Air-coupled ultrasound detection using capillary-based optical ring resonators

We experimentally demonstrate and theoretically analyze high Q-factor (~107) capillary-based optical ring resonators for non-contact detection of air-coupled ultrasound. Noise equivalent pressures in air as low as 215 mPa/√Hz and 41 mPa/√Hz at 50 kHz and 800 kHz in air, respectively, are achieved. Furthermore, non-contact detection of air-coupled photoacoustic pulses optically generated from a 200 nm thick Chromium film is demonstrated. The interaction of an acoustic pulse and the mechanical mode of the ring resonator is also studied. Significant improvement in detection bandwidth is demonstrated by encapsulating the ring resonator in a damping medium. Our work will enable compact and sensitive ultrasound detection in many applications, such as air-coupled non-destructive ultrasound testing, photoacoustic imaging, and remote sensing. It will also provide a model system for fundamental study of the mechanical modes in the ring resonator.


S1. Transducer calibration
In the experiment, an air coupled transducer (Japan Probe 0.9K14x20N-RX) was used to generate the ultrasound. There was an air space (approximately 2 cm) between the transducer and the resonator. It is necessary to estimate the acoustic pressure levels reaching the resonator under different external driving voltages. Usually a well-calibrated hydrophone can be employed to estimate the acoustic pressure in water. However, in the case of air, hydrophone cannot be used directly in air due to big acoustic impedance mismatch between air and the hydrophone surface. Furthermore, calibrated microphone at this frequency range is not readily available. For our current work, we calibrated the transducer in an indirect manner as described as follows.
A transducer can be treated as an ultrasound generator with pressure intensity (A0) at given driving voltage, which is coupled to an outside environment through a multi-layered structure that has an equivalent acoustic impedance of Z0 (see Fig. S1 for illustration). A0 and Z0 are intrinsic to the transducer and important in obtaining the pressure exiting the transducer at a given driving voltage. The equation governing the output pressure at the outer surface of transducer is given as: where A0 is the input pressure at the inner side of the transducer surface at a given driving voltage. Z0 is the effective acoustic impedance of the transducer. B is the output pressure at the location very close to the transducer, but separated by a medium with an impedance of Zm (see Fig. S1). If the output pressure can be measured inside two different media with known acoustic impedances, A0 and Z0 can be calculated from: where subscript 1 and 2 stand for two different liquid media. Since Zair, the acoustic impedance of air, is well-known, the output pressure of the transducer in air can be calculated using the following equation: Finally, the pressure at the resonator can be obtained by taking into account the attenuation of the pressure wave when it travels in air 1 . Figure S2a illustrates the experimental setup. A hydrophone (ONDA HNR-0500) was used to measure the pressure within a liquid medium. This is because due to the impedance mismatch between the hydrophone surface and air, the surface of the hydrophone would act as a reflecting surface if it were used in air.
To overcome such an issue, in the experimental setup in Fig. S2a, the hydrophone was immersed in water so that the unwanted reflection from the hydrophone could be minimized since the hydrophone is designed to match the impedance of water. A thin membrane chamber was used to separate water and the liquid medium. In our experiment, we used isopropyl alcohol and sodium silicate as two different liquid media with acoustic impedances of 0.919 MRayl (10 6 N-s/m 3 ) and 2.6035 MRayl, respectively. Ignoring ultrasound attenuation in liquids due to the short propagation distance, the pressure reading of the hydrophone, C, is related to the pressure at the output of the transducer, B1 and B2, by: By plugging Eq. (5) into Eqs. (2), (3), and (4), the output pressure the transducer can be deduced. Since the shape of the transducer head are rectangular and the geometry are comparable to the propagating distance in our experiment, the distance dependence of pressure decrease due to ultrasound beam divergence can be ignored. However, attenuation of the ultrasound in air due to absorption needs to be taken into account 1 , which is about 104 dB/m for 800 kHz. Figure S2b is the calibration curve that relates the pressure (peak-to-peak) at the resonator in air to the input driving voltage (peak-to-peak).

S2. Pressure sensitivity enhancement using a balanced photodetector
Inherit noise in a laser source can lead to decreased sensitivity in optical resonator-based sensors. Here we confirm that by using a balanced photodetector to remove the laser noises and improve pressure sensitivity 2 . Balanced photodetectors have two optical inputs. One input collects the light from the laser source, while the other collects the signal of interest. At the output of the balanced photodetector, common-mode noises are removed.
In this experiment, the laser was split into two paths using a fiber coupler (Fig. S3a). One path sent the laser to the tapered fiber where ultrasound was detected using the resonator, while the other path sent laser to the reference channel of a balanced detector (New Focus 1617). The output of the tapered fiber, which carried the detected ultrasound signal, was again split into two paths. One path sent the ultrasound signal to the single input photodetector (New Focus 1611) and the other path sent the ultrasound signal to the signal channel of the balanced photodetector.
Before ultrasound transducer was turned on, the difference between DC-intensities of reference and signal channels of the balanced detector was minimized using a fiber attenuator to ensure proper noise rejection. When ultrasound transducer was turned on, the difference between DCintensities of reference and signal channels was continuously monitored. The radius of the resonator was 85 m. The distance between the detector and the transducer was ~16 cm. Figs.
S3b and S3c show the temporal response from each photodetector towards air-coupled ultrasound signal generated by a 50 kHz Tx (AirMar AR 50). The data was averaged 512 times.
No filtering around 50 kHz was performed. The balanced photodetector had 37% higher SNR compared to single input photodetector.

S3. Mechanical resonance modes of a ring resonator
It is well known that a mechanical system can exhibit resonance behaviors at specific frequencies. Due to the annular shape and the homogeneity of the material, silica based ring resonators without damping layers are usually very good mechanical resonators with high mechanical Q-factors [3][4][5][6] Figure S3. a) Schematic of the experiment. The intensity of the laser output to the balanced detector was adjusted so that it matches base level of the signal output from the taper. b-c) temporal responses of a ring resonator towards the 50 kHz air-coupled ultrasound. b) Temporal response recorded by a single input photodetector. Measured SNR was 6.5. c) Temporal response recorded by a balanced photodetector. Measured SNR was 8.8. Figure S4. Calculated wineglass mode of the ring resonator using finite element method. The mechanical mode at 1.65 MHz is a wineglass mode of the resonator. Wireframe shows the ring resonator's geometry before the deformation. Color and deformation show the acoustic amplitude and displacement of the resonator.