LAUSR

Abstract Modulated by the spatial phase, Airy-like beams that possess the faster and better self-healing as well as the greater acceleration along the desired arbitrary trajectory are introduced. Airy-like beams have the strong spontaneous-focusing ability and the peak value of the focal plane is 5.4 times that of the initial plane when traveling along the quadratic function trajectory. Besides, the larger quadratic coefficient and the smaller constant term of the quadratic function can enhance the self-healing and the spontaneous-focusing of the beams. When the beams transmit along the snakelike trajectory, the original main lobe separates a new main lobe, and the energy will concentrate on the new main lobe. Airy-like beams, along a hyperbolic-secant trajectory, can remain non-diffraction over long distances. However, when traveling along a hyperbolic trajectory, the evolution process is very similar to that of Airy-Gaussian vortex beams. These excellent properties can be applied to the special beams’ modulation and optimization. Furthermore, it may provide a way for constructing beams along the special trajectory with the desired spontaneous-focusing and self-healing.