Broadband Acoustic Vibration Sensor Based on Cladding-Mode Resonance of Double-Cladding Fiber

We have proposed and demonstrated a double-cladding fiber (DCF) with cladding-mode resonance property for broadband acoustic vibration sensing. Since the fundamental mode in the core waveguide is able to be coupled to LP05 mode in the tube waveguide once the phase-matching condition is fulfilled, the transmission spectrum can exhibit a dip with a large extinction ratio. An acoustic vibration could induce the wavelength shift of such transmission spectrum, so that the intensity variation at a wavelength near the dip is coded with the information of the acoustic vibration signal. By demodulating the response of intensity variation, the frequency of the applied acoustic vibration signal can be recovered. Such a DCF-based sensor with an intensity modulation could measure the acoustic vibration with a broadband frequency range from 1 Hz to 400 kHz and exhibits the maximum signal-to-noise ratio (SNR) of ~80.79 dB when the vibration frequency is 20 kHz. The obtained results show that the proposed DCF-based acoustic vibration sensor has a potential application in environmental assessment, structural damage detection, and health monitoring.


Introduction
Acoustic vibration detection has been widely applied in many fields such as environmental assessment [1], structural damage detection [2], and health monitoring [3]. In the past few years, the fiber optic acoustic vibration sensors attracted the great attention due to their unique advantages including electromagnetic immunity, compactness, robustness, remote sensing, high sensitivity, and broadband [4,5]. In previous works, various fiber optic acoustic vibration sensors have been reported such as Michelson interferometer (MI) [6−8], Mach-Zehnder interferometer (MZI) [9], Fabry-Perot interferometer (FPI) [10], Sagnac interferometer [11,12], fiber Bragg gratings (FBGs) [13−16], and long period gratings (LPGs) [17]. The fiber interferometer acoustic vibration sensors are designed based on the theory of phase modulation, and even a very little phase change caused by the acoustic signal can be discovered, which makes them show an ultrahigh sensitivity. Recently, L. Liu et al. [6] used two sides of the polypropylene/poly (PP/PET) diaphragm as the reflector of the sensing arm and reference arm to build up an MI, which gained a doubled optical path difference compared with FPI. However, for this kind of sensors, the complicated demodulating algorithms are always required to restore the signal, and their sensing systems usually are large in size. Other sensors are based on the effect of wavelength modulation. In [13], Campopiano et al. adopted two different coating materials of low elastic modulus to enhance FBG based hydrophones' sensitivity. Gaudron et al. [17] used the LPGs to detect sound at a distance of up to 2 m − 3 m from the sensor. Although the FBGs and LPGs acoustic vibration sensors show a good sensing response, their difficult post fabrications may influence the consistency of the sensors and increase the cost.
Recently, many researchers have focused on the new simple sandwich sensor structure of single mode fiber (SMF)-special fiber-SMF for acoustic vibration test. The middle fiber structure includes photonic crystal fiber (PCF) [18], multimode fiber [19−21], and tapered fiber [22−24]. These sensors mostly use the middle structure to excite higher-order modes or construct an in-fiber interferometer to achieve high sensitivity for vibration acoustic measurement. Nevertheless, in the above sensors, their middle structures are usually very fragile so they often require special drawing craft and packaging technique. Some of these structures need extra fabrication such as tapering, etching, and grating to help excite the higher-order modes, which degrades the robustness of fiber sensors. Ni et al. [25] proposed using the polyethylene terephthalate film to gain two flat frequency responses of 70 Hz to 200 Hz and 1 kHz to 3 kHz based on the thin core ultra-long period fiber grating. But the polyethylene terephthalate film limits its frequency response range for its own resonant frequency when its thickness is fixed.
In this work, a double-cladding fiber (DCF) with cladding-mode resonance property for broadband acoustic vibration sensing has been demonstrated. Such DCF has a lower refractive index of the inner cladding than that of the core and outer cladding, which can couple the fundamental mode in the core waveguide to LP 05 mode in the coaxial tube waveguide at the resonant wavelength. By splicing a piece of DCF with the standard single mode fiber (SMF), the transmission spectrum presents a dip due to the cladding-mode resonance. An acoustic vibration could induce the shift of wavelength of such transmission dip, so that the intensity variation of DCF at a wavelength near the dip is coded with the information of the acoustic vibration signal. By demodulating the intensity variation, the applied acoustic vibration signal can be detected. Such DCF-based sensor with an intensity modulation could measure the acoustic vibration with a broadband frequency range. Compared with the aforementioned fiber-based acoustic vibration sensor, the proposed DCF sensor has advantages including simple structure, elimination of post fabrication and complicated algorithms of demodulation, broadband, low cost, and compatibility to the commercial SMF. The obtained results show that the proposed DCF-based acoustic vibration sensor has a potential application in environmental assessment, structural damage detection, health monitoring, etc.

Sensing principle
The acoustic vibration sensor is based on a double-cladding fiber. The DCF consists of three layers: core, inner cladding, and outer cladding. The refractive index profile of the DCF is depicted schematically in Fig. 1(a). The refractive index of the core n 1 is equal to that of the outer cladding n 3 , higher than that of the inner cladding n 2 , i.e. n 1 =n 3 >n 2 . Attributed to the thin layer of the inner cladding, the core and the outer cladding form coaxial waveguides, named as core waveguide and tube waveguide. The core waveguide as well as the tube waveguide only contains two layers, as shown in Fig. 1(b). According to the coupled mode theory, optical power exchanges between each waveguide through the evanescent wave. Due to the asymmetric twin coupling waveguide structure, it only satisfies the phase matching condition at particular wavelengths: where core eff -co 2 n π β λ = and tube eff -tube 2 n π β λ = are propagation constants for modes in the core waveguide and the modes in the tube waveguide, respectively; λ is the operating wavelength; eff -co n and eff -tube n are the effective indices of the core mode and tube modes, respectively. Figure 1(c) plots the effective refractive index of modes propagating in the two waveguides with the parameter of a = 4 μm, b = 13 μm, c = 62.5 μm, n 1 = n 3 = 1.4685, and n 2 = 1.4665. It shows that LP 01 mode in the core waveguide has a similar effective refractive index (RI) of LP 05 mode in the tube waveguide near C band, indicating the phase-matching condition could occur there. At the phase-matching wavelength, there is strong coupling between the core mode and cladding mode.
In our design, the sensor with the SMF-DCF-SMF structure is proposed. For a piece of DCF, the optical power in the core can be calculated as follows [26]: where k is the coupling coefficient that could be calculated from the overlapping integral of the mode in the core waveguide and the modes in the tube waveguide.
core tube β β β Δ = − is the propagation constant difference between the coupled two modes. L refers to the access length of the DCF. According to (2) Here, the coupling length 0 L is named as the beat length. Therefore, the transmission spectrum presents a band-reject filter spectrum near the resonant wavelength, which can be utilized for acoustic vibration sensing.
The principle of the acoustic vibration sensor based on the DCF is illustrated in Fig. 1(d). Once the DCF sensor head is attached to the acoustic vibration source, the resonant filter spectrum of the DCF will change with the pull strength. According to the photo-elastic effect of an optical fiber, the axial strain applied to the fiber decreases the refractive index [27]. Because the fluorine-doped silica in the inner cladding has a lower photo-elastic coefficient than the pure silica, the refractive index difference between the core and the inner cladding becomes smaller gradually with the strain strength. In this case, the dispersion curves of the mode in the core waveguide and the mode in the tube waveguide shift differently. Consequently, the axial strain from the acoustic vibration leads to a blue shift of the resonant spectrum [27]. At a fixed wavelength, the intensity of the proposed sensor is periodically changed due to the shift of the resonant spectrum, and the acoustic vibration can be traced back by detecting the periodic change in intensity. Such an SMF-DCF-SMF sensor with intensity modulation can simplify its installation in real application of acoustic vibration measurement.

Experimental setup
The RI profile of the used DCF is measured by an RI profiler (S14, Photon Kinetics) as shown in Fig. 2(a). The reference is RI matching oil with RI of 1.4605, so that all the parameters of the DCF are calculated to be around a = 4 μm, b = 13μm, c = 62.5 μm, n 1 = n 3 = 1.4685, and n 2 = 1.4665. By accessing a piece of DCF with standard SMF, the transmission spectrum with a dip can be measured. We have found that the transmission dip with the largest extinction ratio of ~40 dB can be obtained when the length of DCF is about 13 mm as shown in Fig. 2(b), and the dip locates around 1530 nm. An infrared camera (HAMAMATSU InGaAs camera C10633) is further used to capture the mode profile at the output of DCF when the input wavelength is 1530 nm. The ring pattern confirms that the excited mode in DCF is LP 05 mode, which is consistent with our simulation results. The measured dip wavelength deviates from the theoretical result. Such deviation can be explained by the principle of mode coupling. Based on (1), although the phase matching refers to a particular wavelength, the transmission dip is also affected by the access length of the DCF according to (2). When we use the fusion splicer to access the DCF, the controllable accuracy of the access length is a few hundred micrometers, so the deviation of the dip position from the theoretical simulation is observed.  Figure 3 shows the response of the proposed DCF-based acoustic vibration sensor subjected to different applied frequencies. When the piezoelectric buzzer is driven by a sinusoidal wave with a frequency of 10 Hz and a voltage of 10 V, the demodulated signal is shown in Fig. 3(a). The inset of Fig. 3(a) shows the detail of oscillation trace. The oscillation trace is originated from the intensity variation of DCF at 1550 nm when the acoustic vibration is changed periodically. Figure 3(b) shows the detected signal in the frequency domain by conducting the fast Fourier transform (FFT) of the oscilloscope trace. In Fig. 3(b), the major strongest frequency response at fundamental component is higher than the harmonic components, so we can accurately figure out the induced vibration frequency. All average SNRs are measured at the fundamental component of the applied signals. Previous report has shown that the highest noise level could be found if the signal fell in the very low frequency [28]. In our experiment for simplicity, all average background noise levels are taken at its relatively large value of −80 dB which is measured for the signal at a few hertz. For estimating SNR of the signal with relatively high frequency, using such a high background noise level might reduce the SNR. In turn, if an SNR with a large value is achieved for a fixed signal strength at such a high noise level, it indicates that the proposed sensor is able to interrogate the signal well. An SNR of ~48.99 dB can be observed at 10 Hz. When the driven frequency is increased to 20 kHz and the driven voltage is kept at 10 V, the DCF-based acoustic sensor shows a good performance in oscilloscopic trace as shown in Fig. 3(c). By conducing FFT, an SNR as high as ~80.79 dB of the demodulated signal is obtained at frequency of ~20 kHz as shown in Fig. 3(d). When the driven frequency is further increased to ~340 kHz with 10 V, the demodulated signal shows an SNR of ~50.58 dB as shown in Figs. 3(e) and 3(f). The demodulated frequency is well matched with the applied frequency, proving that the proposed DCF can be an effective acoustic vibration sensor. We further investigate the broadband response of the DCF-based acoustic vibration senor ranging from 1 Hz to 748 kHz as shown in Fig. 4, which covers bands of the infrasound, audible sound, and ultrasound. The buzzer is driven by a 10 V sinusoidal wave. Between 1 Hz and 100 Hz, the frequency response of DCF exhibits a smooth response characteristic, and the SNR is above 30 dB with an average value of ~50 dB. In 100 Hz − 1 kHz, the frequency response of DCF fluctuates with an average SNR of ~60 dB. Between 1 kHz and 20 kHz, the SNR is relatively high, and the maximum SNR reaches ~80.79 dB at 20 kHz. Between 20 kHz and 400 kHz, although the SNR is gradually dropped, the SNR can be still higher than 30 dB. The results prove DCF to be a broadband acoustic vibration sensor. Beyond 400 kHz, the SNR shows a sharp downward trend, and its SNR is reduced to 15.4 dB at 748 kHz. The acoustic vibration signal of DCF has different response characteristics in different frequency segments, which is believed to be originated from the acoustic vibration sensing system, the structural characteristics of the DCF fiber, and the frequency response of the piezoelectric ceramic buzzer. For most of the reported optic-fiber acoustic vibration sensors including the thin core ultralong period fiber grating [25], multimode fused coupler [28], the tapered fibers [29], the fiber microcantilever [30], and the multicore fibers [31], the sensing systems have a relatively limited frequency response ranging from a few hertz to tens of kilohertz. Compared with the above fiber based acoustic vibration sensors, our proposed DCF-based acoustic vibration sensors can measure the acoustic vibration with a broadband frequency range from 1 Hz to 400 kHz with the SNR larger than 30 dB and exhibit the maximum SNR of ~80.79 dB when the vibration frequency is 20 kHz. In the experiment, the DCF vibrates with the piezoelectric buzzer. Because the piezoelectric buzzer has a narrow working bandwidth, the limit of frequency response is believed to be mainly due to the piezoelectric buzzer rather than the DCF itself. Previous works have shown a tapered fiber-based acoustic vibration sensor with frequency response ranging from 30 Hz to 40 kHz, and the working bandwidth of the applied speaker source is only from 30 Hz to 6 kHz [32]. It is found that although SNRs vary at different frequencies, the trend of the SNR curve of the sensor is similar to that of a standard accelerometer, both of which depend on the frequency response of the speaker. Similarly, in our work, the piezoelectric buzzer also has been working frequency limitation which is less than a few kilohertz, so it affects the SNRs at different frequencies, especially, far beyond the bandwidth. 1 Frequency (Hz) Since the applied voltage of the driven signal as well as the access length of DCF influences the SNR of the demodulated signal, we have studies four DCF sensors with the access length of 9 mm, 13 mm, 17 mm and 21 mm, receptively, by turning the input voltage of the piezoelectric buzzer from 500 mV to 10 V at 20 kHz. The SNRs of the fiber sensor are plotted in Fig. 5, and the SNRs of the fiber sensor increase rapidly first, then fall to a steady value with the input voltage rising from 500 mV to 10 V. The maximum SNR is achieved to be ~80.79 dB for DCF of 13 mm subjected to the vibration with the frequency of 20 kHz. The obtained results suggest that the optimized access length is required when we need to achieve a high SNR. The sensitivity of the sensor is defined as the ratio of the detected peak-to-peak voltage captured by the oscilloscope to the applied sound pressure level. The sound pressure level (L P ) of the acoustic source generated by the piezoelectric buzzer is characterized by a handheld sound level meter (SLM), which is commonly used in acoustic measurement. The SLM shows the values in the logarithmic scale that can be transformed into a linear scale as follows:

Experimental results and discussion
where P is the sound pressure, and 0 P is the reference sound pressure where 0 P =2×10 −5 Pa in the air [33]. For the acoustic vibration signal at 20 kHz with 10 V driven signal, the sound pressure level of 79 dB is tested by using the SLM, and the corresponding sound pressure is approximate to 0.18 Pa. Because the peak-to-peak amplitude of the detected signal is 2 V, the sensitivity of the whole system is calculated to be ~11.1 V/Pa.

Conclusions
A broadband acoustic vibration sensor with the SMF-DCF-SMF scheme has been proposed for the first time. Such scheme presents a band-reject filter spectrum due to the cladding-mode resonance of DCF, which is sensitive to the acoustic vibration induced structure change. By accessing DCF with the length of 13 mm, a transmission dip with the largest extinction ratio of ~40 dB can be obtained around 1530 nm. The acoustic vibration signal could be encoded by detecting the intensity variation of DCF near the resonant wavelength. Such a DCF-based sensor could measure the acoustic vibration with a broadband frequency range from 1 Hz to 400 kHz with the SNR larger than 30 dB, and it exhibits the maximum SNR of ~80.79 dB when the vibration frequency is 20 kHz. Because of the merits including broadband response, compact structure, low cost, and the compatibility with commercially standard SMF, the proposed DCF-based acoustic vibration sensor shows the potential applications in environmental assessment, structural damage detection, health monitoring, etc.
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