Self-accelerating and self-breathing Bessel-like beams along arbitrary trajectories

We theoretically and experimentally study self-accelerating and self-breathing Bessel-like beams that follow arbitrary trajectories, including hyperbolic, hyperbolic secant, and three-dimensional (3D) spiraling trajectories. The beams have an overall Bessel-like profile in transverse dimensions; however, the intensity of their central main lobe breathes while traveling along a curved trajectory. Such beams can be readily generated experimentally through appropriate phase modulation of the optical wavefront. The beams contribute to the design of new families of self-accelerating beams.