Theoretical framework to describe the reflection of circularly polarized light by a natural photonic crystal: elytron of a Chrysina resplendens scarab

A theoretical treatment of the optical properties of chiral materials exhibiting a photonic crystal behavior is summarized and extended. It can be applied to interpret the photonic characteristics of synthetic cholesteric liquid crystals and natural elytra of jewel scarabs showing graded spatial periods or pitches. The model is applied here to analyze the photonic properties of the cuticle of a C. resplendens scarab which reflects both components of circular polarization when illuminated with non-polarized light. The structural composition of the elytra has shown to consist of an optically homogenous epicuticle, an upper left-handed twisted arrangement of chitin fibrils embedding uric acid crystallites, followed by a unidirectional layer, and a second left-handed thicker helicoid. The basic information about this morphological structure is taken from the pioneering work of Caveney [Proc. Roy. Soc. Lond. B178, 205 (1971)10.1098/rspb.1971.0062]. Some of his findings are also obtained within the context of our theory (birefringence of the unidirectional layer, average volume fraction for the whole structure, and typical spectral composition of left- and right-handed reflectance spectra), and new ones are reported. Novel expressions for the photonic band gap and its width, the ordinary and extraordinary effective refractive indices and birefringence are also reported.