When waves propagate through a weak disordered potential with correlation length larger than the wavelength, they form channels (branches) of enhanced intensity that keep dividing as the waves propagate1. This fundamental wave phenomenon is known as branched flow. It was first observed for electrons1,2,3,4,5,6 and for microwave cavities7,8, and it is generally expected for waves with vastly different wavelengths, for example, branched flow has been suggested as a focusing mechanism for ocean waves9,10,11, and was suggested to occur also in sound waves12 and ultrarelativistic electrons in graphene13. Branched flow may act as a trigger for the formation of extreme nonlinear events14,15,16,17 and as a channel through which energy is transmitted in a scattering medium18. Here we present the experimental observation of the branched flow of light. We show that, as light propagates inside a thin soap membrane, smooth thickness variations in the film act as a correlated disordered potential, focusing the light into filaments that display the features of branched flow: scaling of the distance to the first branching point and the probability distribution of the intensity. We find that, counterintuitively, despite the random variations in the medium and the linear nature of the effect, the filaments remain collimated throughout their paths. Bringing branched flow to the field of optics, with its full arsenal of tools, opens the door to the investigation of a plethora of new ideas such as branched flow in nonlinear media, in curved space or in active systems with gain. Furthermore, the labile nature of soap films leads to a regime in which the branched flow of light interacts and affects the underlying disorder through radiation pressure and gradient force.
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We are indebted to M. V. Berry, for suggesting to us that what we saw in the experiments is related to branched flow. This research was supported by the German-Israeli DIP project, and by the Israel Science Foundation.
The authors declare no competing interests.
Publisher’s note Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
This file contains Supplementary Text and Data, including Supplementary Figures 1-13.
Branched flow Typical patterns of branched flow. The light is launched into the soap film through an optical fiber. The optical beam propagates within the thin film, which acts as a slab waveguide with a locally varying thickness. The light scatters from the thickness variations and forms the pattern of branched flow.
Branched flow and background potential visualization The video shows branched flow patterns superimposed on top of the landscape of the scattering potential. The system is similar to video #1, but with additional RGB illumination incident upon the film from the top. The RGB light is used to map the thickness fluctuations as a function of position in the plane of the film. The film acts as a Fabry-Perot interferometer for the RGB light, giving rise to the colourful pattern shown in the video. The colours provide the information about the thickness of film as a function of lateral position. From these colours, we calculate the potential landscape, as explained in the SI. The thickness variations in the film act as a weak slowly-varying potential for the laser beam guided within the membrane.
Branched flow in curved space In this video, the soap film forms a (semi) spherical bubble, and the branched flow forms within a positively curved 2D shell. In this case, in addition to thickness variations of the film, there is a global curvature of the film that affects the propagation. The curvature acts as an additional focusing potential and makes the branches propagate in a parallel fashion.
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Patsyk, A., Sivan, U., Segev, M. et al. Observation of branched flow of light. Nature 583, 60–65 (2020). https://doi.org/10.1038/s41586-020-2376-8