Knots made from light could be used to transmit data, measure turbulence in the air, and for optical trapping. However, the behavior of optical knots in unstable, turbulent environments remains largely unexplored. Researchers at Duke University developed a theoretical approach to sculpting optical knots. Their approach provides precise control of the knot formation, allowing for on-demand changes to be made in the shape, orientation, and size of the individual segments within a 3D knot as well as to its rotation and shifts. The researchers’ rigorous method for forming 3D optical knots is universally applicable to knots created using braided zero lines. The team validated its approach through theoretical analysis and experimental measurements. The researchers also investigated the effects of atmospheric turbulence on the stability of optical knots. They found that the optical knots developed using their approach could be preserved in a weak turbulence regime, but might not survive under stronger turbulence conditions, despite the topological nature of the knots. Turbulence effect on optical knots. Courtesy of Nature Communications (2025). DOI: 10.1038/s41467-025-57827-1. The team showed that information embedded in the optical knots could endure the effects of lasers that were traveling through turbulent air, albeit not as easily as scientists originally believed. “People thought that because these shapes are mathematically stable objects, they should be able to be transmitted through complex environments without any complications,” professor Natalia Litchinitser said. “As it turns out, they’re not guaranteed to be stable, but we can make them more stable.” In a space the size of a small dining-room table, the team replicated a laser traveling through turbulence over a long distance. “We used a small, toaster-oven-sized device with a hot plate in the bottom and fans to create air turbulence,” researcher Danilo Gomes Pires said. “Then we shrunk the light beam and bounced it off several mirrors to mimic it traveling almost 1000 feet.” The team surmised that if the laser beam remained unperturbed during this journey, the resulting optical knot would appear as one continuous, flowing string with three loops. However, the researchers found that as the turbulence became more intense, the knot was more likely to devolve into two interconnected rings, or even a single ring, and lose any information it contained. Such topology transitions occur through reconnection events, where the additional optical modes resulting from the interactions with the turbulent medium change the vortex lines in space. The researchers further discovered that degradation was not inevitable and that the stability of the knot could be made to last for a longer time. They developed an optimization algorithm to maximize the distance between the phase singularities at each longitudinal plane, facilitating measurements of the optical knots and improving their performance in the presence of turbulence. Schematics of the proposed optical knot shaping method. Courtesy of Photonics Research (2024). DOI: 10.1364/PRJ.533264. The results indicate that, although the topological structure of optical knots is relatively stable in the weak-turbulence regime, knot optimization and post- or pre-correction algorithms may be needed to maintain the shape of the knot in strongly perturbed environments, such as a strong-turbulence regime. Therefore, the topological stability of mathematical knots does not inherently imply the stability of optical knots, at least in terms of the commonly used topological invariant — that is, the number of singularity crossings. The researcher’s approach to shaping and optimizing optical knots could enable new degrees of freedom in multidimensional singularities shaping, including rotations, shifts, and rescaling to enhance stability in complex media. It could be used in the fields of 3D optical trapping, manipulation, and subwavelength microscopy as well as for probing and imaging through atmospheric or underwater turbulence. Information could be encoded into the shapes of optical knots and transmitted over long distances. The ability to measure how much a knot was disrupted by its travels could lead to ways to measure the amount of turbulence the knot passed through. “Before we can actually use optical knots for any kind of application, we have to really study them and understand how they behave,” Litchinitser said. “Ours is the first demonstration of propagating through real turbulence, so from here we can take the next step and scale it up to continue exploring how these work in free space.” The research was published in Photonics Research (www.doi.org/10.1364/PRJ.533264) and Nature Communications (www.doi.org/10.1038/s41467-025-57827-1).