Accelerating light beams along arbitrary trajectories

Wave-packets of light propagating along curved trajectories in space are rapidly gaining importance since their introduction. Interestingly, all such "non-diffracting self-accelerating" beams studied thus far followed a parabolic trajectory as they propagated in free space. Here we generate continuous sets of accelerating optical beams propagating along arbitrary 1D curves in space, with the only condition being that the curves are convex. We present a general method to construct such beams, and demonstrate them theoretically and experimentally.