Structural coloration produces some of the most brilliant colors in nature
and has many applications. However, the two competing properties of narrow
bandwidth and broad viewing angle have not been achieved simultaneously in
previous studies. Here, we use numerical optimization to discover geometries
where a sharp 7% bandwidth in scattering is achieved, yet the peak wavelength
varies less than 1%, and the peak height and peak width vary less than 6% over
broad viewing angles (0--90∘) under a directional illumination. Our
model system consists of dipole scatterers arranged into several rings;
interference among the scattered waves is optimized to yield the
wavelength-selective and angle-insensitive response. Such designs can be useful
for the recently proposed transparent displays that are based on
wavelength-selective scattering
