Light can be described as rays that travel in straight lines, which is convenient for explaining a large number of phenomena such as reflection or propagation through free space. Consequently, natural intuition about light relies on rays, and we expect light to go from one point to another in a straight line. However, light is actually a wave and therefore exhibits numerous features that are unique to waves. In recent years, researchers have shown that optical wave packets (beams) can propagate in a self-accelerating manner, where the structure of a beam is engineered to move along a curved trajectory. This field has attracted major interest, with many potential applications. Here, we take these accelerating beams one step further, demonstrating them in a medium that has a curved space geometry, where the trajectory of the accelerating beam is determined by the interplay between the curvature of space and interference effects arising from the beam’s structure.

The simplest example of a curved object is a sphere because it has the same constant curvature everywhere. Normally, optical beams that are confined to propagate on the surface of a sphere would move along geodesic paths, the largest circle on the sphere’s surface. But, as we show theoretically and experimentally, one can shape the structure of a beam such that it will accelerate and evolve in a shape-preserving manner on a nongeodesic line, such as a circle close to the North Pole. We use a thin hemispheric glass shell as the curved-space landscape for the light, and we couple a specifically shaped beam into this glass waveguide. The brightest lobe of this beam bends away from the shortest (geodesic) path, which is the trajectory that light would normally take on the sphere.

These experiments provide new avenues for controlling trajectories of light in nonplanar 3D settings and offer new opportunities for emulating general relativity.