## 2 Materials and Methods
### Directivity Measurement  
Although this receiver uses ultrasonic waves, our goal was to focus an audible-band sound beam, so we measured the directivity of the parametric audio generated by the ultrasonic waves using an audible-band sound pressure meter. We measured the directivity of a beam a very short distance from a radiator with a diameter of only 6 mm. The microphone aperture of the audio level meter must be very small to measure the directivity  
Figure 3: Frequency response of the PU receiver measured at distances of 3 mm, 6 mm, and 10 mm from the radiator, compared with that of a BA receiver at 10 mm. A 130 kHz carrier (SRAM) with 80% modulation was used to drive the PU receiver (10 Vpeak, delivering -1.3 mW); the BA receiver was driven with the same power for a fair comparison.  
of the beam. Therefore, in this experiment, a probe microphone system with a 0.5 mm diameter tube was used to ensure sufficient beam measurement resolution.  
We also used the small directivity measuring device shown in Figure 4a to measure the directivity within a few centimeters. The silicone tube connected to the measurement microphone is flexible, so this directivity-measuring instrument involved inserting a rigid guide tube with an inner diameter of 1 mm. We used a slider with a groove depth of 7 mm and groove width of 2 mm that can be moved by inserting a protractor or ruler to measure the directivity by moving in circles or straight lines.  
Figure 4: (**a**) Photograph of the experimental setup used to measure the beam directivity within a few centimeters of the 6 mm diameter radiator. (**b**) Measured radial directivity patterns of 1 kHz and 9 kHz audio outputs at a distance \(l=10\) mm from the radiator (where \(l\) is the distance from the radiator to the microphone), using a 130 kHz carrier modulated at 80%. (**c**) Measured axial sound pressure distributions (beam cross-section profiles) of 1 kHz, 5 kHz, and 9 kHz audio at \(l=6\) mm. During these measurements, the PU receiver was driven with 10 V\({}_{\text{EMS}}\) and the BA receiver was driven with 0.1 V\({}_{\text{EMS}}\).  
The diameter of the radiator was only 6 mm, so it was difficult to measure the directivity of an audio beam radially at a distance of 6 mm or less from the radiator. Therefore, at 6 mm, we measured the sound pressure of the beam cross-section across a straight line. At a distance of 10 mm, we measured directivity in the radial direction. Measurements in the radial direction were determined by dividing the sound pressure measured by moving the slide at 5\({}^{\circ}\) intervals in the angular range of \(\pm\)90\({}^{\circ}\) by the value of the sound pressure at the center of the ultrasound beam (0\({}^{\circ}\)). Figure 4b presents the measurements in the radial direction at 1 and 9 kHz; the results revealed that the measured sound pressure level was in good agreement with the calculated directional pattern value. Figure 4c presents the measured sound pressure profile, i.e., the axial sound pressure distribution of the cross-section of the audio beam of the PU and BA receivers at 1, 5, and 9 kHz. At the time of measurement, a 100 mV signal was applied to a BA receiver; it was normalized to the maximum sound pressure at the center of the beam and compared with the PU receiver.  
During measurement, 10 V was applied to the PU receiver and 100 mV to the BA receiver because the BA receiver is driven by a low-voltage current due to its low internal resistance, while the PU receiver is a potential driving element with a very large internal resistance. The results confirmed that the sound generated by the SRAM modulated ultrasound signal focused more than 95% of the energy within the diameter of the eardrum at 8 mm. To characterize the intrinsic beam pattern, directivity measurements were performed under free-field conditions (i.e., without a baffle or ear). This setup follows standard practices in transducer characterization [13]. Previous studies also evaluated ultrasonic hearing devices in free-field or quasi-free-field setups [17].