Engineering correlated disorder for exotic light scattering diagrams

Abstract

Diffuse scattering of light from disordered assemblies is traditionally viewed as an uncontrollable broadband scattering background resulting in whitish hues. Here, we demonstrate that correlated disorder enables precise engineering of light scattering from 2D arrays of emitters resulting in strong observable colors. Our analytical framework shows that introducing controlled noise, with tunable probability density functions and correlations, generates three distinct scattering components: diffraction orders, diffuse background, and correlation halos. Correlation halos, often mistaken for broadened diffraction peaks, are independent features whose positions depend on correlation range and can appear between Bragg peaks. Crucially, they persist far beyond the regime where diffraction orders vanish. The noise probability density function provides an additional control: specific diffraction orders can be selectively suppressed while preserving others. This approach reproduces the scattering signatures of natural photonic structures, e.g. found in Morpho butterflies, and reveals multiple pathways from order to disorder, each with distinct optical properties. Our work provides a practical method for inverse design -finding the disorder that produces desired scattering patterns. This establishes diffuse scattering as a designable quantity, expanding the toolkit for metasurfaces and structural color beyond periodic and hyperuniform structures.

Figures (6)

• Figure 1: (a--c) Angular distribution of the scattered light intensity from disordered geometries with different degrees of disorder. The left panels show examples of 20x20 quasi-periodic ensembles of points, for different values of $S_d$ and $L_c$, generated using Eq. \ref{['eq:disorder']}. The right panels show calculated k-space scattering patterns obtained from incident white light by a 20 x 20 ensemble of scatterers, averaged over 5 random ensembles. Note the difference in angular properties and color clarity.
• Figure 2: Scattered intensity by a structure with 1000 nanostructures, $S_d=0.45$, $L_c=4.5$, no averaging. (inset): Definition of the $k_x$ in-plane scattering wavevector
• Figure 3: Average scattered intensity of a correlated disordered structure generated with Eq. \ref{['eq:disorder']} ($S_d=0.3$, $L_c=1$), with the decomposition of the average intensity formula.
• Figure 4: Evolution of the average angular diagram of the scattered light around the first diffraction order as a function of a) $S_d$ and b) $L_c$. The black dotted line is the one corresponding to Fig. \ref{['fig:Morpho']}.
• Figure 5: Example of a probability distribution removing all diffracted orders except the third; a) $\rho(\epsilon)$ of an ensemble of nanostructures, b) Corresponding $|\tilde{\rho}_\epsilon(k)|$, c) Resulting scattered intensity. 1000 nanostructures, no averaging.