## 3 Optical Features of \(\mathrm{CeO_{2}}\) Nanoporous Coatings  
### Refractive Index  
Variable angle spectroscopic ellipsometry (VASE) was used to measure the refractive index of the coatings and we limited ourselves to coatings made of the thinnest grade of nanoparticles where the final material does significantly scatter the light (empirical observation). VASE provides ellipsometric raw data (here \(\psi\) and \(\Delta\) angles) that need to be parametrized in order to extract the complex refractive index \(\bar{n}=n+ik\)[26].  
Figure 3: (**A**) Materials engineered with \(\upmu\)-pervaporation made of densely packed \(\mathrm{CeO_{2}}\) nanoparticles, structured with two different designs. In each case, the large figure shows the entire material through a tiled image obtained from optical microscopy in bright field mode and the insert is a SEM view of the top surface of the material. In the upper case, the thickness is about 180 nm; in the bottom case, the thickness is about 260 nm (measured with optical profilometry). (**B**) Optical microscopy (**left**) and 3D reconstruction from optical profilometry (**right**) of the micro-structured materials.  
The optimisation approach requires knowledge of the refractive index \(\bar{n}_{NP}\) of CeO\({}_{2}\) nanoparticles, their packing density \(\phi_{c}\) inside the coating (\(1-\phi_{c}\) being the void fraction or porosity), and the thickness of the coating \(h\). We then compute the ellipsometric angles of the coating with a refractive index calculated via the Bruggeman effective-medium approximation [27] of a flat nano-porous film with no roughness and deposited of a semi-infinite silicon substrate with an oxidized top surface, namely a 2 nm thick silica layer.  
To guide the input parameters, we used the coating thickness measured by mechanical profilometry (\(h=18\pm 3\) nm), the packing density \(\phi_{c}=0.64\) of a random close packing structure, and the refractive index \(\bar{n}_{NP}\) based on literature data [28] and parametrized according to [29]. The optimisation is then performed through the Horiba software and eventually yields \(\phi_{c}=0.61\), \(h=15\) nm, a model of \(\bar{n}_{NP}\) (not shown), and ultimately, a very good agreement with ellipsometric raw data (Figure 4 left). The refractive index of CeO\({}_{2}\) nanoparticles is comparable yet smaller in magnitude than bulk cerium oxide, which could be attributed to a synthetic route that is likely to lead to a material different from bulk CeO\({}_{2}\).  
We thus obtain a satisfactory measurement of the refractive index of the nanoporous coating of CeO\({}_{2}\) on a specific range of photon energy (\(1-5\) eV, i.e., \(\lambda=1250-250\) nm, Figure 4): \(\bar{n}\) shows a significant absorption of light in the UV-visible regime up to \(\lambda\approx 500\) nm where the material becomes a loss-less dielectric with \(n\approx 1.75\), \(k\approx 0\). We assume it remains true even up to the mid-IR range, for instance \(\lambda=4\) um, which we will also use to characterize the transmittance of the coating in this regime.  
Also, we assume that this measurement obtained on a specific coating is intrinsic and thus holds, whatever the thickness of a homogeneous coating made out of the same grade of particles.