Wave propagation in correlated disordered media
An important research activity in this theme is the study of wave propagation in correlated disordered media. These media are obtained by introducing local order into the position of the scatterers. This corresponds to the introduction of structural correlations. These correlations can arise naturally through self-organization. This is the case, for example, with a set of hard spheres that cannot interpenetrate. Other, more complex interaction potentials also exist, enabling the level of order and therefore the level of correlations to be adjusted. The resulting materials are thus halfway between a totally disordered material and an ordered crystal. There are many examples of this in nature. One example is the human cornea, where correlations between collagen fibrils play a fundamental role in optical properties.
Recently, we have turned our attention to a particular type of correlation that is attracting growing interest: so-called hyperuniform correlations. Hyperuniform point patterns are characterized by a vanishing structure factor near the origin. When dressed with scattering particles, these patterns form materials with optical properties largely driven by disorder correlations. We have shown that the scattering mean free path can tend towards infinity in these materials. A totally opaque medium can thus become totally transparent in a certain wavelength range simply by introducing a little order, i.e. by simply rearranging the scatterers (see Fig. 1 (a)) [1]. In a second step, we investigated the behavior of such a medium in the case of both scattering and absorbing particles. A theoretical and numerical study showed that the absorbed power can be much greater in a hyperuniform material than in a totally disordered one (see Fig. 1 (b)) [2]. This type of material even maximizes absorbed power [3]. This is because the wave penetrates the medium much more easily. This results in a blackbody-like behavior at low material density. We can imagine applications for photovoltaics, for example.
Figure 1 Illustrations of the transparency (a), absorption (b) and localization (c) properties of hyperuniform media. (a) Comparison of the angular scattering pattern of a medium made up of randomly arranged scatterers (red) with that obtained by placing the same scatterers in a hyperuniform configuration (blue). (a) Absorbed power normalized by incident power as a function of the absorption level in the scatterers. The hyperuniform case is shown in black, the totally disordered case in red. Solid lines correspond to exact numerical calculations (solving the wave equation), dashed lines represent theoretical predictions. (c) Example of an interferentially localized eigenmode in a hyperuniform ensemble.
In addition to these properties of transparency and absorption, which are essentially related to light transport, we can also investigate the changes induced by disorder correlations on more complex propagation regimes such as strong localization (also known as Anderson localization). Studies have shown that this regime does not exist in 2D and 3D for a set of uncorrelated point scatterers, once the vectorial nature of light is taken into account. The essential reason is the presence of significant optical near-field effects at the densities required to achieve the localization regime. These effects are non-existent in the scalar case, and the localized regime exists. A recent fine theoretical and numerical study has enabled us to show that the introduction of structural correlations enables the localization regime to be restored for vector lightwaves thanks to the formation of a pseudo-gap similar to those that can form in photonic crystals (see Fig.1 (c)) [4].
These results are promising, but we must not forget the difficulties encountered in fabricating hyperuniform or correlated materials in general, especially at visible wavelengths. As a first step, and in collaboration with a team from the Institut Pierre-Gilles de Gennes, we have demonstrated the existence of hyperuniform self-organization in bidisperse microdroplet emulsions [5]. In a completely different field, a collaboration with a team from Sorbonne University has explained the origin of transparency in biomimetic structures based on collagen fibrils [6].
Footnotes
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