Self‐Imaging Effect Based on Circular Airy Beams

The self-imaging effect for a superposition of the fundamental circular Airy beams with successively changing radial displacements is investigated. In free space, this self-imaging along a parabolic trajectory can persist before the focal point. In the linear index potentials with a gradient, the propagation trajectory of circular Airy-Talbot effect can follow some predefined trajectories determined by engineering the index gradient, and the self-imaging extent can expand provided that each truncated constituent circular Airy beam maintains its form and continues to accelerate before dispersing strongly.