Experimentally controlling scattering of water waves in correlated disorder

TL;DR

The study addresses how correlated disorder, specifically stealthy hyperuniform (SHU) patterns, can suppress wave scattering in disordered media with dissipation. Using two-dimensional SHU and uncorrelated scatterer layouts in a water-wave platform, the authors image the complex wavefield to extract the extinction length, effective scattering coefficient $\alpha_e$, and energy-current patterns across a range of wavenumbers, identifying the SHU threshold $k_{\rm hyp} = K/2$ that separates non-scattering from scattering regimes. They demonstrate that SHU suppresses scattering and yields deterministic transport below the threshold, while fluctuations across realizations are greatly reduced in this regime; above threshold, SHU and uncorrelated media exhibit comparable scattering. This work validates SHU transport predictions in a lossy, real-world system and highlights hyperuniformity as a practical design principle for controlling wave propagation across optics, acoustics, and related wave disciplines.

Abstract

Wave propagation in complex media is a universal problem spanning optics, acoustics, mechanics, and condensed matter physics. While disorder usually causes strong scattering, recent theory predicts that a special class of correlated disorder, known as stealthy hyperuniformity, can suppress scattering at long wavelengths, making a material transparent despite remaining structurally disordered and far from a simple homogenization regime. Experimental evidence of this remarkable transport regime within a medium has, however, remained limited. Here we report a direct, spatially resolved experimental observation of a transition between scattering and non-scattering wave transport induced by hyperuniform correlations. Using water waves as a model platform, we image both the amplitude and phase of the wavefield as it propagates through a two-dimensional disordered structure. This enables us to extract quantitative transport observables, including extinction lengths, statistical fluctuations, and energy-flow patterns, and to directly identify the boundary of the hyperuniform transparency regime. Our results provide a quantitative experimental validation of the transport regimes predicted for stealthy hyperuniform disorder and demonstrate that correlated disorder offers a powerful and practical route to control wave propagation in realistic systems across wave physics.

Figures (8)

• Figure 1: Disordered patterns used in the experiments. Uncorrelated pattern (A) and SHU pattern (B), together with their corresponding structure factors $S$ (C) and (D). The SHU region around $q=0$ is clearly visible in (D). The uncorrelated medium scatters the incoming wave in all directions (red arrows in frame A), whereas the SHU medium allows waves below a threshold frequency to propagate without scattering, (frame B). Note that the number density of scatterers is the same in both cases.
• Figure 2: (A) Schematic representation of the experiment. A loudspeaker drives a 40-cm paddle to generate monochromatic surface waves in a 150 × 60 cm water tank. A camera placed above the tank records the deformation of a checkerboard located beneath the transparent bottom, enabling reconstruction of the water surface elevation (wavefield). A sloped absorbing beach suppresses unwanted reflections. (B) Photograph of the actual setup, showing the tank, the paddle, the illumination system, and a hyperuniform medium.
• Figure 3: Analysis of a single scatterer. (A) Amplitude of the extracted scattered field at an excitation frequency of 7.5Hz. (B) Phase of the scattered field at 7.5Hz. (C) Measured scattering cross-section $\sigma_s$, averaged over several values of the radius [see \ref{['eq:sigma_s']}] versus the excitation frequency $f=\omega/2\pi$ for a single scatterer.
• Figure 4: Maps of measured wavefields. (A) Uncorrelated medium excited at frequency $f=\unit{5}{Hz}$ by a plane wave propagating from left to right along the $z$ direction. (B) Uncorrelated medium at $f=\unit{8}{Hz}$. (C) SHU medium at frequency $f=\unit{5}{Hz}$. The unperturbed wavefield reveals the absence of scattering. (D) SHU medium at $f=\unit{8}{Hz}$ above the critical value. Colors indicate the water surface elevation, and the black dots correspond to the positions of the scatterers.
• Figure 5: Maps of the phase of the measured wavefields. (A) Phase map of an uncorrelated medium excited by a plane wave propagating from left to right along the $z$ direction at frequency $f=\unit{5}{Hz}$. (B) Uncorrelated medium at $f=\unit{8}{Hz}$. (C) SHU medium at $f=\unit{5}{Hz}$, showing an essentially unperturbed wavefront. (D) SHU medium at $f=\unit{8}{Hz}$, above the critical frequency, where scattering becomes significant. Colors represent the phase of the wavefield, and black dots indicate the positions of the scatterers.