Accelerating light beams along arbitrary trajectories

Wave-packets of light propagating along curved trajectories in space are rapidly gaining importance since their introduction in 2007 [1-2]. Interestingly, all such non-diffracting self-accelerating beams studied thus far followed a parabolic trajectory as they propagated in free space [1-5]. 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. As examples, we present theoretically and experimentally light beams whose peak intensity accelerates along the curves x = zⁿ, with n = 1.5, 2,3,4,5, and an Exponential Beam which follows the curve x=(e^k1), k being some positive constant. Such beams are presented in Figure (1a-1b) below.