## 1 Introduction  
Nanoporous alumina structures (NPASs) obtained by electrochemical anodization of aluminum foils according to the two-step anodization method [1, 2] are of great interest due to their application as nanofilters, drug deliverers, templates for nanoparticles, nanotubes, nanowires, platforms for sensors, and medical devices [3, 4, 5, 6, 7, 8, 9]. Lately, other applications of NPASs such as spintronics, solar cells, light emitting diodes, and photonic crystals have been studied [10, 11, 12, 13, 14, 15, 16]. Most of these applications are related to the high structural regularity of NPAS, which exhibit almost ideal cylindrical pores with narrow pore radius distribution and without tortuosity, but their thermal and chemical resistance are also of great interest when used as nanofilters or membranes due to their stability under cleaning protocols commonly used to reduce fouling (adsorption/deposition of transported molecules or particles), which is the main problem in such applications [17; 18]. The two-step anodization method creates samples with a wide range of pore radii (r\({}_{\text{P}}\) ranging between 10 nm and 200 nm) and interpore distances (D\({}_{\text{Int}}\), between 20 nm and 1000 nm) depending on the electrolyte solution, applied voltage, and temperature used during the first step, while pore length (l\({}_{\text{P}}\)) and film thickness, which usually range between 10 \(\upmu\)m and 100 \(\upmu\)m, are basically associated to the second anodization step duration [2]. Although small differences in pore radii of both NPAS surfaces can exist due to the etching process needed for back pore opening, they are considered symmetric structures [19]. However, the use of asymmetric commercial alumina membranes for diffusive transport of specific cations (terbium, americium, europium... ), as well as NPASs with sequential gradation of pore radii and porosity for improving retention efficiency in drug delivery or gas permeation reduction have also been reported [20; 21; 22]. Another significant characteristic of NPASs is the easy modification of geometrical and/or functional parameters by surface coverage/modification using different techniques such as dip coating, chemical vapor deposition, or atomic layer deposition (ALD), which can be selected depending on layer characteristics or specific NPAS application [23; 24; 25; 26; 27; 28]. Particularly, surface coverage of NPASs with an Al\({}_{2}\)O\({}_{3}\) layer by the ALD method for pore size/porosity reduction was performed, and these results indicate only a small effect on diffusive ionic transport as determined by concentration potential measurements, but surface coverage with layers of other ceramic oxides (SiO\({}_{2}\), TiO\({}_{2}\), Fe\({}_{2}\)O\({}_{3}\), or ZnO) seems to affect electrochemical transport parameters [26; 28; 29; 30]. Moreover, NPASs coverage with monolayers and bilayers of different ceramic oxides seems to modify characteristic optical parameters such as the refraction index or the extinction coefficient of the original sample according to spectroscopic ellipsometry (SE) results [29; 30]. In this context, changes in different optical characteristics of NPASs associated to differences in their geometrical parameters (pore size, porosity, and thickness) have also been reported [15; 31; 32; 33]. SE is a non-destructive and non-invasive technique commonly used for optical characterization of thin films, since it allows for the estimation of modifications related to both film surface and bulk phase by measuring changes in light polarization due to its reflection from a solid structure, although it has also been employed for optical analysis of thicker samples (around 15 \(\upmu\)m) [34]. SE results allow for the estimation of different optical parameters (refraction index, extinction coefficient, or real and imaginary parts of the dielectric constant) as well as layer thickness [34; 35]. In this work, the effect of pore radii/porosity and asymmetry on both optical and electrochemical characteristic parameters of NPASs were analyzed.