Researchers have uncovered an unusual wave phenomenon that links engineered materials to principles found in ocean physics.
Waves bouncing around an irregularly shaped space typically follow increasingly unpredictable paths. Scientists have now shown that certain materials can produce the opposite effect, guiding waves into stable, repeating patterns instead of chaotic trajectories.
Researchers at the Advanced Science Research Center at the CUNY Graduate Center (CUNY ASRC) discovered this behavior in hyperbolic materials, whose unusual properties restrict the directions in which waves can travel. Their study, published in Nature Physics, identifies structures called “hyperbolic wave attractors” that could eventually help engineers control light, sound, and electromagnetic signals.
“This work shows how geometry and the properties of a material can work together to produce wave behavior that is both surprising and useful,” said Andrea Alù, the study’s principal investigator, director of the Photonics Initiative at the CUNY ASRC, and Distinguished Professor of Physics at the CUNY Graduate Center. “By understanding how waves organize themselves in these hyperbolic media, we can begin to explore new approaches to controlling energy, information, and communication signals in complex environments.”
When Waves Defy the Usual Rules of Reflection
In ordinary materials, waves generally reflect at the same angle at which they strike a surface. Repeated reflections inside an irregular enclosure can produce chaotic motion, a phenomenon studied through a classic physics problem known as a dynamical billiard.
Hyperbolic materials behave differently. Named after the mathematical curve called a hyperbola, these materials direct waves along specific paths and alter how they reflect from angled surfaces. Inside an irregular cavity, these unusual reflection rules can cause waves to converge toward organized trajectories.
“Normally, we expect a complicated cavity to produce complicated, chaotic wave patterns,” said Simon Yves, a postdoctoral researcher in Alù’s lab and a first author of the study. “Here, the opposite happens. The unusual propagation and reflection of waves create a strong geometric organization, producing well-defined paths that can persist across a broad range of wavelengths.”
How Waves Organize Into Stable Patterns
The researchers found that repeated reflections can guide waves into closed trajectories that remain stable across different scales. This behavior arises partly from broken mirror symmetry in the reflection process, which causes wavelengths to progressively shrink as waves travel through the cavity.
These wave attractors also exhibit handedness, meaning their paths circulate clockwise or counterclockwise. Their stability and direction depend on the geometry of the cavity and the material’s unusual wave properties. The team demonstrated the phenomenon using a mechanical metamaterial engineered to control vibrations.
“The most exciting aspect of these results is that they connect a simple geometric idea with a rich set of wave phenomena,” said Enrico Renzi, a doctoral student in Alù’s lab and a first author of the study. “We can observe how the waves become organized, and we can connect that organization to properties such as stability and handedness. This gives us a framework for designing wave behavior rather than simply observing it.”
From Ocean Waves to Nanoscale Light
Related wave attractors occur in oceans, where internal waves traveling through water layers of different densities reflect unusually from underwater slopes. These reflections can concentrate energy along closed paths and contribute to wave turbulence.
The new study demonstrates a similar effect in an engineered solid, allowing researchers to investigate the underlying physics in a controlled laboratory setting. The principles could also extend to hyperbolic phonon polaritons, hybrid light and matter excitations found in certain crystals, including hexagonal boron nitride and molybdenum trioxide.
These materials can confine infrared light to extremely small regions, making them promising candidates for nanophotonic technologies. Potential applications of hyperbolic wave attractors include compact optical circuits, optical signal separation, particle trapping, analog wave computing, and sensitive biological sensors, although these uses have not yet been demonstrated.
“This research opens a path toward engineering stable and robust wave patterns in systems where waves would normally be expected to rapidly become chaotic,” Alù said. “Our goal is to understand how these effects can be harnessed to create new functionalities for photonics, phononics, and wave-based technologies.”
Reference: “Hyperbolic wave attractors” by Simon Yves, Enrico M. Renzi, Sander A. Mann and Andrea Alù, 28 September 2026, Nature Physics.
DOI: 10.1038/s41567-026-03453-7
The research was supported by the Simons Foundation and the National Science Foundation Science and Technology Center “New Frontiers of Sound.
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