Analytical study on the self-healing property of Bessel beam

With the help of Babinet principle, an analytical expression for the self-healing of Bessel beam is derived by using the Gaussian absorption function to describe the obstacle. Based on the analytical expression, the self-healing properties of Bessel beam are studied. It shows that Bessel beam has the ability to reconstruct its beam shape disturbed by an obstacle. However, during the self-healing process, not only the intensity of the beam behind the obstacle but also the other part will be affected by the obstruction. Meanwhile, the highlight spot, which intensity is larger than that without the obstacle will appear, and the size and strength of the highlight spot is determined by the size of the obstacle. From the change of Poynting vector and Babinet principle, the physical interpretations for the self-healing ability, the effects of the obstruction on the other part and the appearance of highlight spot are given.