*5.1. Calculated Reflectance*

Here, the reflectance *R* of a nanoporous coating of CeO2 is calculated on silicon substrates as described in the main text as a function of its thickness *h* with the measured refractive index (Figure 4) and over a large range of wavelengths. Results are shown in Figure 10 where we set a threshold to *R* at 5% in order to best highlight the performance zones in terms of anti-reflection; the mapping is split in two zones: small *h* in the visible to near-IR range and large *h* in the mid-IR range. In all cases, the near-zero *R* shows as blue cones with quite narrow bands and which are clearly sometimes degenerated, namely several regions with *R* ≈ 0 show as a function of *λ* for a single *h*.

**Figure 10.** Reflectance *R* calculated for a nanoporous CeO2 coatings of variable thickness *h* deposited on a silicon substrate. (**A**): Small thickness *h* in the visible and near-IR range; (**B**): Large thickness in the mid-IR range.

**Figure 11.** (**A**): Transmittance *T* calculated for a nanoporous CeO2 coatings of variable thickness *h* (red curves) deposited on a silicon substrate (blue curve). (**B**): Transmittance excess Δ*T* = *T*Si+coat − *T*Si as a function of wavelength and coating thickness *h*.

#### *5.2. Calculated Transmittance*

The same type of calculation was performed for transmittance *T* on double-sided polished silicon substrates in the range of mid-IR, see Figure 11. In part A, a few examples of *T* against *λ* are given for three different coating thicknesses (30, 280, and 500 nm, red curves) and are compared to the transmittance of the bare substrate in blue. Obviously, the silicon substrate is opaque (*T* = 0) below some *λ* which actually depends on its thickness, here *λ* ≈ 1 μm for a 325 μm thick substrate. Above this opacity cut-off, the substrate is basically homogeneously semi-opaque (e.g., *T* ≈ 0.57 at 4 μm) while adding a thin coating can dramatically enhance the transmittance. Part B of Figure 11 shows a mapping of the increase of transmittance that the coating provides, namely Δ *T* = *T*Si+coat − *T*Si, against *h* and *λ*. In the mid-IR range, up to 15% of transmittance enhancement can be observed; obviously, this enhancement depends significantly on *λ* but can nevertheless be of some interest for monochromatic processes such as imaging.
