🔬 condensed matter

Experimentally controlling scattering of water waves in correlated disorder

This paper presents a direct experimental observation using water waves that validates theoretical predictions by demonstrating how stealthy hyperuniform correlations in a disordered medium can suppress scattering and induce a transparent transport regime.

Original authors: Angélique Campaniello, Rémi Carminati, Marcel Filoche, Emmanuel Fort

Published 2026-07-09

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CC BY 4.0

Original authors: Angélique Campaniello, Rémi Carminati, Marcel Filoche, Emmanuel Fort

Original paper licensed under CC BY 4.0 (http://creativecommons.org/licenses/by/4.0/). ✨ This is an AI-generated explanation of the paper below. It is not written or endorsed by the authors. For technical accuracy, refer to the original paper. Read full disclaimer

Imagine you are standing by a calm pond, tossing a pebble to create ripples. Usually, if you drop a bunch of random rocks into the water, those ripples get messy, chaotic, and scattered in every direction. It's like trying to shout through a crowded, noisy room; the sound gets lost in the chaos.

But what if you could arrange those rocks in a very specific, secret pattern? A pattern that looks totally random to the naked eye but actually holds a hidden order? That is exactly what this team of scientists did, but instead of rocks in a pond, they used water waves and tiny plastic cylinders.

The Magic of "Stealthy" Disorder
The researchers were testing a strange idea called "stealthy hyperuniformity." Think of it like a crowd of people at a party. In a normal, random crowd, people bump into each other, creating a chaotic mess. But in a "stealthy" crowd, everyone is standing in a way that looks random, yet they are secretly coordinating their positions to avoid bumping into each other when they move slowly.

The team built two different water tanks. Both had the exact same number of plastic cylinders (401 of them) floating in the water, with the same density.

Tank A (The Chaos): The cylinders were placed randomly, like someone just threw them in.
Tank B (The Stealth): The cylinders were arranged in a "stealthy hyperuniform" pattern.

They sent water waves through both tanks at different speeds (frequencies between 3.5 and 10 Hz).

The Big Discovery: The Invisible Wall
Here is the cool part. When they sent waves at a slow speed (specifically, a frequency of 5 Hz), something magical happened in Tank B. The waves sailed right through the plastic cylinders as if they weren't even there! The water surface remained perfectly flat and smooth, just like a calm pond. The waves didn't scatter, didn't bounce, and didn't get messy.

In contrast, in Tank A (the random one), those same slow waves got completely scrambled and bounced off the cylinders in every direction.

However, the "magic" had a limit. When they sped up the waves to a faster speed (8 Hz), the stealthy pattern stopped working. Suddenly, the waves in Tank B started scattering just like they did in the random tank. The "invisible wall" had a specific threshold.

Why This Matters
The scientists measured exactly how far the waves could travel before they died out. They found that in the "stealthy" tank, the waves traveled much further without losing energy at the slow speeds. They calculated a specific "cutoff point" (a wavenumber of about 1.12 cm⁻¹). Below this point, the stealthy pattern made the material transparent to the waves. Above it, the transparency vanished.

They also looked at how the energy flowed. In the random tank, the energy flow was a tangled mess of curves and bends. But in the stealthy tank, at the slow speeds, the energy flowed in straight, clean lines, like a highway with no traffic jams.

What It's Not
It's important to note that this isn't because the water became a solid block or because the waves were too big to see the cylinders. The waves were actually quite small (between 2.3 cm and 14 cm long), and the cylinders were small too. The transparency wasn't a result of "smoothing out" the material; it was a specific property of the arrangement of the obstacles.

Also, the water wasn't perfectly still; it had some natural friction and absorption (dissipation). The scientists showed that even with this natural "leakiness" in the water, the stealthy pattern still managed to stop the waves from scattering. It wasn't a perfect, loss-free magic trick, but it worked surprisingly well in a real, messy environment.

The Bottom Line
This experiment proved that you can control how waves move through a material just by arranging the obstacles in a special, correlated way. You don't need to build a perfect crystal or a solid wall. You can use a "disordered" material that looks messy but behaves like a clear window for specific types of waves.

The team didn't just guess this; they measured it. They mapped the height and phase of the water waves with high precision, showing exactly where the waves stopped scattering and where they started bouncing again. This suggests that in the future, we might be able to design materials that let sound, light, or other waves pass through them without getting lost, simply by arranging the tiny bits inside them just right.

Technical Summary: Experimentally Controlling Scattering of Water Waves in Correlated Disorder

Problem Statement
Wave propagation in complex media is governed by the interplay of disorder, interference, and dimensionality. While disorder typically induces strong scattering, theoretical predictions suggest that a specific class of correlated disorder known as stealthy hyperuniformity (SHU) can suppress scattering at long wavelengths. SHU structures are characterized by a structure factor $S(q)$ that vanishes in a neighborhood of the origin in reciprocal space ( $S(q)=0$ for $q \le K$ ), effectively suppressing density fluctuations at large scales. This property is predicted to render materials transparent despite remaining structurally disordered and far from a homogenization regime. However, experimental validation of this transport regime has been limited. Previous studies have largely relied on global transmission measurements or qualitative intensity maps, leaving the internal wavefield structure and quantitative transport observables unresolved. Furthermore, the robustness of these predictions in realistic, lossy environments (where dissipation competes with correlation-induced transparency) had not been directly characterized.

Methodology
The authors employed water waves as a model platform to probe wave transport in two-dimensional disordered structures. The experimental setup consisted of a $150 \times 60$ cm water tank filled to a depth of 7 cm. Monochromatic surface waves (frequencies 3.5–10 Hz) were generated by a 40-cm-wide paddle driven by a loudspeaker.

Disordered Media: Two types of scattering media were fabricated using vertical cylindrical PMMA scatterers (1 cm diameter) inserted into a transparent plate. Both media had an identical scatterer density ( $\rho = 0.2 \text{ cm}^{-2}$ $ρ = 0.2 cm^{- 2}$ , $N=401$ $N = 401$ scatterers).
1. Uncorrelated Disorder: Generated via random sequential addition.
2. Stealthy Hyperuniform (SHU) Disorder: Generated using a reciprocal-space optimization procedure to enforce $S(q)=0$ for $q \le K$ , with a correlation parameter $\chi = 0.5$ and a threshold wavenumber $K \approx 2.24 \text{ cm}^{-1}$ .
Wavefield Imaging: A camera positioned 2 m above the tank recorded the deformation of a checkerboard pattern placed beneath the transparent tank bottom. Using Fast Fourier checkerboard demodulation, the authors reconstructed the complex wavefield (amplitude and phase) with high spatial resolution ( $\sim 0.3$ mm lateral, $\sim 20$ $\mu$ m vertical).
Data Analysis: The researchers extracted quantitative transport observables by:
1. Measuring the extinction length ( $\ell_e$ ) of the average field to determine the effective scattering coefficient ( $\alpha_e$ ), correcting for background viscous absorption.
2. Analyzing statistical fluctuations of the scattering strength across different disorder realizations.
3. Calculating energy current density ( $J = \text{Im}(\psi^* \nabla \psi)$ ) to visualize energy flow patterns.
4. Rotating the scatterer plates by 90° to obtain four distinct realizations for ensemble averaging.

Key Contributions and Results
The study provides the first direct, spatially resolved, and quantitative experimental observation of the transition between scattering and non-scattering regimes induced by hyperuniform correlations in an absorbing medium.

Observation of the Transparency Regime:
- At frequencies below the critical threshold ( $f < 6$ Hz, corresponding to wavenumber $k \le K/2 \approx 1.12 \text{ cm}^{-1}$ ), the SHU medium exhibited suppressed scattering. The wavefronts remained planar, and phase maps showed no distortion, indicating transparency despite the disordered structure.
- In contrast, the uncorrelated medium at the same frequencies showed significant wavefront deformation and phase distortion.
- Above the threshold ( $f > 6$ Hz, $k > K/2$ ), the SHU medium transitioned to a strongly scattering regime, with wave behavior similar to the uncorrelated case.
Quantitative Validation of Transport Regimes:
- Extinction Length: The effective scattering coefficient $\alpha_e$ for the SHU medium dropped significantly below the theoretical threshold $K/2$ , reaching values dominated by background absorption. Above the threshold, $\alpha_e$ increased substantially.
- Statistical Fluctuations: A key finding was the self-averaging nature of the SHU medium in the non-scattering regime. The standard deviation of the scattering coefficient across different disorder realizations nearly vanished for $k \le K/2$ . This contrasts with the uncorrelated medium, which exhibited large sample-to-sample fluctuations. This confirms that a single SHU realization faithfully reflects the ensemble behavior in the transparency window.
- Energy Flow: Current density maps revealed that in the SHU transparency regime, energy flux lines remained straight and uniformly oriented, preserving the directionality of the incident wave. In the scattering regime (both SHU and uncorrelated), flux lines became tortuous.
Robustness in Lossy Environments:
The experiment demonstrated that the transparency window persists even in the presence of viscous dissipation and boundary friction, provided the absorption length is sufficiently large compared to the wavelength ( $\ell_a \gg \lambda$ ).

Significance and Claims
The paper claims to provide the first in-medium experimental characterization of wave transport in SHU disorder within an absorbing background. By directly imaging both amplitude and phase, the authors validate theoretical predictions regarding the full phase diagram of SHU transport (transparency vs. scattering).

The authors assert that their results demonstrate that correlated disorder offers a powerful and practical route to control wave propagation in realistic systems. Specifically, they show that SHU correlations can suppress scattering and yield deterministic transport behavior at the level of individual realizations, without requiring ensemble averaging or homogenization. This establishes hyperuniformity as an experimentally accessible design principle for controlling wave propagation across various wave physics domains, extending the design principles for disorder-based metamaterials.

Technical Summary: Experimentally Controlling Scattering of Water Waves in Correlated Disorder

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