Modeling the photonic response of biological nanostructures using the concept of stratified medium: The case of a natural three-dimensional photonic crystal

Naturally grown nanostructures found in living organisms are among the most sophisticated devices the human mind could imagine. Such structures can be studied using the theoretical concept of stratified medium because, in many instances, one can conceptually slice the structure into layers within which the refractive index does not vary in the direction perpendicular to the interfaces. If the layers are homogeneous in the lateral directions (parallel to the interfaces), the stratified medium reduces to a multilayer structure and thin-film computational codes can be used to calculate the photonic response (reflectance, transmittance, absorption). If the layers are inhomogeneous but exhibit periodicity of the material constants (permittivity or refractive index) in the lateral directions, the medium can be viewed as a stack of two-dimensional photonic crystal layers and a transfer matrix computational code is perfectly adapted to calculate the photonic response of these structures. With the aim to show the usefulness of the stratified medium concept, we discuss here the remarkable case of a three-dimensional photonic crystal (periodicity in all directions, parallel and perpendicular to the interfaces) which was recently discovered in the scales of Entimus imperialis (Curculionidae).