## 2 Materials, Modeling and Characterization  
### Materials  
A number of thin micro-porous materials, ranging from MPPs with sub-millimetric circular holes to MCPs with micron-sized cylindrical channels, are described in Table 1 according to the diameter \(d\) of their holes, the center-to-center distance \(\Lambda\) between the holes (or holes pitch), their perforation ratio \(\sigma\) and their thickness \(t\). Magnified views of their morphology are shown in Figure 1 (resp. Figure 2) for the micro-capillaries of MCP1 (resp. MCP2). Figure 2 also shows the micro-perforations of a UMPP and MPP. Two groups of materials are distinguished: highly porous materials (MCP1 and MCP2) with a perforation ratio greater than 50% and more standard materials with a porosity lower than 10% (UMPPs and MPPs). MCP1 and MCP2 are composed of 113,000 (resp. 1600) channels per cm\({}^{2}\) for MCP1 (resp. MCP2), as seen in Figure 1, resulting in a perforation ratio exceeding 50% for both materials. By comparison, the UMPP and MPP only have 25 holes per cm\({}^{2}\), as can be seen in Figure 2b,c. In the first group, MCP1 is an innovative material with both a high porosity and micron-sized channels, whereas MCP2 is a highly porous material with only sub-millimetric sized channels (0.2 mm). It can be seen in Sections 2.2 and 3 that MCP1 has a pure calibrated resistance with a negligible \"effective mass\" effect [1]. In the second group, the size of UMPP apertures (0.3 mm) is smaller than that of MPP holes (0.88 mm), but they are comparable to that of MCP2 channels with, however, a much scarcer distribution of the apertures. This results in an increasing \"effective mass\" effect (defined in Section 2.2) for MCP2, the MPP and the UMPP, which limits the broadband performance of the absorber, as verified in Section 4.  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Material** & **Hole Diameter** & **Hole Pitch** & **Perforation Ratio** & **Thickness** \\
**Acronym** & **(\(\upmu\)m)** & **(\(\upmu\)m)** & **(\(\%\))** & **(mm)** \\ \hline MCP1 & 28 & 32 & 69.4 & 1 \\ MCP2 & 200 & 268 & 50.5 & 1 \\ UMPP & 300 & 3000 & 1.8 & 0.5 \\ MPP & 880 & 3000 & 6.8 & 1 \\ \hline \hline \end{tabular}
\end{table}
Table 1: Geometric parameters of the micro-porous panels.  
Figure 1: (**a**) Photograph of MCP1 with an outer diameter of 35 mm and thickness of 1 mm; (**b**) Magnification (factor 4) of MCP1 revealing a hexagonal distribution for the set of micro-channels; (**c**) Magnification (factor 10) of MCP1 showing micro-channel staggered alignments; (**d**) Magnification (factor 40) of MCP1 showing 60\({}^{\circ}\) staggered cylindrical micro-channels with diameters of 28 \(\upmu\)m and hole pitches of 32 \(\upmu\)m.  
Figures 1d and 2a show that MCP1 and MCP2 are composed of 60\({}^{\circ}\) staggered circular channels so that their perforation ratio is calculated as \(\sigma=\pi\,d^{2}/\left(2\sqrt{3}\Lambda^{2}\right)\), whereas the UMPP and MPP are composed of aligned circular holes so that \(\sigma=\pi\,d^{2}/\left(4\Lambda^{2}\right)\). The UMPP and MPP are manufactured using micro-machining stainless steel and aluminum panels, respectively. MCP1 and MCP2, composed of leaded glass, are produced via an acid-etching process. Soluble fibers are inserted into an insoluble glass matrix that is melted and stretched. After slicing to the desired thickness, the plates are placed in an acid bath to solve the fibers, hence producing a porous solid with a high density of micro-channels per cm\({}^{2}\). Usually, MCPs are used to enhance the resolution of optical sensors such as cosmic ray intensifiers. On top of their channel density, another distinct feature of MCPs compared to MPPs is their high thickness-to-diameter ratio, \(t/d\), that reaches values of 37 for MCP1 and 5 for MCP2, whereas it has values of 1.7 for UMPPs and 1.1 for MPPs.