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Abstract
By using radial acoustic modes induced forward Brillouin scattering (FBS) in a highly nonlinear fiber (HNLF), to the best of our knowledge we have demonstrated acoustic impedance sensing with the sensitivity reaching beyond 3MHz for the first time. Benefiting from the high acousto-optical coupling efficiency, both radial acoustic modes (R0,m) and torsional-radial acoustic modes (TR2,m) induced FBS in HNLF have larger gain coefficient and scattering efficiency than those in standard single-mode fiber (SSMF). This provides better signal-to-noise ratio (SNR) and hence larger measurement sensitivity. By using R0,20 mode in HNLF, we have achieved a higher sensitivity of 3.83 MHz/[kg/(s · mm2)], in contrast to that of 2.70 MHz/[kg/(s · mm2)] when measured using R0,9 mode (with almost the largest gain coefficient) in SSMF. Meanwhile, with the use of the TR2,5 mode in HNLF, the sensitivity is measured to be 0.24 MHz/[kg/(s · mm2)], which is still 1.5 times larger than that reported when using the same mode in SSMF. The improved sensitivity would make the detection of the external environment by FBS based sensors more accurate.
© 2023 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement
1. Introduction
Backward Brillouin scattering (BBS) takes place due to the interaction among a pump wave, a counter-propagating Stokes wave and a longitudinal acoustic wave in optical fibers [1]. BBS has been widely used to realize distributed temperature and strain sensing which has attracted widespread attention [2]. However, due to the confinement of the lightwave and longitudinal acoustic wave inside the fiber core, BBS based fiber sensors cannot detect the surrounding environment outside the fiber. On the other hand, forward Brillouin scattering (FBS), also regarded as guided acoustic wave Brillouin scattering (GAWBS) [3], is an opto-mechanical effect based on the transverse acoustic wave along the radial direction of the fiber, which makes it possible to detect the substance outside the fiber [4]. The GAWBS in the single mode fiber (SMF) was first studied by R.M. Shelby et al. in 1985 [3], since then the FBS in different fibers and their applications have been widely studied [5–7]. By tailoring the acoustic modes in a photonic crystal fiber (PCF), D. Elser et al. has demonstrated the reduction of GAWBS in a broad frequency range, which is regarded as a noise source in quantum-optics experiments [5]. M.S. Kang et al. has reported the observation of a gigahertz nonlinear FBS in the small core of a PCF [6]. J. Wang et al. has found that the gain coefficient in highly nonlinear fiber (HNLF) is larger than that of SMF due to the tight confinement of the light and acoustic field [7]. During the FBS process, two kinds of acoustic waves are involved: the radial-mode acoustic wave (${R_{0,m}}$) and the torsional-radial mode acoustic wave ($T{R_{2,m}}$). The ${R_{0,1}}$-like and $T{R_{2,1}}$-like acoustic modes in PCF was studied by M.S. Kang et al. [6,8]. The ${R_{0,1}}$-like mode is excited more efficiently and the $T{R_{2,1}}$-like acoustic mode causes forward stimulated interpolarization scattering in the solid-core PCF. L.A. Sanchez et al. has demonstrated a method for the characterization of both ${R_{0,m}}$ and $T{R_{2,m}}\; $ induced FBS by means of the effective refractive index modulation, using a narrowband long-period grating (LPG) [9]. The polarization characteristics of the TR modes induced FBS has been studied by Nishizawa from 1995 [10,11]. And H.H. Diamandi et al. has analyzed the polarization characteristics of the torsional-radial modes induced FBS in standard SMF [12].
By enhancing the intensity of the GAWBS, the FBS has been used for temperature and tensile strain sensing [13–15]. And it is reported that the FBS can also be used to measure some other parameters, such as the sound velocity [16], fiber diameter [17], core-cladding concentricity [18]. Recently, the use of FBS has enabled the detection of the environment where it can distinguish the substance outside the fiber according to the measured acoustic impedance [4,19]. Due to the participation of transverse acoustic waves, the FBS based sensors can measure the acoustic impedance of the substance outside the fiber, which can be performed by using ordinary fibers without the need of special structures. Table 1 summarizes some of the previous works on the acoustic impedance sensing using FBS in optical fibers. Simultaneous measurement of temperature and acoustic impedance by using the ${R_{0,8}}$ acoustic mode is performed in a large effective area fiber (LEAF), and the measurement sensitivity of the acoustic impedance sensing is 1.3 $\textrm{MHz}/[{\textrm{kg}/({\textrm{s} \cdot \textrm{m}{\textrm{m}^2}} )} ]$ [19]. The acoustic impedance sensing also has been demonstrated using the standard single mode fiber (SSMF) and the sensitivity by $T{R_{2,5}}$ mode is calculated to be 0.16 $\textrm{MHz}/[{\textrm{kg}/({\textrm{s} \cdot \textrm{m}{\textrm{m}^2}} )} ]$ according to the results in Ref. [18]. Besides those single-point sensors [4,19–22], multipoint acoustic impedance sensing has been proposed using SMF with different diameters [23], and the sensitivity is found to be 1.86$\textrm{MHz}/[{\textrm{kg}/({\textrm{s} \cdot \textrm{m}{\textrm{m}^2}} )} ]$. Based on the opto-mechanical time-domain reflectometry (OMTDR) [24], local light phase recovery [25] and opto-mechanical time-domain analysis (OMTDA) [26], distributed acoustic impedance sensing has been successfully demonstrated in SSMF, and the sensitivity for ${R_{0,7}}$ acoustic mode is 2.28, 2.38 and 1.89$\textrm{MHz}/[{\textrm{kg}/({\textrm{s} \cdot \textrm{m}{\textrm{m}^2}} )} ]$, respectively. It is seen from Table 1 that in most of the works, the sensing fiber used to measure FBS spectrum and acoustic impedance is the standard SMF (SSMF), whose FBS gain coefficient is small, resulting in low signal-to-noise ratio (SNR) and measurement sensitivity. Although the work in Ref. [22] has used HNLF for the measurement, the sensitivity of $0.98\textrm{MHz}/[{\textrm{kg}/({\textrm{s} \cdot \textrm{m}{\textrm{m}^2}} )} ]$ is still low due to the weak response of the $T{R_{2,47}}$ mode. It is desirable to improve the measurement sensitivity for more accurate acoustic impedance sensing.
Table 1. Previous work on the acoustic impedance sensing using FBS in optical fibers
In this paper, we propose and demonstrate the acoustic impedance sensing with high sensitivity by using strong ${R_{0,m}}$ modes in an uncoated HNLF. The use of $T{R_{2,5}}$ mode in HNLF for sensing is also demonstrated. The gain coefficient and scattering efficiency for different acoustic modes in HNLF are simulated and compared with those in SSMF, which indicates that HNLF has higher FBS gain, thus supporting better SNR and larger measurement sensitivity. For acoustic impedance sensing experiment, a 10-m-long HNLF with the coating removed is placed in the sucrose solution with different concentrations. For comparison, the sensing by using SSMF is also carried out. By using ${R_{0,20}}$ mode in HNLF, the measurement sensitivity is improved to be $3.83\textrm{MHz}/[{\textrm{kg}/({\textrm{s} \cdot \textrm{m}{\textrm{m}^2}} )} ]$, which is larger than that of $2.70\textrm{MHz}/[{\textrm{kg}/({\textrm{s} \cdot \textrm{m}{\textrm{m}^2}} )} ]$ when using ${R_{0,9}}$ mode (with almost the largest gain coefficient) in SSMF. To the best of our knowledge, this is the first time that the sensitivity is improved to beyond $3\textrm{MHz}/[{\textrm{kg}/({\textrm{s} \cdot \textrm{m}{\textrm{m}^2}} )} ]$. Moreover, the sensitivity by using $T{R_{2,5}}$ mode in HNLF is also enhanced to be $0.24\textrm{MHz}/[{\textrm{kg}/({\textrm{s} \cdot \textrm{m}{\textrm{m}^2}} )} ]$, which is still higher than $0.16\textrm{MHz}/[{\textrm{kg}/({\textrm{s} \cdot \textrm{m}{\textrm{m}^2}} )} ]$ reported when using the same mode in SSMF.
2. Theory and simulation results
For ideal cylinder fiber, the center frequency of the ${m^{th}}$ order acoustic resonance mode ${R_{0,m}}$ can be expressed by [3]:
where ${V_d}$ is the longitudinal acoustic wave velocity, a is the radius of the fiber cladding and ${y_m}$ is the ${m^{th}}$ solution of the following equation: where $\alpha = {V_s}/{V_d}$ is the ratio between transverse acoustic wave ${V_s}$ and longitudinal acoustic wave velocity ${V_d}$. Both ${V_s}$ and ${V_d}$ are dependent on the material of the fiber, and for the slightly doped silica fiber, $\textrm{}{V_d} \approx 5996\; m/s$ and ${V_s} \approx 3740\; m/s$ [23]. And ${J_n}(x )$ represents the ${n^{th}}$ order Bessel function. Similarly, the center frequency for the $\textrm{T}{R_{2,m}}$ mode is determined by [3]: where ${y_m}$ is derived by:Similar to the gain spectrum of the BBS, the FBS spectrum also shows a Lorentzian line shape as well [7,27], which can be expressed as:
When the external environment changes, it will cause the change of ${\mathrm{\Gamma }_m}$. By measuring the linewidth, the acoustic impedance of the external environment can be detected. Obviously, larger FBS gain is desirable for better SNR and hence measurement sensitivity. The gain coefficient ${g_{0(m )}}$ is related to the acousto-optic coupling efficiency and can be given as [7]:
Based on Eq. (7), Fig. 1(a) shows the simulated intensity of the fundamental optical mode HE11 and the density variation ${\rho _{0,m}}$ of different acoustic modes ${R_{0,m}}$ in HNLF. As a comparison, the result for SSMF is also given in Fig. 1(b). The datasheets of both fibers used in the simulation are shown in the Table 2. During the simulation, we set $b = 1.65\; \mu m$ for HNLF and $b = 4\; \mu m$ for SSMF according to the fiber datasheet, respectively. The diameter of the cladding is set to be 127$\mu m$ for HNLF and 125$\mu m$ for SSMF, respectively, and the fiber length is set to be 10 m. In both Fig. 1(a) and (b), ${\rho _{0,1}}$ of the acoustic mode ${R_{0,1}}$ is given as a reference. ${\rho _{0,21}}$ in Fig. 1(a) corresponds to the acoustic mode with the highest gain coefficient in HNLF, i.e. ${R_{0,21}}$ mode, which is verified as shown below. Similarly, ${\rho _{0,9}}$ in Fig. 1(b) represents the one with the highest gain coefficient in SSMF, i.e. ${R_{0,9}}$ mode. As can be seen, for higher-order acoustic modes, ${\rho _{0,m}}$ becomes denser within the fiber core which means the better overlap between the acoustic wave and optical wave. As a result, the coupling efficiency as well as the gain coefficient would be larger for high-order acoustic mode in HNLF than that of acoustic mode in SSMF.
Fig. 1. The intensity of the fundamental optical mode HE11 and the density variation ${\rho _{0,m}}$ of different acoustic modes ${R_{0,m}}$ in (a)HNLF and (b)SSMF, respectively.
Table 2. Datasheets of HNLF and SSMF used in the simulation
The values of acousto-optic coupling coefficients ${Q_{0(m )}}$ and ${Q_{1(m )}}$ for different acoustic modes are depicted in Fig. 2(a), (b) for HNLF and in Fig. 2(d), (e) for SSMF, respectively. Those values are all normalized with respect to the corresponding maximum values for HNLF. Note that the value of ${Q_{1(m )}}$ is negative, and its absolute value is used here. Comparing Fig. 2(a), (b) with Fig. 2(d), (e), we can see that the values of acousto-optic coupling coefficients for HNLF are still large at high resonance frequency while those for SSMF become small. Combining the two coupling coefficients, we calculate the normalized gain coefficient for different ${R_{0,m}}$ modes in HNLF and SSMF by using Eq. (8), as shown in Fig. 2(c) and (f). As can be seen in Fig. 2(c), due to the high acousto-optical coupling efficiency, the normalized gain coefficient in HNLF reaches maximum value of 1.0 when the resonance frequency is 979.5 MHz (corresponding to ${R_{0,21}}$ mode) and still maintain a relatively high value of 0.5 even if the center frequency of the acoustic modes reaches 1.5 GHz. In contrast, the gain coefficient in SSMF reaches its maximum value of only 0.41 when the resonance frequency is 419.3 MHz (corresponding to ${R_{0,9}}$ mode), as shown in Fig. 2(f). Moreover, the gain coefficient is almost zero in SSMF when the resonance frequency exceeds 900 MHz. We can see that HNLF has larger FBS gain than that of SSMF, which is helpful to achieve high sensitivity for acoustic impedance sensing. In our following experiment, we choose the FBS spectrum induced by ${R_{0,20}}$ mode (center frequency of 932.3 MHz) instead of ${R_{0,21}}$ mode for the acoustic impedance sensing since it can be easily measured without the overlap of other $T{R_{2,m}}$ modes. And according to Fig. 2, the value of the gain coefficient by ${R_{0,20}}$ mode, i.e., 0.99, is almost equal to the maximum value. Fig. 3(a) and (b) plots the FBS spectrum by ${R_{0,20}}$ in HNLF and ${R_{0,9}}$ in SSMF, respectively. The linewidth of the FBS spectrum is frequency dependent and is approximated as $\textrm{}{\mathrm{\Gamma }_m} = {\mathrm{\Omega }_m}/1000$ [27]. As a result, the linewidths for ${R_{0,20}}$ mode in HNLF and ${R_{0,9}}$ mode in SSMF are set to be 0.93 MHz and 0.42 MHz, respectively.
Fig. 2. Normalized acousto-optic coupling coefficient ${Q_{0(m )}}$, ${Q_{1(m )}}$, and normalized gain coefficient for ${R_{0,m}}$ modes in (a)-(c) HNLF and (d)-(f) SSMF.
On the other hand, the forward scattering efficiency $\mathrm{\eta }$ indicates the scattering capability of each acoustic resonance, which can be expressed as [3]:
where the L is the length of the fiber and $\Delta \phi $ is the phase shift of the incident light. Based on the FBS theory given in Ref. [29], we can derive the expression for the scattering efficiency of the GAWBS induced by ${R_{0,m}}$ modes:Similarly, based on the theory in Ref. [30], the scattering efficiency of the GAWBS induced by $T{R_{2,m}}$ modes can be obtained as well:
Based on Eq. (11)–(12), we simulate the normalized scattering efficiency of the GAWBS induced by ${R_{0,m}}$ and $T{R_{2,m}}$ modes in HNLF and SSMF, respectively, as shown in Fig. 4. The values for the parameters in the simulation are set as follows: $\textrm{n}$=1.5, ${k_0} = 4.054 \times {10^6}\textrm{}{\textrm{m}^{ - 1}}$, T=300 K, ${P_{11}} = 0.121$, ${P_{12}} = 0.270$ and $\rho = 2210\textrm{}kg/{m^3}$. Due to the different values of effective mode radius b, the HNLF and SSMF has completely different intensity distribution. Fig. 4(a),(b) show the normalized scattering efficiency induced by ${R_{0,m}}$ modes in HNLF (blue) and SSMF (red), respectively. The scattering efficiency is normalized with respect to the corresponding maximum value in HNLF. For HNLF, the normalized scattering efficiency reaches a maximum value of 1.0 when the resonance frequency is 601.7 MHz (corresponding to ${R_{0,13}}$ mode). For the ${R_{0,20}}$ mode used in the experiment, the normalized scattering efficiency is 0.73. While for SSMF, the highest scattering efficiency is 0.41, which occurs at the resonance frequency of 227.2 MHz (corresponding to ${R_{0,5}}$ mode). And the scattering efficiency for ${R_{0,9}}$ mode of SSMF used in the experiment is 0.26, which is quite low when compared with that of ${R_{0,20}}$ mode in HNLF. As for $\textrm{T}{R_{2,m}}$ modes in HNLF, the normalized scattering efficiency reaches maximum of 1.0 when the resonance frequency is 463.2 MHz (corresponding to $T{R_{2,25}}$ mode). While the highest scattering efficiency of 0.45 happens at a resonance frequency of 137.8 MHz (corresponding to $T{R_{2,7}}$ mode) in SSMF. In the experiment, we choose $T{R_{2,5}}$ mode (resonance frequency of 106.9 MHz) in HNLF for acoustic impedance measurement since this selection can completely avoid the crosstalk from other ${R_{0,m}}$ modes but still maintain a good scattering efficiency of 0.51. The scattering efficiencies induced by ${R_{0,m}}$ and $T{R_{2,m}}$ modes in HNLF and SSMF are compared in Table 3 and Table 4, respectively. As we can see that HNLF has much higher scattering efficiency when compared with SSMF, which is more obvious for higher-order modes. The results again support our scheme to achieve large SNR in the measurement and hence high sensitivity for acoustic impedance sensing. Note that the maximum values of the gain coefficient and scattering efficiency take place at different acoustic modes, which may be due to the use of approximated and empirical values of the linewidth ${\mathrm{\Gamma }_m}$ (i.e. ${\mathrm{\Gamma }_m} = {\mathrm{\Omega }_m}/1000$ [27]) in Eq. (8) for simple calculation. Since the gain coefficient and scattering efficiency emphasize the superiority of the HNLF over SSMF from different directions, both of them are calculated and shown for reference. And both the results in Fig. 2 and Fig. 4 are consistent that the values of the gain coefficient and scattering efficiency in HNLF are much larger than those in SSMF at high acoustic resonance frequency, e.g. beyond 500 MHz. In the following experiment we select the modes with nearly the highest gain coefficient in HNLF for the acoustic impedance sensing, and perform the comparison with the SSMF.
Fig. 4. Normalized FBS scattering efficiency of GAWBS for ${R_{0,m}}$ and $T{R_{2,m}}$ modes in (a), (c) HNLF (blue) and (b), (d) SSMF (red).
Table 3. Comparison of the scattering efficiency by ${{\boldsymbol R}_{0,{\boldsymbol m}}}$ modes in HNLF and SSMF
Table 4. Comparison of the scattering efficiency by ${\boldsymbol T}{{\boldsymbol R}_{2,{\boldsymbol m}}}$ modes in HNLF and SSMF
3. Experiment setup and results
In this section, we employ a fiber Sagnac loop setup in Fig. 5 to measure the FBS spectrum and demonstrate the proposed acoustic impedance sensing. The output of a continuous-wave laser at 1550.12 nm is amplified by an erbium-doped fiber amplifier (EDFA) and serves as the pump light. The amplified spontaneous emission (ASE) noise is eliminated by a bandpass filter. The light is directed to the Sagnac loop which consists of a 50:50 coupler, a fiber under test (FUT) and a polarization controller (PC). Inside the FUT, the GAWBS is stimulated by the pump light. By carefully adjusting the PC, ${R_{0,m}}$ and $T{R_{2,m}}$ modes can be stimulated or suppressed, and the phase modulation induced by the acoustic modes is converted to intensity modulation when the counter-propagating optical waves interfere at the coupler output. The output beat signal is received by using a 1.5 GHz photodetector (PD) and the electrical signal is sent to the electrical spectrum analyzer (ESA) for the analysis of the FBS spectrum.
Fig. 5. Experimental setup for acoustic impedance sensing using FBS in HNLF. EDFA: erbium-doped fiber amplifier; PC: polarization controller; FUT: fiber under test; PD: photodetector. ESA: electrical spectrum analyzer.
The HNLF used in the experiment has a core diameter of 4.45$\mu m$ and cladding diameter of 127$\textrm{}\mu m$, respectively, and its mode field diameter (MFD) is 3.3$\textrm{}\mu m$. Its attenuation coefficient is less than 1.5 dB/km. Figure 6(a) and (b) show the measured FBS spectrum for both ${R_{0,\textrm{m}}}$ modes and $\textrm{T}{\textrm{R}_{2,m}}$ modes in a 940-m-long HNLF within the frequency range of 0-1.5 GHz. As a comparison, the corresponding FBS spectrum in a 1-km-long SSMF is also measured. For fair comparison, the EDFA output is slightly adjusted to ensure that the optical power after passing through SSMF is consistent with the case of HNLF. As can be seen in Fig. 6(a), the resonance peaks for ${R_{0,m}}$ modes in HNLF are still strong when the frequency is beyond 1.2 GHz, which is due to the high gain coefficient provided by the HNLF. In contrast, the resonance peaks in SSMF almost disappear when the resonance frequency reaches 800 MHz, as shown in Fig. 6(a). Similarly, for $T{R_{2,\textrm{m}}}$ modes HNLF has stronger resonance peaks over a wide frequency range, while resonance peaks in SSMF almost disappear beyond the frequency range of 500 MHz. Note that in Fig. 6 the values in the vertical axis are in the logarithmic form, while those in Fig. 2 and Fig. 4 are in the linear form. Thus there would be some difference in visual sense if one compares the results in Fig. 6(a) with Fig. 2 or Fig. 4 directly. Actually according to Fig. 2, there is 2.4 times difference for the two maximum values of the normalized gain coefficient for HNLF and SSMF, which corresponds to 3.8 dB difference in the logarithmic form. And if the base lines for the results of HNLF and SSMF in Fig. 6(a) are placed at the same level, the maximum RF power in HNLF is found to have at least 3 dB larger than that in SSMF, which agrees well with our simulation. The different base lines result from the use of slightly different pump powers for HNLF and SSMF to compensate the fiber loss for fair comparison. Table 5 and Table 6 give both theoretical and measured resonance frequency for ${R_{0,\textrm{m}}}$ modes and $T{R_{2,\textrm{m}}}$ modes in HNLF, respectively. From the two tables, we can see that the values of the measured resonance frequency agree well with the theoretical ones. Note that due to the extreme low scattering efficiency for $T{R_{2,6}}$ mode (i.e. 0.01 in Table 4), we do not observe it in the experiment. For $T{R_{2,16}}$/$T{R_{2,17}}$ and $T{R_{2,24}}$/$T{R_{2,25}}$ modes, the frequency spacing between them is too small to distinguish them, so there is only one broad peak observed during the experiment.
Fig. 6. Measured FBS spectrum using HNLF (blue) and SSMF (red) for (a) ${\textrm{R}_{0,m}}$ modes and (b) $\textrm{T}{\textrm{R}_{2,m}}$ modes, respectively.
Table 5. Theoretical and measured resonance frequency for ${{R}_{0,{\boldsymbol m}}}$ modes in HNLF
Table 6. Theoretical and measured resonance frequency for ${T}{{R}_{2,{\boldsymbol m}}}$ modes in HNLF
For acoustic impedance sensing experiment, we remove the coating of a 10-m-long HNLF and use the uncoated HNLF as the FUT, which is immersed into the sucrose solution with different concentrations (0-40%). Note that the concentration of the sucrose solution has nearly linear relationship with its acoustic impedance when the concentration is below 50% [19,31]. Both ends of the HNLF are spliced with very short SSMFs in order to couple the light into the HNLF. We have measured the total coupling loss after splicing, which is 8 dB for both ends (i.e., 4 dB per coupling end). As mentioned in Section 2, we choose the FBS spectrum induced by ${R_{0,20}}$ mode for the demonstration since it can be easily measured without the overlap of other $T{R_{2,m}}$ modes. ${R_{0,20}}$ mode still has almost the maximum gain coefficient according to the results in Fig. 2 and Fig. 6(a). The measured FBS spectra when the HNLF is placed under different environment are shown in Fig. 7. As a reference, Fig. 7(a) also plots the measured FBS spectrum when the uncoated HNLF is placed in air, and the small peak originates from the incomplete suppression of the $T{R_{2,49}}$ mode. By using Lorentzian curve fitting (LCF), the linewidth of the FBS spectra measured under different environment can be obtained. The FBS linewidth is found to be 1.60 MHz when the HNLF is exposed to air. The value is a little larger than that in the simulation which may be due to the inhomogeneity of the fiber cladding [26]. When the solution is pure water (i.e. 0% concentration), the linewidth in Fig. 7(b) is calculated to be 4.76 MHz. Compared with the case in air, the linewidth in pure water is significantly broadened while the peak intensity of the FBS spectrum is reduced. Fig. 7(c)-(f) depicts the measured spectra for the sucrose solution with 10%∼40% concentration and the corresponding linewidth are calculated to be 5.01 MHz, 5.76 MHz, 6.05 MHz and 6.66 MHz, respectively. We can see that when the concentration of the sucrose solution increases, the spectrum linewidth also increases gradually. The center frequency of the ${R_{0,20}}$ mode induced FBS spectrum is 930.7 MHz. Fig. 7(g) plots the relationship between the measured linewidth and the acoustic impedance of the sucrose solution. By linear fitting, the measurement sensitivity is calculated to be $\textrm{}3.83 \pm 0.19\textrm{MHz}/[{\textrm{kg}/({\textrm{s} \cdot \textrm{m}{\textrm{m}^2}} )} ]$ for ${R_{0,20}}$ mode in HNLF. Note that the 5th data point (corresponding to the 20% concentration) in Fig. 7(g) deviates a little from the fitting curve when compared with that of other points, which may be due to the fact that the concentration of the sucrose may not be exactly controlled and would be slightly larger than the desired value when the measurement is performed. Even if this data point is discarded, the sensitivity is still found to be $3.83\textrm{MHz}/[{\textrm{kg}/({\textrm{s} \cdot \textrm{m}{\textrm{m}^2}} )} ]$ for ${R_{0,20}}$ mode in HNLF. Moreover, we also carry out the acoustic impedance sensing by using some other acoustic modes. When using ${R_{0,19}}$, ${R_{0,21}}$ and ${R_{0,22}}$ modes in HNLF, the sensitivity is measured to be 3.70, 3.73 and 3.68 $\textrm{MHz}/[{\textrm{kg}/({\textrm{s} \cdot \textrm{m}{\textrm{m}^2}} )} ]$, respectively, as shown in Fig. 8(a)-(c). As can be seen, there is only little difference in the measurement sensitivity when using adjacent acoustic modes. As a contrast, a 10-m-long uncoated SSMF is used as the FUT and the same procedure is performed except ${R_{0,9}}$ mode is measured due to its relatively large gain coefficient in SSMF. The FBS spectra for different environment are shown in Fig. 9(a)-(f). The linewidth is calculated to be 0.60 MHz for the air and 4.03, 4.40, 4.74, 5.00, 5.43 MHz for the sucrose solution with 0-40% concentration (10% step), respectively. The center frequency for ${R_{0,9}}$ mode in SSMF is 417.8 MHz. By linear fitting, the sensitivity for ${R_{0,9}}$ mode in SSMF is calculated to be $2.70\textrm{} \pm 0.13\textrm{MHz}/[{\textrm{kg}/({\textrm{s} \cdot \textrm{m}{\textrm{m}^2}} )} ]$, as shown in Fig. 9(g). With the use of ${R_{0,7}}$ and ${R_{0,8}}$ modes in SSMF, the acoustic impedance sensing is also performed and the sensitivity is measured to be 2.46 and 2.21, respectively, as illustrated in Fig. 10(a) and (b). Note that there is large overlap of the spectrum between ${R_{0,5}}$ and $T{R_{2,21}}/T{R_{2,22}}$ modes in SSMF, so we do not use ${R_{0,5}}$ for sensing experiment. Comparing the results in Fig. 7 and 8 with Fig. 9 and 10, we can see that the value of the sensitivity for acoustic impedance sensing is improved beyond 3$\textrm{MHz}/[{\textrm{kg}/({\textrm{s} \cdot \textrm{m}{\textrm{m}^2}} )} ]$ when using HNLF, which is due to its high FBS gain. We also calculate the frequency uncertainty of the measured linewidth based on Eqs. (5)–(6) in Ref. [32] for both HNLF and SSMF. The linewidth frequency uncertainty is 0.08 MHz for ${R_{0,20}}$ mode in HNLF and 0.05 MHz for ${R_{0,9}}$ mode in SSMF, respectively. The uncertainty by HNLF is slightly worse than that by SSMF, which may be due to the linewidth difference. According to Eqs. (5)–(6) in Ref. [32], the frequency uncertainty is proportional to the linewidth of the Brillouin gain spectrum. And according to the choice of the acoustic mode we used for acoustic impedance sensing, the linewidth is larger for ${R_{0,20}}$ mode in HNLF, which may cause the slightly larger frequency uncertainty.
Fig. 7. Measured FBS spectrum for ${R_{0,20}}$ mode in HNLF under different external environment: (a) air, (b) 0%, (c) 10%, (d) 20%, (e) 30%, (f) 40% concentration sucrose solution; (g) measured linewidth of the FBS spectrum versus acoustic impedance. The red dashed line shows the linear fitted result.
Fig. 8. Measured linewidth of the FBS spectrum versus acoustic impedance for (a) ${R_{0,19}}$, (b) ${R_{0,21}}$, and (c) ${R_{0,22}}$ mode in HNLF. The red dashed line shows the linear fitted result.
Fig. 9. Measured FBS spectrum for ${R_{0,9}}$ mode in SSMF under different external environment: (a) air, (b) 0%, (c) 10%, (d) 20%, (e) 30%, (f) 40% concentration sucrose solution; (g) measured linewidth of the FBS spectrum versus acoustic impedance. The red dashed line shows the linear fitted result.
Fig. 10. Measured linewidth of the FBS spectrum versus acoustic impedance for (a) ${R_{0,7}}$ and (b) ${R_{0,8}}$ mode in SSMF. The red dashed line shows the linear fitted result.
Finally, we also demonstrate the use of $T{R_{2,\; m}}$ mode in HNLF for acoustic impedance sensing. $T{R_{2,5}}$ mode is selected since there is less crosstalk from other ${R_{0,m}}$ modes when performing the measurement. Moreover, according to Fig. 4(c), $T{R_{2,5}}$ mode in HNLF still has a good scattering efficiency. The results are given in Fig. 11. Figure 11(a) plots the FBS spectrum when the fiber is exposed to air and its linewidth is measured to be 0.13 MHz. Figure 11(b)-(f) depict the spectra when the fiber is immersed into the sucrose solution with 0%-40% concentration. The linewidth is calculated to be 0.23 MHz, 0.25 MHz, 0.27 MHz, 0.30 MHz and 0.35 MHz, respectively. Obviously, the linewidth increases as the acoustic impedance of the substance outside the fiber becomes large. The measurement sensitivity by using $T{R_{2,5}}$ mode in HNLF is calculated to be $0.24\textrm{MHz}/[{\textrm{kg}/({\textrm{s} \cdot \textrm{m}{\textrm{m}^2}} )} ]$, as shown in Fig. 11(g). Compared with the sensitivity of $0.16\textrm{MHz}/[{\textrm{kg}/({\textrm{s} \cdot \textrm{m}{\textrm{m}^2}} )} ]$ by the same acoustic mode in SSMF [20], the sensitivity using HNLF is improved by1.5 times.
Fig. 11. Measured FBS spectrum for $T{R_{2,5}}$ mode in HNLF under different external environment: (a) air, (b) 0%, (c) 10%, (d) 20%, (e) 30%, (f) 40% concentration sucrose solution; (g) measured linewidth of the FBS spectrum versus acoustic impedance for $T{R_{2,5}}$ mode in HNLF. The red dashed line shows the linear fitted result.
4. Conclusion
We have proposed and demonstrated the use of radial acoustic modes in an uncoated HNLF for highly sensitive acoustic impedance measurement. Both the simulation and experiment indicate that due to the high acousto-optical coupling efficiency, the gain coefficient and scattering efficiency by both ${\textrm{R}_{0,\textrm{m}}}$ and $\textrm{T}{\textrm{R}_{2,\textrm{m}}}$ acoustic modes in HNLF are much higher than those in SSMF, which gives rise to better SNR and measurement sensitivity. The sensitivity using ${\textrm{R}_{0,20}}$ mode in HNLF is measured to be $3.83\textrm{MHz}/[{\textrm{kg}/({\textrm{s} \cdot \textrm{m}{\textrm{m}^2}} )} ]$. In contrast, the sensitivity is measured to be $2.70\textrm{MHz}/[{\textrm{kg}/({\textrm{s} \cdot \textrm{m}{\textrm{m}^2}} )} ]$ when using ${\textrm{R}_{0,9}}$ mode (with almost the largest gain) in SSMF. Moreover, the sensitivity by using $\textrm{T}{\textrm{R}_{2,5}}$ mode in HNLF is measured to be $0.24\textrm{MHz}/[{\textrm{kg}/({\textrm{s} \cdot \textrm{m}{\textrm{m}^2}} )} ]$, which is 1.5 times higher than that using the same mode in SSMF. The high sensitivity is greatly desirable for many scenarios, especially when the change of external environment is small. The improved sensitivity will also benefit distributed measurement of acoustic impedance with enhanced SNR and sensing distance. Finally we want to mention that this preliminary work shows better sensitivity in HNLF, however, the measurement precision and confidence requires further works of characterization and standardization. For example, the level of ASE noise from EDFA may be different in the measurements for HNLF and SSMF, since the pump power is adjusted by using EDFA to compensate larger loss in the HNLF, possibly leading to the base noise difference for the measurements. To solve this problem, one may use the lock-in frequency measurement with a probe wavelength different from the pump wavelength. Moreover, the frequency uncertainty is just estimated based on the theoretical model in Ref. [32], and it is believed that more accurate values of the frequency uncertainty can be experimentally obtained by performing the measurement for multiple times and then calculating the standard deviation from multiple measurements.
Funding
National Key Research and Development Program of China (2022YFB2903403); National Natural Science Foundation of China (62005087); Science Foundation of Donghai Laboratory (DH-2022KF01015); Open Projects Foundation of Yangtze Optical Fiber and Cable Joint Stock Limited Company (YOFC) (SKLD2006).
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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