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Abstract
In this paper, a simple sensing method based on a silicon oxide microcavity optomechanical oscillator (OMO) is proposed and demonstrated for the detection of acoustic signals. Firstly, the resonance damping was reduced by improving the optical quality factor (Qo) and increasing the sphere-to-neck ratio. After optimizing the process, a microsphere OMO was fabricated, which has an ultra-high mechanical quality factor (6.8 × 106) and greater sphere-to-neck ratio (∼11:1), based on which ultra-narrow linewidth phonon laser (∼1 Hz) is constructed. Secondly, by changing the refractive index of the coupling interval, the low-frequency acoustic pressure signal is efficiently coupled into the microcavity OMO to construct a high-resolution acoustic sensor. This sensing mechanism can not only measure the acoustic pressure, but also use the sideband signal in the modulation mechanism to measure the frequency of acoustic signals (15 Hz∼16 kHz), the sensitivity is 10.3 kHz/Pa, the minimum detectable pressure is 1.1 mPa, and noise-limited minimum detectable pressure is 28.8 µPa/Hz1/2. It is the highest detection resolution compared with the same type of low-frequency acoustic signal detection currently reported. This OMO-based acoustic sensing detection method opens up a new path for future miniaturized, ultra-high-precision, and cost-effective acoustic sensing.
© 2024 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement
1. Introduction
In recent years, low-frequency acoustic sensors have been widely used in various fields such as national defense and security [1], vibro-acoustic signal analysis [2], and acoustic resonance spectrometry detection [3]. High-resolution acoustic sensing technology has shown great potential and has become a research hotspot. Among them, the acoustic sensor based on optical resonator has the advantages of high precision and small volume, anti-electromagnetic interference and large dynamic range and has been widely studied in recent years [4,5]. In particular, the optical resonator based on the whispering gallery mode (WGM) is an important sensitive structure for acoustic sensing due to its excellent characteristics of high-quality factor and extremely small mode volume [6–8]. To date, various microcavity systems such as polystyrene, SU8, PDMS and other polymer microcavities [9–11], microfiber junctions [12], microtoroid [13], and microbubble cavities [14] and other optical cavities resonant cavities [15–17] have been used in acoustic sensor research. However, these acoustic sensors are flexible, the sensing mechanism is the detuning of the light wavelength caused by the deformation of the microcavity caused by the acoustic pressure, the spectrum itself is broad and results in a relatively low optical detection resolution and these acoustic sensors are affected by the sensitive structure material and manufacturing process limitations [18].
Acoustic sensing based on WGM optomechanical oscillator (OMO) can drive and read out mechanical motion through purely optical manipulation in optomechanical systems, using its high mechanical frequency to improve anti-jamming capability and sensing bandwidth, and its detection resolution can be lower than standard quantum limit [19,20], greatly improving sensitivity [21–23]. For example, Westerveld et al. used an opto-mechanical ultrasonic sensor formed by a gap of 15 nm between a silicon microring cavity and a thin film, and achieved a sensitivity of mPa/Hz1/2 in the frequency range of tens of MHz [24]; Li et al. used a microtoroid with an optical quality factor (Qo) of 107 and a mechanical quality factor (Qm) of 700 to achieve ultrasonic sensing with a sensitivity of 46 µPa/Hz1/2-10 mPa/Hz1/2 in the range of 0.25-3.2 MHz [25]. However, on one hand, these studied sensors are complicated in process, difficult to manufacture and expensive; on the other hand, most of them are concentrated in the ultrasonic range, and there are few studies on low-frequency acoustic signals. Jiang et al. were the first to report a compact, inexpensive, and highly sensitive cantilever microsphere OMO system with a frequency response range of 0 to 6 kHz and a noise equivalent pressure of 52 µPa/Hz1/2 at 900 Hz [26]. However, the relationship between OMO and acoustic sensing has not been explored.
In this work, cost-effective microsphere OMO with tiny dimensions and a high sphere-to-neck ratio (ratio of microsphere and attached-fiber-pillar diameters) are created through a simple manufacturing process using CO2 laser de-fused silica fiber cones. The microsphere OMO with ultra-high Qo and Qm at room temperature is used as a sensitive structure, which can cause sustained self-sustained oscillation and excite high-frequency and stable mechanical signals. Loading the acoustic signal, the mechanical signal is modulated by the baseband signal of the acoustic signal as a carrier signal. The size of the acoustic pressure can be detected by the frequency drift of the optical mechanical signal driven by the acoustic pressure. The narrow line width of the mechanical signal can improve the detection resolution and obtain ultra-high resolution acoustic sensing.
2. Theoretical analysis
The acoustic signal detection mechanism based on WGM-OMO is shown in Fig. 1(a). When the incident laser power (Pin) is higher than the optomechanical excitation threshold (Pth), utilizing the ultra-high quality factor microsphere OMO, the radiation pressure causes the self-sustained oscillation of the cavity at a certain frequency, which excites a high-frequency and stable mechanical signal (frequency, fm), when the acoustic wave signal is loaded, the acoustic wave is usually first incident on the very thin spherical neck, and then coupled into a WGM of the microsphere (radius, R). The mechanical signal is modulated by the baseband signal (frequency, fb) of the acoustic signal as a carrier signal (frequency, fc), so fc = fm. By exciting mechanical signals of different frequencies, the acoustic signal can be read out at different frequencies, and by adjusting the frequency of the acoustic signal, the signal can also be accurately read out in a sideband manner, as shown in Fig. 1(b). Leveraging the ultra-narrow linewidth characteristics of this phonon laser, low-frequency acoustic pressure signal is effectively coupled into the microsphere OMO by modulating the refractive index of the coupling gap. This establishes a high-resolution acoustic sensor.
Fig. 1. (a) Operational principle of the device based on WGM. (b) Spectrum of the OMO’s output in the presence of modulated acoustic pressure P = 1 Pa). The discontinuity between high and low frequency is made on purpose to help observing both parts of spectrum with high resolution.
The radial component (r(t)) of the mechanical deformation of the microsphere OMO caused by the acoustic pressure modulates the resonant frequency of the WGM (ωp = ω0 + ω0r(t)/R, where ω0 is the eigenfrequency of the cavity) and the deformation of the resonant cavity is caused by the combined action of the optical radiation pressure (Frad) and the equivalent acoustic pressure (FA), which is obtained from the equations as follows [27–29]:
3. Experimental results
The acoustic sensing sensitive structure is composed of a single-ended microsphere with an attached-fiber-pillar and a tapered optical fiber. The microsphere prepared by a CO2 laser, and optical fiber is prepared by melting operation. In the experiment, to achieve a microsphere optomechanical oscillator (OMO) with a high quality factor (Qm) and a narrow linewidth, it is necessary to address two key aspects. Firstly, reducing the effective mass of the microsphere is essential to ensure a low damping coefficient of the OMO, leading to a smaller mechanical energy dissipation rate. This reduction in mass facilitates the localization of mechanical energy in the microsphere, minimizing vibrational energy dissipation. Secondly, it is crucial to diminish the clamping region between the sphere and the neck, thereby reducing the mechanical loss path and lowering clamping losses. This strategy localizes more mechanical energy in the microsphere, further decreasing the dissipation rate of vibrational energy. This is achieved by increasing the sphere-to-neck ratio [30].
The preparation process has been reported in detail in the previous work [31]. It is important to control the length of attached-fiber-pillar, the diameter and shape of microspheres to make the microspheres more round and more uniform. The length (10 µm∼100 µm) of the attached fiber pillar is controlled by accurately adjusting the laser power, which is also related to the focal length and collimator. The diameter of microspheres (50 µm∼120 µm) is controlled by controlling the length of the remaining optical fiber (500 µm∼1 mm). The shape of microspheres is controlled by controlling the melting time and the alignment of microspheres with laser. When the size of the microspheres is small, focusing the laser spot on the microspheres leads to excessive local heat and difficult molding. This will lead to the deviation and sinking of the sphere and neck, impacting the optical Q-factor and mechanical quality factor. Additionally, the neck diameter must have the capacity to withstand the weight of the microsphere, preventing it from being infinitely thin. From a coupling perspective, the size of the microsphere is also restricted by the diameter of the coupled fiber cone. There is a matching relationship between the two, ensuring optical transparency, robustness of the fiber cone, and coupling efficiency. As a result, we ultimately selected a microsphere with a radius of approximately 30 µm and a sphere-to-neck ratio of around 11:1.
The coupling tapered fiber with a diameter of 1∼2 µm is drawn by heating a single-mode fiber (core layer 9/125 µm) with a hydrogen-oxygen flame, and requires one-time molding, which is the key to maintaining the toughness of the fiber. By monitoring the transmission of the tapered fiber in real time, the preparation of a single-mode fiber is guaranteed. On one hand, the diameter of the fiber taper is easy to match with the microsphere OMO. On the other hand, when the fiber is prepared to a single mode, multi-mode interference can be reduced. It affects the detection of acoustic signals. In this experiment, a three-dimensional platform is used to control the coupling between the microsphere OMO and the tapered optical fiber, and the coupling adjustment process can be monitored in real time by CCD.
The linewidth of the oscillation is inversely proportional to the mechanical energy stored in the oscillator. In the experiment, when the optical power is increased to reach the power threshold, the scanning is stopped, and the microcavity achieves continuous and regular sinusoidal oscillation. At this point, the mechanical energy stored in the oscillator significantly increases, leading to the excitation of a phonon laser with an ultra-narrow linewidth [31].
Experimental setup schematic of the acoustic sensing is shown in Fig. 2. The system consists of three parts: acoustic input system, optical transmission system and mechanical detection system. The acoustic input system consists of a loudspeaker, a power amplifier and a sound level meter. The loudspeaker emits low-frequency sounds audible to the human ear with a frequency in the range of 0 Hz∼20 kHz. The sound intensity can be controlled by the sound amplifier and calibrated by the sound level meter. In the optical transmission system, a tunable single frequency laser (TOPTICA CTL-1550) with a linewidth of 10 kHz operates as the pump laser, which has a continuous scanning function, its scanning range can reach 140 V. The output laser sequentially goes through an isolator and a polarization controller in sequence. After being amplified by the booster optical amplifier (BOA, Thorlabs BOA1004P). The laser light is coupled into the microsphere cavity through a 1-3 µm diameter fiber taper and single-mode fiber. The output light signal is detected by a photodetector (PD Thorlabs DET08CFC), and its time and frequency domains are analyzed using an oscilloscope (Tektronix MSO64) and spectrum analyzer (R&S FSV3030), respectively, to observe signal.
Fig. 2. Schematic diagram of experimental setup for the acoustic sensing. ISO: isolator. PC: polarization controller. BOA: booster optical amplifier. PD: photodetector. SA: spectrum analyzer.
In experiment, the Qo and Qm of the microsphere OMO are tested using this system, the Qo reaches 6.04 × 108, and the linewidth method is used to test, the scanning coefficient of the laser is 236 MHz/V, the Qm reaches 6.8 × 106, the mechanical frequency fm is 20.3 MHz, and the mechanical linewidth is about 3 Hz, as shown in Fig. 3.
Fig. 3. (a) The optical transmission spectrum of the microsphere (dimensions: microsphere diameter, 66.1 µm; the neck diameter, 6.13 µm; sphere-to-neck ratio, 10.78) at room temperature around 1548.75 nm. The input power is maintained low enough to characterize the intrinsic optical property of the device, which exhibits an intrinsic optical Q-factor of 6.04 × 108. (b) The detailed spectrum of the fundamental oscillation tone with a stable signal-to-noise ratio (SNR) of 76 dB, which exhibits a full-width at half maximum of 3 Hz, corresponding to an effective mechanical Q-factor of 6.8 × 106.
As the minimal detectable frequency shift of OMO is determined by its linewidth, the narrow linewidth of OMO offers great advantages for high-resolution detection of acoustic sensing. According to the following formula [32],
Acoustic sensing indicators such as frequency response, directional response, scale factor and detection resolution are tested respectively.
In the frequency response test, a loudspeaker with a frequency response range of 0 Hz-20 kHz is used to produce sound, and a sound level meter is used for calibration. Figure 4(a1-a3) shows the frequency response characteristics from 15 Hz to 16 kHz are more comprehensively tested, and all signal-to-noise ratios are greater than 20 dB. In Fig. 4(b1-b6), representative frequency response characteristics are displayed for frequencies of 15 Hz, 40 Hz, 50 Hz, 500 Hz, 1 kHz, and 16 kHz, demonstrating that acoustic signals can be detected in the form of sideband signals. It can be found from Fig. 4(a) and Fig. 4(b) that, except for 1 kHz, the response of other frequencies gradually increases between 15 Hz and 50 Hz, the response gradually decreases from 50 Hz to 500 Hz, and the response gradually becomes flat thereafter.
Fig. 4. Frequency response of the proposed sensor. (a) Frequency response characteristics from 15 Hz to 16 kHz. (b) Analysis of several representative frequency response characteristics at frequencies of 15 Hz, 40 Hz, 50 Hz, 500 Hz, 1 kHz, and 16 kHz corresponding to (1)-(6) respectively.
When the acoustic frequency is less than 15 Hz, the frequency of the acoustic signal as a sideband signal is too close to the frequency of the optomechanical signal, which greatly affects the detection of acoustic signal. When the acoustic frequency > 16 kHz, the vibration amplitude of the acoustic signal decreases, the intensity of the incoming cavity is weakened, and the signal intensity is close to the sideband signal intensity and frequency of the OMO itself, which greatly affects the acoustic signal readout.
So, the recommended frequency range for acoustic sensing is therefore 15 Hz to 16 kHz. It is worth noting that when the acoustic signal is at 1 kHz, since this frequency resonates with the frequency of the tapered optical fiber, the enhancement effect of the acoustic signal is more obvious than other frequencies. Therefore, the acoustic frequency of 1 kHz is used as the test frequency in subsequent experiments.
In the directional response characteristic experiment, changing the direction angle of the incident acoustic signal proved that the sensing mechanism is caused by changing the refractive index of the coupling region. The most effective coupling into the mechanical signal, as shown in Fig. 5(a), compared with the vertical incidence of the loudspeaker placed under the microsphere, as shown in Fig. 5(b), it can be clearly seen that its intensity is stronger, respectively in under the above two incident directions, change the acoustic pressure intensity and test the change of its intensity. In Fig. 5(b), the sensitivity of 16.45 dB/Pa and 13.17 dB/Pa are obtained respectively, then in the 360° direction on the same height plane, the influence of the change of acoustic pressure on the drift of the mechanical frequency is more comprehensively tested, and it is more intuitive to find that when the acoustic signal injection direction is parallel to the tapered fiber and the same as the light injection direction, it is defined as 0°. In Fig. 5(d), it can be found that the sensitivity of the acoustic signal is similar between 0° to 180° and 180° to 360°, showing a nearly symmetrical state. But at 90°, the sensitivity is much higher than 270°. Because this direction is more likely to cause the refractive index of the coupling area to change due to low-frequency vibration of sound, which provides good experimental conditions for the next sensing sensitivity test.
Fig. 5. Directional response map of the proposed sensor. (a)-(b) The intensity responses on the frequency spectrum of the signal output under different acoustic pressures when the loudspeaker is placed above and below the microsphere, respectively. (c) The intensity sensitivity comparison between the two. (d) Sensitivity analysis in the 360-degree direction on the same height plane.
The scale factor and detection resolution of the acoustic sensor are measured at a 90° direction and the sound frequency of 1kHz. In Fig. 6(a), when the acoustic pressure value changes, the changes in mechanical frequency and intensity can be observed more intuitively by using the spectrum analyzer. The darker the color, the higher the intensity of the mechanical spectral line. By uniformly increasing and decreasing the input acoustic signal to adjust the microcavity OMO in the forward and reverse strokes, the path is in the direction pointed by the arrow as shown in Fig. 6(b), the maximum difference between forward and backward travel is 140 Hz. The operability of the acoustic pressure sensing is demonstrated, and the sensor is found to have certain hysteresis loop characteristics, which is caused by the energy competition between the acoustic signal and the thermal effect in the thermal mode-locked state of the phonon laser. In Fig. 6(c), the scale factor of the acoustic pressure from 0.01 Pa to 0.11 Pa is tested, and its scale factor is 10.3 kHz/Pa. In Fig. 6(d), the detection resolution of the acoustic sensor is tested. According to the accuracy of the sound level meter, the accuracy is one decimal place, the sound decibel are 73.2 dB and 73.3 dB, respectively, the corresponding acoustic pressures are 0.0914 Pa and 0.0925 Pa, the mechanical frequency has changed by 11 Hz, and the minimum detectable acoustic pressure is 1.059 mPa, while the ultimate resolution of the spectrum analyzer is 1 Hz, at this resolution, the minimum detectable pressure by this sensing theory is about 97 µPa, but it is limited by testing the mechanical line width of the sensitive structure.
Fig. 6. Output signal of the proposed sensors for varying applied sound pressure levels at the frequency of 1 kHz when the loudspeaker is placed above the microsphere OMO. (a) Spectrogram of the frequency response characteristics of the proposed system. (b) Diagram of forward and reverse stroke drift of optomechanical frequency with sound intensity. The path is in the direction pointed by the arrow in the figure. (c) Sensitivity test results in the form of frequency drift. (d) Resolution test results are obtained by detecting the minimum frequency drift. The result is related to the accuracy of the sound level meter. In the experiment, the output decibel value is only accurate to one decimal place.
The SNR of the acoustic signal @1kHz and Papplied =0.089 Pa is 57 dB, the linewidth is 19 Hz, and its noise-limited minimum detectable pressure calculated by the following equation is about 28.8 µPa/Hz 1/2 [25].
In Table 1, the resolution and frequency range of several types of acoustic sensors are listed, which are roughly divided into several types. One is the low-frequency sound detection that can be heard by the human ear, several sensors with higher resolution have complex processes and the cost is high; one is mostly used in the field of ultrasonic sensing, which uses a micro-disk cavity or a micro-ring core cavity as a sensitive structure, and the process is more complicated. Among the acoustic sensors that use microspheres and other simple processes and can be used as acoustic sensors that can detect low-frequency sounds that can be heard by the human ear and simultaneously detect frequency and sound pressure, our scheme is simple, and the detection resolution has reached the highest level reported so far.
Table 1. Fabrication process and performance paramerers of selected acoustic sensors in recent years
4. Conclusions
In this paper, a high-resolution acoustic sensor based on ultra-high Q WGM-OMO is designed. It has been demonstrated that ultra-narrow linewidth phonon lasers using OMOs can greatly improve detection resolution. Using a microsphere OMO with a diameter of about 66µm, high Qo of 6.04 × 108, Qm of 6.8 × 106 and fm of 20.3 MHz, the frequency response and directional response characteristics of low-frequency acoustic signals are explored, and it is found that when the frequency of the acoustic signal is 1 kHz and the loudspeaker is positioned vertically above the fiber cone, the acoustic signal has the most obvious response. A scale factor of 10.3 kHz/Pa and a minimum detectable sound pressure of 1.059 mPa are achieved in the frequency range of 15 Hz ∼16 kHz. Furthermore, the theoretically detectable minimum acoustic pressure is 97 µPa with the ultimate resolution of 1 Hz from the instrument, and the thermal-noise-limited pressure sensitivity is reached to 28.8 µPa/Hz1/2. Ultra-high-resolution opto-mechanical acoustic sensing has been realized.
Funding
National Key Research and Development Program of China (2022YFB3203400); National Natural Science Foundation of China (U21A20141, 62273314, 51821003); Fundamental Research Program of Shanxi Province (202303021224008); Shanxi province key laboratory of quantum sensing and precision measurement (201905D121001).
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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