Ewald sphere construction for structural colors

TL;DR

This paper introduces an Ewald sphere construction method to analyze and explain the spectral and directional properties of structural colors produced by disordered thin films, highlighting their suitability for short wavelength colors and potential for long wavelength colors.

Contribution

It presents a simple geometrical Ewald sphere approach to predict scattering direction and efficiency in disordered structures, validated by electromagnetic simulations.

Findings

Ewald sphere construction effectively predicts scattering features.

Disordered structures are better suited for short wavelength colors.

Total internal reflection can enable long wavelength structural colors.

Abstract

Disordered structures producing a non-iridescent color impression have been shown to feature a spherically shaped Fourier transform of their refractive-index distribution. We determine the direction and efficiency of scattering from thin films made from such structures with the help of the Ewald sphere construction which follows from first-order scattering approximation. This way we present a simple geometrical argument why these structures are well suited for creating short wavelength colors like blue but are hindered from producing long wavelength colors like red. We also numerically synthesize a model structure dedicated to produce a sharp spherical shell in reciprocal space. The reflectivity of this structure as predicted by the first-order approximation is compared to direct electromagnetic simulations. The results indicate the Ewald sphere construction to constitute a simple geometrical tool that can be used to describe and to explain important spectral and directional features of the reflectivity. It is shown that total internal reflection in the film in combination with directed scattering can be used to obtain long wavelength structural colors.