Self-healing properties of cosh-Airy beams

Analytical optical field of the cosh-Airy beam partially blocked by a finite opaque obstacle that has Gaussian absorption efficiency is derived. The distributions of the normalized intensity and Poynting vector for a cosh-Airy beam with and without an opaque obstacle are demonstrated in the observation planes. The effects of the obstacle size, the central coordinates of the opaque obstacle, the cosh parameter, the decay factor, and the transverse scale factor on the self-healing process and ability are analyzed, respectively. The meaningful case that the main lobe of the cosh-Airy beam is blocked partially by an obstacle is considered. In the process of beam propagation, the energy flow in the direction of the negative transverse axis converges into the center of the opaque obstacle, so as to reform the cosh-Airy beam. With the increase of the axial propagation distance, the convergence of the energy flow decreases and finally disappears. When the obstacle size is smaller, the self-healing process is faster, and the self-healing ability is higher. The more the central coordinates of the opaque obstacle deviate from the origin, the slower the self-healing process is, and the lower the self-healing ability is. For larger cosh parameter, the self-healing process is faster, and the self-healing ability is higher. The smaller the decay factor is, the faster the self-healing process is, and the higher the self-healing ability is. The smaller the transverse scale factor is, the faster the self-healing process is, and the lower the self-healing ability is. The self-healing ability of the cosh-Airy beam is higher than that of the corresponding Airy beam. The self-healing properties of cosh-Airy beams are robust.