Topological invariance in whiteness optimisation

Abstract Maximizing the scattering of visible light within disordered nano-structured materials is essential for commercial applications such as brighteners, while also testing our fundamental understanding light-matter interactions. The progress in research field has been hindered by lack how different structural features contribute to properties. Here we undertake a systematic investigation correlated structures. We demonstrate that efficiency systems mainly determined topologically invariant features, filling fraction and correlation length, residual variations are largely accounted surface-averaged mean curvature systems. Optimal can thus be obtained from broad range structures, especially when anisotropy included parameter. These results suggest any system optimised whiteness give comparable performance, which far-reaching consequences industrial use low-index optical scattering.