The research based on nanoporous anodic alumina (NAA) has attracted significant attention in nanoscience and engineering due to its self-assembled, densely packed, and nanoscale-ranged porous structure that naturally forms when aluminum (Al) films are anodized in an acidic electrolyte solution in the appropriate conditions [1, 2]. These pores are straight through the film thickness, parallel to each other, and with diameters in the range of 10 to 100 nm. The structural characteristics of the NAA such as pore diameter, interpore distance, porosity, film thickness, and barrier layer thickness are dependent on the anodization conditions [3, 4]. These physical properties have made the NAA a suitable material for use as a template to synthesize metal [5, 6], polymer [7], and ceramic [8] nanowires and nanotubes. Porous materials, like NAA, have large surface area and specific surface properties that enable them to adsorb watery molecules and thus significantly change their effective refractive index, so chemical and biological sensors have been invented to take advantage of this property [9–12].

Since NAA is a self-assembled porous material with a two-dimensional (2D) pattern having a characteristic interpore distance (which in some fabrication conditions can be in the order of the wavelength of visible light [13, 14]), it is possible to control light propagation inside its structure. Its low absorption coefficient, excellent thermal stability, wide electronic band gap (7 to 9.5 eV), and easy handling have made it a potential candidate as a two-dimensional photonic crystal material in the visible and infrared range [15]. Furthermore, nonperiodic nanostructures based on NAA have been demonstrated to show photonic stop bands for all in-plane propagation directions [16, 17]. If this in-plane 2D photonic stop band could be combined with vertical optical confinement provided by a periodic change of refractive index in the direction parallel to the pores, then three-dimensional (3D) confinement of light could be achieved. This confinement of light in a small volume and in a porous material could find applications in sensing, LED light extraction, or laser light generation.

Three-dimensional (in-depth) structuring of NAA has drawn great interest for a large range of applications such as high-density storage media [18] or spintronics [19]. Recently, multilayer nanoporous structures or Bragg’s stacks have been applied to chemical and biological sensing due to its high reflectivity for a certain incident light wavelength [20–22]. These works report on the fabrication of Bragg mirrors based on NAA with a cyclic porosity with depth, but they do not show control over the optical properties of every cycle. Other authors have also reported on the fabrication of complex pore architectures with modulated pore diameters by cycling between mild and hard anodization conditions [23, 24], although the works do not focus on the optical properties of the obtained nanostructures.

In this work, we investigate the possibility of obtaining an in-depth structuring of NAA in layers with controlled thickness and refractive index by using an electrochemical process where the anodization voltage is the only varying parameter, while both the type of electrolyte and its concentration are kept constant. Furthermore, we aim at demonstrating that this can be achieved without changing from mild anodization conditions.

In order to fabricate in-depth structured NAA with significant optical properties, it is necessary to have different layers with the highest possible refractive index contrast. However, it is known that in the self-ordering regime of pore growth, porosity depends weakly on the applied voltage [4, 25]. Thus, if a cycling voltage is applied to obtain the NAA, the different layers will have a small refractive index contrast.

Here, we present an innovative approach for obtaining the highest possible refractive index contrast. Our aim is to show that although porosity of as-anodized layers is very similar for all anodization voltages, if a subsequent pore-widening step is applied, the rate at which porosity increases is indeed different. Thus, if a cyclic voltage is applied to obtain NAA, the index contrast between layers obtained with different voltages will be increased with the pore widening.

A simple model can be developed to justify this assumption. The porosity of a NAA layer of vertically straight pores of radius

*r* separated by an interpore distance

*D*_{int} is proportional to the square of the ratio

*r*/D

_{int}[

4]:

$p=\alpha {\left(\frac{r}{{D}_{int}}\right)}^{2}$

(1)

A geometrical analysis reveals that in a perfectly ordered hexagonal structure, the proportionality constant

*α* is

$2\pi /\sqrt{3}$. However, if ordering is not perfect, this constant may vary slightly, but in any case, it is weakly dependent on the applied voltage

*U*. It is widely accepted that the interpore distance depends linearly on

*U*[

4]:

${D}_{\text{int}}=kU\text{,}$

(2)

where

*k* is the proportionality constant, approximately

*k* ≈ 2.5 nm/V. Furthermore, the porosity of the as-anodized samples is also weakly dependent on

*U*[

4], with a value

*P*_{0}. Thus, from Equations

1 and

2, assuming a perfect triangular ordering, the radius of the as-anodized sample can be written as:

${r}_{0}\approx k\sqrt{\frac{\sqrt{3}{P}_{0}}{2\pi}}U\text{.}$

(3)

The pore-widening process consists of the dissolution of the alumina by 5 wt.% phosphoric acid (H

_{3}PO

_{4}). This is a process that takes place at the interface between the alumina and the solvent, and it is reasonable to assume that the pore radius increases linearly with time for constant reaction speed:

$r\left(t\right)={r}_{0}+\beta t\text{,}$

(4)

where the linearity constant

*β* depends only on the chemical nature of the alumina and of the solvent and on the process temperature, but there is no reason to think it may depend on the anodization voltage. By substituting this radius in Equation

1, the evolution of the porosity with time can be expressed as:

$P=\alpha {\left(\frac{{r}_{0}+\beta t}{{D}_{int}}\right)}^{2}\text{.}$

(5)

The derivative of this porosity with respect to time corresponds to its rate of growth if we consider small reaction times (

*t* → 0):

${\frac{dP}{dt}|}_{t=0}=\frac{2\alpha {r}_{0}\beta}{{D}_{int}^{2}}=\frac{2\alpha \beta}{k}\sqrt{\frac{\sqrt{3}}{2\pi}{P}_{0}}\frac{1}{U}\text{,}$

(6)

where the dependence on the anodization voltage has been made explicit. Thus, the rate of pore widening should be inversely proportional to the anodization voltage.

In the following section, we describe an experiment in order to check this hypothesis, with the details of the fabrication procedure and the characterization methods. Then, the results of the experiment are presented and discussed, and finally, the conclusions are summarized.