[Paper Review] Engineering correlated disorder for exotic light scattering diagrams

Denis Langevin, Emma Bosbaty-Galliot+6 more|arXiv (Cornell University)|Feb 19, 2026

Metamaterials and Metasurfaces Applications0 citations

TL;DR

The paper shows that correlated disorder in 2D arrays of emitters can tailor light scattering, revealing diffraction orders, diffuse background, and correlation halos, and enables inverse design of scattering patterns.

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.

Motivation & Objective

• Motivate the study of disorder as a design tool for optical scattering beyond periodic and hyperuniform structures.
• Develop an analytical framework linking perturbation statistics to far-field scattering components.
• Enable inverse design by controlling disorder statistics to achieve desired scattering signatures.

Proposed method

• Model the emitter positions as x_n = n d + ε_n with controlled noise ε_n.
• Define Δ_m^(j) = ε_{j+m} - ε_j to characterize spatial correlations.
• Derive the ensemble-averaged scattered intensity I(k_x) with terms for diffuse background, Bragg-like diffraction, and correlation halos.
• Show how the noise distribution's PDF ρ_ε(ε) and its Fourier transform shape scattering, including selective suppression of diffraction orders.
• Provide a practical method to generate noise with defined S_d (noise strength) and L_c (correlation length).
• Extend the analysis from 1D to 2D structures and discuss implications for natural structures like Morpho butterflies.

Experimental results

Research questions

• RQ1 How do perturbation statistics of disorder (PDF and correlations) influence far-field scattering patterns?
• RQ2 What are the distinct scattering components arising from correlated disorder beyond traditional diffraction and diffuse background?
• RQ3 Can the disorder be engineered to selectively suppress or enhance specific diffraction orders while maintaining others?
• RQ4 Do correlation halos persist beyond regimes where Bragg peaks vanish, and how can they be controlled?
• RQ5 How can this framework enable inverse design of scattering diagrams in 2D metasurfaces?

Key findings

• Three scattering components emerge: diffuse background, diffraction-like terms, and correlation halos.
• Correlation halos are independent features whose positions depend on correlation range and can appear between Bragg peaks.
• Increasing disorder strength can suppress diffraction peaks while preserving correlation halos.
• The correlation term can create negative contributions, producing holes in the diffuse background near specular directions.
• The noise PDF ρ_ε(ε) and its Fourier transform control which diffraction orders are observed, enabling selective suppression or enhancement.
• The framework extends to 2D, producing 2D correlation halos and asymmetric scattering patterns that mimic natural structures.