Quarter-wave design criteria for omnidirectional structural colors

Abstract

Structural colors are caused by light interference from periodic multi-layer dielectric stacks and exhibit rich, highly-chromatic colors. However, avoiding a color shift due to angular variation remains a challenge. The design criteria for angle-independent structural colors have been studied by treating a quarter-wave stack of alternating dielectric material layers as a one-dimensional photonic crystal. A refractive index zone has been identified that exhibits narrowband omnidirectionality for structural colors in the visible wavelength range. It was found that a quarter-wave stack of high refractive index (RI) paired-layers (n _H = 2.85 and n _L = 2.5), which have low RI contrast (n _H /n _L = 1.14), is key in fabricating omnidirectional structural color materials. The theoretical predictions discussed here are verified experimentally using a titania/halfnia (TiO₂/HfO₂) multilayer stack.

Keywords:

• structural color
• omnidirectional reflector
• angular dispersion
• photonic crystal

Acknowledgements

The authors thank Mr Masahiko Ishii of Toyota Motor Corporation, Japan for helpful discussions and Dr Michael Rowe of Toyota Institute of North America for assisting with the manuscript preparation. The authors also wish to acknowledge Dr Kai Sun at the University of Michigan for the TEM images reported.