Non-iridescent structural colors based on disordered arrangement of monodisperse spherical particles, also called photonic glass, show low color saturation due to gradual transition in the reflectivity spectrum. No significant improvement is usually expected from particles optimization, as Mie resonances are broad for small dielectric particles with moderate refractive index. Moreover, the short range order of a photonic glass alone is also insufficient to cause sharp spectral features. We show here, that the combination of a well-chosen particle geometry with the short range order of a photonic glass has strong synergetic effects. Using a first-order approximation and an Ewald sphere construction the reflectivity of such structures can be related to the Fourier transform of the permittivity distribution. The Fourier transform required for a highly saturated color can be achieved by tailoring the substructure of the motif. We show that this can be obtained by choosing core-shell particles with a non-monotonous refractive index distribution from the center of the particle through the shell and into the background material. The first-order theoretical predictions are confirmed by numerical simulations.

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.

Reciprocal space engineering allows tailoring the scattering response of media with a low refractive‐index contrast. Here it is shown that a quasiperiodic leveled‐wave structure with well‐defined reciprocal space and random real space distribution can be engineered to open a complete photonic bandgap (CPBG) for any refractive‐index contrast. For these structures, an analytical estimation is derived, which predicts that there is an optimal number of Bragg peaks for any refractive‐index contrast. A finite 2D or 3D CPBG is expected at this optimal number even for an arbitrarily small refractive‐index contrast. Results of numerical simulations of dipole emission in 2D and 3D structures support the estimations. In 3D simulations, an emission suppression of almost 10 dB is demonstrated with a refractive index down to 1.38. The 3D structures are realized by additive manufacturing on millimeter scale for a material with a refractive index of n ≈ 1.59. Measurements confirm a strong suppression of microwave transmission in the expected frequency range.

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Photonic glass provides angle-independent, spectrally selective scattering that can be used as structural colors. We show how the core-shell geometry of the particles can be used to improve the saturation of blue color.