Periodic self-accelerating beams by combined phase and amplitude modulation in the Fourier space

We propose and demonstrate the generation of periodic self-accelerating beams through both phase and amplitude modulation in the Fourier space. For small amplitude variations, an accelerating beam still follows a smooth convex trajectory, which can be traced by acting on the spectral phase only. However, large modulations such as those generated from the Heaviside function with a zero amplitude distribution partially modify the convex trajectory due to the appearance of straight-line paths. Furthermore, periodic self-accelerating beams along convex trajectories are realized by employing an array of "spectral wells" in both the paraxial and nonparaxial regimes.