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Conventional caustic methods in real or Fourier space produced acceleratingoptical beams only with convex trajectories. We develop a superposition causticmethod capable of winding light beams along non-convex trajectories. Weascertain this method by constructing a one-dimensional (1D) accelerating beammoving along a sinusoidal trajectory, and subsequently extending totwo-dimensional (2D) accelerating beams along arbitrarily elliptical helicaltrajectories. We experimentally implement the method with a compact and robustintegrated optics approach by fabricating micro-optical structures on quartzglass plates to perform the spatial phase and amplitude modulation to theincident light, generating beam trajectories highly consistent with prediction.The theoretical and implementation methods can in principle be extended to theconstruction of accelerating beams with a wide variety of non-convextrajectories, thereby opening up a new route of manipulating light beams forfundamental research and practical applications.

Winding light beams along elliptical helical trajectories