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Patterns typically observed in water can also be found in light

Patterns typically observed in water can also be found in light

Solitons are solitary waves that may travel great distances while keeping their shape and speed even after clashing with other waves.

However, in rare circumstances, soliton collisions may produce complex wave patterns, which are frequently referred to as “alphabet waves” because they resemble the letters X, Y, and H, as well as combinations of these shapes. Since its discovery in the nineteenth century, soliton waves and their collision patterns have captivated scientists.

Soliton wave interactions in shallow water. Credit: Liron Barakiva

Researchers show that the same equation used to simulate water soliton interactions, known as the Kadomtsev-Petviashvili II (KPII) equation, can also be used to model optical soliton interactions, demonstrating a strong relationship between the wave dynamics of water and light.

When an optical medium’s reaction to light depends not only on the point where the external optical field is applied (as in a local media), but also on the whole surface and volume of the medium, it is said to be nonlocal. Light that strikes a specific spot in a nonlocal medium is transported away to the surrounding region, allowing a narrow localized optical beam to produce a spatially wide reaction of the medium. The similarity between the weak surface tension of water and the strong nonlocality in some optical medium allows the KPII equation to be used to describe optical solitons.

Patterns typically observed in water can also be found in light
Simulation results showing different patterns emerging in optical soliton interactions. Credit: Horikis and Frantzeskakis. ©2019 The Royal Society

“We have shown that optical soliton propagation in nonlocal media—which include plasmas, nematic liquid crystals and liquid solutions with thermal nonlinearities—is governed by the same model that is used to describe shallow waters, with nonlocality playing the role of surface tension. Thus, indeed, ‘light meets water,’ as we predict that X-, Y-, H-shaped, and even more complicated wave structures that we observe in flat beaches can also be observed in optics, as optical beams propagating in nonlocal nonlinear media.”

“What is important in our article is that these two phenomena, nonlocality in optics and surface tension in water, seem to have a one-to-one correspondence, so to speak,” Horikis said.

Their discoveries imply that in the future, even more complicated patterns, such as web-like wave structures, may be discovered in collisions of optical solitons. They also intend to look into whether other highly nonlocal systems, such as Bose-Einstein condensates (macroscopic quantum systems composed of ultracold atoms) and colloids (mixtures containing particles suspended in solution), can provide the necessary ingredients to support the emergence of these patterns.

See Also

Patterns of water in light, Theodoros P. Horikis and Dimitrios J. Frantzeskakis

Published: July 2019
DOI: https://doi.org/10.1098/rspa.2019.0110

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