From rings to resonance: an inverse method links biophotonic structural color to inverse photonic glasses

Abstract

Structural color arises from the interaction of light with nanoscale structures and is widespread in nature. As structural complexity increases, the mechanisms governing coloration become progressively less understood. The optical response of periodic photonic crystals with a spatially periodic refractive index is well described by Bloch theory, whereas that of photonic glasses composed of randomly assembled uniform spheres is more subtle yet well studied. In contrast, disordered photonic networks found in many beetles are among the most complex natural photonic architectures, and the fundamental relationships between their structure and color remain unclear. Here, we use an inverse method to identify the structural features encoded in the reflectance spectrum. By comparing the spectrum of an unknown system with a database of simulated spectra from computer-generated photonic networks, we infer its structural properties. Applying this approach to both simulated networks and the biophotonic network responsible for the blue coloration of the weevil Pachyrhynchus congestus mirabilis, we identify rings and pores as the key local scattering motifs. Their characteristic sizes govern the spectral position of the reflectance peak, whereas short-range disorder controls its width. The inverse method reveals clear spectral signatures of short-range order, whereas the influence of hyperuniformity and primitive similarity appears comparatively weak. This suggests that blue structural coloration is governed by local scattering mechanisms rather than photonic band-gap effects. We propose an analogy to an inverse photonic glass, in which pores and rings act as correlated local resonators. This perspective provides new design principles for bio-inspired structural-color materials.