Refocusing of the optical branched flow on a rough curved surface

Abstract

The phenomenon of branched flow has attracted researchers since its inception, with recent observations of the light branching on soap bubbles. However, previous studies have primarily focused on the flat spacetime, overlooking the effect of surface curvature on branched flows. In this paper, we explore the branched flow phenomenon of light on a rough curved surface called constant Gaussian curvature surfaces (CGCSs). Compared with flat space, a CGCS demonstrates that the first branching point advances due to the focusing effect of the positive curvature of the surface. Furthermore, unlike on flat space, optical branches on curved surfaces do not consistently become chaotic during its transmission in a random potential field. On the contrary, the “entropy” decreases at specific positions, which reveals a sink flow phenomenon following the generation of branched flows. This result highlights the time inversion characteristics of CGCSs. Lastly, we demonstrated that the anomalous entropy reduction is related to the transverse and longitudinal coherence transformations of light. We suppose these efforts would fuel further investigation of the thermodynamic evolution and spatiotemporal inversion of random caustics, as well as their future application in the information transmission of random potentials in curved spacetime.