Self-focusing effect on the characteristics of Airy beams

The self-focusing effect on the characteristics of Airy beams is studied, and the physical explanations are also given. It is shown that the self-focusing effect on the self-healing of an Airy beam with the main lobe blocked can be ignored. Due to the self-focusing effect, an Airy beam with main lobe blocked can keep its Airy profile to further propagation distance than a complete Airy beam. This may offer a way to keep the acceleration of an Airy beam under the effect of nonlinearity. Due to the self-focusing effect, the self-accelerating of Airy beams becomes stronger when the beam power is not very high, which may be applied in practice. In particular, it is found that the resistance of an Airy beam to self-focusing effect is more remarkable than that of a Gaussian one.