Disordered animal multilayer reflectors and the localization of light

Abstract

Multilayer optical reflectors constructed from ‘stacks’ of alternating layers of high and low refractive index dielectric materials are present in many animals. For example, stacks of guanine crystals with cytoplasm gaps occur within the skin and scales of fish, and stacks of protein platelets with cytoplasm gaps occur within the iridophores of cephalopods. Common to all these animal multilayer reflectors are different degrees of random variation in the thicknesses of the individual layers in the stack, ranging from highly periodic structures to strongly disordered systems. However, previous discussions of the optical effects of such thickness disorder have been made without quantitative reference to the propagation of light within the reflector. Here, we demonstrate that Anderson localization provides a general theoretical framework to explain the common coherent interference and optical properties of these biological reflectors. Firstly, we illustrate how the localization length enables the spectral properties of the reflections from more weakly disordered ‘coloured’ and more strongly disordered ‘silvery’ reflectors to be explained by the same physical process. Secondly, we show how the polarization properties of reflection can be controlled within guanine–cytoplasm reflectors, with an interplay of birefringence and thickness disorder explaining the origin of broadband polarization-insensitive reflectivity.