Modeling additive color effect in natural photonic polycrystals using the layer homogenization method: The case of the diamond weevil

The original method we propose allows to compute the spectral reflectance of photonic crystals whose unit cell is composed of form-birefringence anisotropic elements such as cylinders or parallelepipeds. This method relies on the layer homogenization of the photonic structure. It is especially useful for the calculation of reflectance according to different crystal orientations. The coloration due to an additive color effect in the photonic polycrystal found on the diamond weevil, Entimus imperialis, was investigated. Simulating the reflectance of photonic polycrystals often turns out to be necessary in the study of such structures as well as in the design and production of bioinspired devices (Vigneron and Lousse, Proc SPIE 6128:61281G, 2006; Deparis and Vigneron, Mater Sci Eng B-Adv 169(1–3):12–15, 2010). In this context, the computation of the reflectance of photonic crystals (PCs) displaying form-birefringence anisotropic elements in the unit cell (e.g., cylinders, parallelepipeds...) turns out to be cumbersome, particularly when the reflectance is calculated for different crystal orientations as in the case of polycrystals. The method proposed here solves this problem in the particular case of a PC with a periodicity that is such that there is only specular reflection and no higher-order diffraction (Mouchet et al. Opt Express 21(11):13228–13240, 2013). In this method, the structure with a particular crystal orientation is sliced into layers and the periodic dielectric function ε (formula displayed) is homogenized within each layer (Fig. 60.1a). Using this Layer Homogenization (LH) method, the reflectance of one single domain of the polycrystal can be computed in an arbitrary orientation thanks to a standard thin film solver. The reflectance due to the additive color effect created by the disorder in the crystal domain orientation of the polycrystal is modeled by averaging reflectance spectra computed for several incidence angles and crystal domain orientations. Our method was applied to the case of a natural photonic polycrystal found on the cuticle of the diamond weevil Entimus imperialis (Fig. 60.2a). Its coloration is due to an additive color effect created by PC domains with various orientations (Fig. 60.2b) (Deparis and Vigneron, Mater Sci Eng B-Adv 169(1–3):12–15, 2010; Mouchet et al. Proc SPIE 8480:848003, 2012): a single PC domain gives rise to a gleaming iridescent color (from blue to orange) but the disorder in the crystal domain orientation results in a non-iridescent dull color (Fig. 60.2a). Investigating such a structure is relevant in the development of bioinspired applications such as biomimetic devices e.g., gas, temperature or pH sensors (Van Opdenbosch et al. Photon Nanostruct 10(4):516–522, 2012).