Topological invariance in whiteness optimisation

TL;DR

This paper demonstrates that the optical reflectance of disordered nanostructured materials is primarily governed by second order statistics, revealing a topological invariance that allows for optimization of whiteness regardless of specific topological features.

Contribution

It systematically analyzes how topological features influence light scattering, showing that reflectance depends mainly on second order statistics and surface properties.

Findings

Reflectance is mainly determined by second order statistics.

Differences in surface area and curvature also affect optical properties.

Disordered systems can be optimized for whiteness through structural tuning.

Abstract

Increasing the light scattering efficiency of nanostructured materials is becoming an active field of research both in fundamental science and commercial applications. In this context, the challenge is to use inexpensive organic materials that come with a lower refractive index than currently used mineral nanoparticles, which are under increased scrutiny for their toxicity. Although several recent investigations have reported different disordered systems to optimise light scattering by morphological design, no systematic studies comparing and explaining how different topological features contribute to optical properties have been reported yet. Using in silico synthesis and numerical simulations, we demonstrate that the reflectance is primarily determined by second order statistics. While remaining differences are explained by surface area and integrated mean curvature, an equal reflectance can be obtained by further tuning the structural anisotropy. Our results suggest a topological invariance for light scattering, demonstrating that any disordered system can be optimised for whiteness.