## 3 Acoustic Properties of Unbacked MCPs and MPPs  
Simulations and measurements were carried out to determine the absorption properties of the thin porous materials listed in Table 1 when unbacked. As shown in Figure 4 on the left, the material samples were inserted at the termination of a Kundt tube, thereby achieving an ultra-thin termination with a millimetric thickness. Their measured absorption properties are shown in Figure 5. Their unbacked transmitting side radiates in an anechoic environment. The radiation properties (impedance and acoustic intensity) of the samples, characterized by a 3D pressure-velocity probe described in Section 2.3, are shown in Figures 6 and 7. Figure 4: Photographs of the Kundt tube used to measure the absorption properties of an unbacked (**left**) and rigidly backed (**right**) MCP in an anechoic environment; a pressure–velocity (p–v) probe characterizes the acoustic radiation of the unbacked MCP. Figure 5: Simulated (dotted) and measured (plain) absorption properties of unbacked MCP1 (red), MCP2 (magenta), UMPP (black), MPP (blue) and open termination (green) assuming flanged radiation conditions and normal incidence. Figure 6: Specific radiation resistance (**a**) and reactance (**b**) of MCP1 (red), MCP2 (magenta), UMPP (black) and MPP (blue) and open termination (green) measured with a p–v probe compared with a radiation impedance model (gray) assuming a flanged open termination. It can be seen from the green curve of Figure 5 that the open termination (reference case) reflects a large amount of the incident energy below 1000 Hz (more than 90%). As the frequency increases, part of the incident energy transmitted by the open outlet gradually rises, reaching unity at 6500 Hz. As shown in Figure 6 (green and gray curves), this open tube behavior is well predicted by the radiation impedance model of [PERSON] et al. [15] described by Equation (6) for a flanged cylindrical termination. It is remarkable to observe that closing the open termination of MCP1 considerably enhances the absorption above 0.9 over a broad bandwidth of between 100 Hz and 1200 Hz (Figure 5 (plain red curve)). MCP1 thus achieves a highly absorbing termination with a deep sub-wavelength thickness 0.0003\(\lambda\) (resp. 0.004\(\lambda\)) at 100 Hz (resp. at 1200 Hz) with \(\lambda\), the acoustic wavelength. Over this wide frequency range that covers almost four octaves, high absorption values are essentially due to visco-thermal dissipation effects through the micron-sized apertures of MCP1. Above 1200 Hz, the absorption slightly decreases down to 0.75 at 6500 Hz due to the progressive decay of the reactance (Figure 3b (red curve)). This plateau-and-decay behavior observed in the measured absorption spectrum of MCP1 is well predicted by the impedance model (Figure 5 (dotted red curve)), assuming that the radiation load impedance behind MCP1 is that of a flanged termination. This assumption is verified when comparing the red and gray curves of Figure 6. They show that the radiation impedance measured behind the highly porous MCP1 material closely follows the impedance of a flanged termination. Like MCP1, MCP2 belongs to a class of highly porous materials with a perforation ratio greater than 50%. However, unlike MCP1, which essentially works on visco-thermal dissipative effects, the apertures of MCP2 are seven times larger than those of MCP1. Therefore, MCP2 has a lower resistance. It is much less dissipative and more transmissive than MCP1. Above 2 kHz, it behaves like an acoustically transparent open termination, as shown by the close proximity between the green and magenta curves in Figure 5. At low frequencies, the low absorption values of MCP2 (around 0.2) are due to moderate dissipation and transmission through the channels of MCP2. Figure 7: Measured intensity vectors at 300 Hz (**a**) and at 5000 Hz (**b**) associated with the acoustic radiation of an open termination (green), MCP1 (red) and MCP2 (magenta).