Electromagnetic characterization of millimetre-scale replicas of the gyroid photonic crystal found in the butterfly Parides sesostris

Abstract

We have used three-dimensional stereolithography to synthetically replicate the gyroid photonic crystal (PC) structure that occurs naturally in the butterfly Parides sesostris . We have experimentally characterized the transmission response of this structure in the microwave regime at two azimuthal angles ( ϕ ) over a comprehensive range of polar angles ( θ ). We have modelled its electromagnetic response using the finite-element method (FEM) and found excellent agreement with experimental data. Both theory and experiment show a single relatively broad transmission minimum at normal incidence ( θ = 0°) that comprises several narrow band resonances which separate into clearly identifiable stop-bands at higher polar angles. We have identified the specific effective geometric planes within the crystal, and their associated periodicities that give rise to each of these stop-bands. Through extensive theoretical FEM modelling of the gyroid PC structure, using varying filling fractions of material and air, we have shown that a gyroid PC with material volume fraction of 40 per cent is appropriate for optimizing the reflected bandwidth at normal incidence (for a refractive index contrast of 1.56). This is the same gyroid PC material volume fraction used by the butterfly P. sesostris itself to produce its green structurally coloured appearance. This infers further optimization of this biological PC beyond that of its lattice constant alone.