Janus acoustic metascreen with nonreciprocal and reconfigurable phase modulations

Integrating different reliable functionalities in metastructures and metasurfaces has become of remarkable importance to create innovative multifunctional compact acoustic, optic or mechanical metadevices. In particular, implementing different wave manipulations in one unique material platform opens an appealing route for developing integrated metamaterials. Here, the concept of Janus acoustic metascreen is proposed and demonstrated, producing two-faced and independent wavefront manipulations for two opposite incidences. The feature of two-faced sound modulations requires nonreciprocal phase modulating elements. An acoustic resonant unit cell with rotating inner core, which produces a bias by a circulating fluid, is designed to achieve high nonreciprocity, leading to decoupled phase modulations for both forward and backward directions. In addition, the designed unit cell consisting of tunable phase modulators is reconfigurable. A series of Janus acoustic metascreens including optional combinations of extraordinary refraction, acoustic focusing, sound absorption, acoustic diffusion, and beam splitting are demonstrated through numerical simulations and experiments, showing their great potential for acoustic wavefront manipulation.


experiments.
As can be seen in Fig. 3(d) in the main text, the non-reciprocity is obtained around the frequency of the quadrupolar resonance mode of the circulators. Therefore the operational frequency bandwidth is limited by the resonance curves in transmission. We estimate from the transmission curves in Supplementary Figure 2 in the main text, if we interchange h1 and h2, that is varying height h2 with fixed h1=3 cm, the curve of φ1 and φ2 will be interchanged, that is, φ2 is modulated by h2 and the phase φ1 remains constant (not shown in Supplementary Figure 4). Thus, at n=720 rpm, the modulation of the phases φ1 and φ2 are completely decoupled.
When we decrease the rotation speed into n=480, 240, 120, 60 rpm, the phase φ1 is modulated by varying the height h1 as shown in Supplementary Figure 4(a) and the phase φ2 is varying as well. This means that the modulation of φ1 and φ2 is not decoupled anymore. When the rotation speed is decreasing, the phase difference between φ1 and φ2 is decreasing, means the effect of nonreciprocity is decreasing. When the rotation speed is are not linearly varying with rotation speeds n. They vary slowly when n is large, but vary rapidly when n is small. So we denote a flat region within 720-240 rpm marked by grey color, in which the background flow has very little impact on φ1 and φ2. This feature leads to high robustness of phase modulation and wavefront manipulation against rotation speed, which will be demonstrated in wavefront manipulation later.
To further study the phase modulation against the rotation speed, we shows the acoustic pressure distribution in the unit cell for different rotation speeds of n=720, 480, 240, 120, 60, 0 rpm, respectively, in Supplementary Figures 4(e-f). In Supplementary   Figure 4(e), we set h1=1.5 cm, h2=3 cm. For n=720 rpm, phase modulator 2 of the unit cell has lowest acoustic pressure distribution that means the incident wave is coupled with phase modulator 1 and nearly decoupled with phase modulator 2 at highest rotation speed. In Supplementary Figure 4(f), we set h1=1.36 cm, h2=3 cm. In this case, the acoustic pressure in phase modulator 2 is always zero. The acoustic pressure distribution for phase jump is shown in the last figure that the acoustic pressure in the second circular is all zero, that means this phase jump (h1=1.36 cm, h2=3 cm, n=0 rpm) is corresponding to zero transmission (T=0).

Supplementary Figure 4. Simulated phase responses with different rotating speed.
(a-b) Simulated phase responses φ1 and φ2 at 6430 Hz for FD (forward direction) and BD (backward direction), by independently varying the parameter h1 (h2 is fixed as h2=3 cm), with the rotating speed of n=720, 480, 240, 120, 60, 0 rpm. A phase jump is marked in the figure for n=0 rpm. (c) For fixed values of h1=1.5 cm, h2=3 cm, the relationship between φ1/φ2 and rotating speed (varying from 720 to 0 rpm) (d) For fixed values of h1=1.36 cm, h2=3 cm, the relationship between φ1/φ2 and rotating speed (changing from 720 to 0 rpm). (e) For fixed values of h1=1.5 cm, h2=3 cm, the acoustic pressure distribution in the unit cell for the rotating speed of n=720, 480, 240, 120, 60, 0 rpm. (f) For fixed values of h1=1.36 cm, h2=3 cm, the acoustic pressure distribution in the unit cell for the rotating speed of n=720, 480, 240, 120, 60, 0 rpm. The acoustic pressure distribution in the unit cell for the phase jump around h1=1.36 cm.
In order to study the robustness of wavefront manipulation against rotation speed, we compared the simulated results for wavefront manipulation of the JAM with the rotation speed n=720, 480, 240, 120, 60, 0 rpm, respectively. We take the same case

Supplementary Note 5. Background noises and signal-to-noise ratio.
We choose "Constant Percentage Bandwidth Analyzer" (CPB) in Brüel&Kjaer software to measure the background noise within broadband frequency range, that is from 125 Hz to 20000 Hz with a step of 1/3 octaves. The average sound pressure amplitudes within every 1/3 octaves are shown in Supplementary Figure 6. Supplementary Figures   6(a-b) show the background noises with and without sound source, respectively. The experimental working bandwidth from about 6380 Hz to 6490 Hz are corresponding to the 1/3 octaves bandwidth with the center frequency of 6300Hz, and when the rotation speed is set at 720 rpm, the normalized noise pressure level is measured at Lnoise= 18.7 dB.
When the source is turned on, the normalized acoustic pressure level is measured at Lac=33.5 dB. Thus, the signal to noise ratio is 15.2 dB, which is large enough to ensure consistent measurements. Figure 6. Background noises. (a) Background noises with sound source for high rotating speed for the rotation speeds of 720, 600, and 480 rpm. (b) Background noises without sound source for high rotating speed for the rotation speeds of 720, 600, and 480 rpm.

Supplementary Note 6. The optimization of predesigned phase profile.
In our design, the expression for extraordinary refraction, acoustic focusing, acoustic diffusion and bean splitting are shown in Eqs. 1-4. (1) where C is an arbitrary constant that means the phase of the unit cell of the center of the metascreen array (y=0 cm). We test C=0, 90, 180, 270 degrees, respectively, in array simulations, and find the best C values with highest efficiency. We finally get the optimized initial phases for the designs in Figs. 5-8 in the main text. The four C values are 270, 90, 180, 90 degrees, respectively, as shown in Supplementary Figure 7. We therefore get the four pairs of phase profiles for Figs. 5-8 in the main text, as follow 1. φ1=83.3y+1.5π rad, φ2=166.6y+1.5π rad.
The different initial phase will lead to different h1/2 values of the phase modulator.
The simulations of the array consider the air gap between neighbouring unit cells, in which the coupling effect may influence the results. Therefore, the change of the initial phase may change the coupling cases, which may improve the results, making the initial (sin sin )+ ,