The damped oscillating propagation of the compensating self-accelerating beams

We report a new form of compensating accelerating beam generated by amplitude modulation of the symmetric Airy beam (SAB) caustics with an exponential apodization mask. Our numerical study manifests that the compensating beam is with one main-lobe beam structure and can maintain the mean-intensity invariant both in the free space and loss media. Specially, the beam inherits the beamlets structure from the SAB and owns a novel damped oscillating propagation property. We also conduct a comparative study of its propagation property with that of the Airy beam theoretically. And by altering the signs of 2D masks, the main lobe of the compensating beam can be modulated to orientate in four different quadrants flexibly. The proposed compensating accelerating beam is anticipated to get special applications in particle manipulation or plasmas regions.