Inferring Structure Factor of Living, Disordered Hyperuniform Systems with Structural Color

Structural color and transparency are common phenomena in life - these optical properties are found in many mammals, birds, insects, and even bacteria species. The mechanisms underpinning these optics are as diverse as the taxa in which they evolved. Studying these natural optical properties such as structural color and transparency opens up the possibility of new photonics and material science based on polymers, proteins, and lipids. A significant technical challenge in developing a fully analytical framework for understanding natural, disordered optical systems is the experimental characterization of the material's structure factor near the origin, in particular at values of the wave vector corresponding to scattering of visible light; Fourier-space analyses are challenging due to the finite size effects of standard biological sampling techniques but they are required to provide information to determine if a system is stealthy hyperuniform in the visible light regime. Here, we analyze these systems in Fourier space by calculating the structure factor across wavenumbers associated with the visible wavelength both computationally and experimentally. We model pair potentials of the arrays to generate large field data and examine the resulting structure factor in light of theoretical approaches for estimating small values of structure factors in hyperuniform systems. We determine the biological cases in which existing theories of how structure factor behaves at very small wave vectors are sufficient to describe the observed optical behavior of the living system.