PC, polarization controller; EDFA: erbium-doped fiber amplifier; EOM: electro-optic modulator.
In order to demonstrate the ability to distinguish multi-parameter sensing information at the same time, a BOTDR measurement setup is illustrated in Fig. 2(b). A fixed wavelength (1549.983 nm) CW light from a 10 dBm, 200 kHz linewidth ECDL is divided into two unequal parts by a 90/10 commercial optical coupler (OC1). Subsequently, the 90% part (the upper branch) is selected to be chopped for the generation of beam2 (back scattered Brillouin sensing signal). The chopped probe light is modulated by a customized electro-optic modulator (EOM: iXblue, MXERLN-20) operating in the carrier-suppressed regime driven by a radio frequency pulse generator into the Gaussian optical pulse. After amplified by an erbium-doped fiber amplifier (EDFA1), the amplified optical pulse with a lower parasitic light spontaneously emitted by the EDFA1 is selected through a 3.5 GHz fiber Bragg grating (FBG1) filter. Then, the modulated pulse is launched into the measured OAM guiding fiber through an optical circulator (CIR). Another part with 10% component used as beam1 (reference signal) is scrambled by a polarization scrambler (PS) to obtain high signal-to-noise (SNR) beat information [32]. The Brillouin beat signals with strain and temperature sensing information are generated through a 3-dB OC2 and detected using a 13.5 GHz bandwidth photo detector (PD). A low-noise amplifier (LNA) is employed to enhance the weak original beat sensing signals. The BFSs can be achieved by changing the output frequency of the local oscillator (LO) and eventually sampled by a data acquisition (DAQ) card to obtain the demodulation traces along the measured FUT at different conditions.
4. Experimental results and discussion
The transmission loss of the used OAM guiding fiber is measured as the parameter defines the ${L_{\textrm{eff}}}$ for the Brillouin scattering process at the first time. Figure 3 plots the power loss versus the sensing range, which indicates the measured sensing link is composed of 1-km optical fiber. Besides, the inset in Fig. 3 highlights that the propagation loss at 1.55 µm is about 0.79 dB/km, which is about 4.38 times larger than that of fused silica fiber.
Fig. 3. Measurement of the OAM guiding fiber power loss as a function of sensing distance at 1.55 µm.
The spectral changes of the back-scattered wave propagating through the 1-km long OAM guiding fiber (${L_{\textrm{eff}}}$ is 691.3 m), as collected by the circulator, are illustrated in Fig. 4 with pump powers of 179.2 mW and 307.1 mW. As displayed in Fig. 4, an anti-Stokes Brillouin component and a Stokes Brillouin component at a separation of about 0.078 nm in the shorter wavelength regime and the longer wavelength regime could be observed, respectively. Besides, the significant jump of the Brillouin-shifted signal measured on the OSA could be seen in the longer wavelength side. Figure 5 shows the power level of the backscattered Stokes from the OAM guiding fiber as a function of the injected pump power. It can be seen that the increasing of the launched pump power as, once the Brillouin threshold (307.1 mW) is reached, a sharp backscattered power increase can be observed in the Stokes wave [33]. Using Eq. (6), the OAM guiding fiber length indicated in Fig. 3, the Brillouin threshold suggested in Fig. 5, $K = \textrm{0}\textrm{.5}$ and ${A_{\textrm{eff}}} = \textrm{28}$ µm2, the peak Brillouin gain coefficient to be 5.54 × 10−12 m/W for the OAM guiding fiber is estimated. Obviously, the OAM guiding fiber is not suitable as sensing medium in BOTDA configuration due to its low Brillouin gain coefficient and the high Brillouin threshold. It should be noted that the corresponding experimental results in Figs. (3–5) are obtained by the experimental apparatus shown in Fig. 2(a).
Fig. 4. Optical spectra of the backward direction collected by the circulator for different injected pump power level into the OAM guiding fiber.
Fig. 5. Power of the backscattered Stokes from the 1-km long OAM guiding fiber versus launching pump power.
The block diagram of the experimental setup is displayed in Fig. 2(b). An overlay of the BGS profile from the BOTDR trace over the experiment results highlighted in Fig. 6 indicates that the multi-peak BGS is an intrinsic characteristic of the OAM guiding fiber. As depicted in Fig. 6, the BFSs of three Brillouin peaks (namely, 1st Brillouin peak, 2nd Brillouin peak, and 3rd Brillouin peak) are 9.589 GHz, 9.720 GHz, and 9.887 GHz, respectively. Furthermore, it can be seen that the measured Brillouin spectrum (blue circles) has a good agreement with the multi-peak Lorentz fitting curve (solid red line). The multi-peak shape is measured in the OAM guiding fiber, indicating that the three Brillouin peaks are due to the coupling between LP01 of the FUT and higher-order acoustic modes, instead of mode leakage. Based on aforementioned facts in Section 2, by estimating the BFSs of any two of the first three peaks in the measured BGS, it is capable of solving the obstacle of cross effects due to the different responses of the acoustic modes to the external strain and ambient temperature. Hence, the 1st Brillouin peak and the 2nd Brillouin peak are selected as the main sensing peaks for its high relative intensity, which could eliminate the influence of noise and enhance the measurement accuracy.
Fig. 6. Multiple Brillouin peaks in the OAM guiding fiber. Blue circles: experimental data points; solid red line: multi-peak Lorentz fitting curve; short dash lines: Lorentz profiles of 1st, 2nd and 3rd Brillouin peak.
The measurements of strain and temperature coefficients then are performed by fixing one segment of the FUT to a motor-driven fiber stretching device (Zolix MC600) to exert the OAM fiber strains and immersing another section of the OAM guiding fiber at the far end into a temperature-controlled water-bath pot (JOANLAB, HH-2) to change the ambient temperature. Nine different strains between 0 µɛ and 800 µɛ are monitored with 100 µɛ per step. The BFSs changes of different ambient temperatures are measured in the range of 25 °C to 95 °C with temperature steps of 10 °C. Since the BFS response of different acoustic modes on ambient temperature and strain is unequal, the different sensing parameters on the FUT are able to be discriminated. The measured BFSs of the first two Brillouin peaks as a function of strain and temperature are given in Fig. 7. From the experimental data points, the strain coefficients for the 1st Brillouin peak and the 2nd Brillouin peak are determined to be 40.17 kHz.µɛ−1, 35.27 kHz.µɛ−1, respectively, and the temperature coefficients for the two Brillouin peaks are calculated to be 0.752 MHz.°C−1, 0.886 MHz.°C−1, respectively. As expected, the corresponding results showed that the distributed multiple parameters sensing information can be simultaneously discriminated. The error analysis for the measurement of temperature and strain is then evaluated through Eq. (4) and Eq. (5). The respective errors of strain and temperature using the 1st and the 2nd Brillouin peaks in Fig. 7 are calculated to be 18.2 µɛ and 0.93 °C.
Fig. 7. Ambient temperature and strain measurement results of the OAM sensing fiber. (a) Measured BFS as a function of ambient temperature for the 1st and 2nd Brillouin peaks, respectively. (b) Measured BFS as a function of strain for the 1st and 2nd Brillouin peaks, respectively.
5. Conclusions
Here, the Brillouin characterization of the OAM guiding fiber was studied experimentally, and the Brillouin gain coefficient measured using threshold of single-pass backscattered Brillouin effect was 5.54 × 10−12 m/W, which indicated that the OAM guiding fiber may not be suitable for BOTDA scheme. Therefore, we proposed and experimentally demonstrated a simple BOTDR sensor based on an OAM guiding fiber for simultaneous demodulation of the distributed ambient temperature and strain sensing information. Higher-order acoustic modes that were responsible for the generation of multiple Brillouin peaks within the FUT resulted in a great difference strain and temperature coefficients. Consequently, distributed Brillouin sensing of strain and temperature was illustrated over a 1-km OAM guiding fiber, with the respective errors of strain and temperature of 18.2 µɛ and 0.93 °C, respectively. With the ability of monitoring both strain and temperature sensing information simultaneously, such OAM guiding fiber would be eventually a promising solution for detecting more than two parameters within a given surrounding.
Funding
Special Support for Post-doc Creative Funding in Shandong Province (202103076); Taishan Series Talent Project (2017TSCYCX-05); Science and Technology on Electronic Test and Measurement Laboratory Foundation (JWD200305, KDW03012003); Qingdao Postdoctoral Applied Research Project (20266153); National Natural Science Foundation of China (61605034).
Disclosures
The authors declare no conflicts of interest.
Data availability
Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.
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