Evolution of an Airy beam obstructed by a transparent particle

As comparing with a beam blocked by an opaque obstacle, a beam blocked by a transparent obstacle is most often encountered in practice, especially in optical micro-control. In present paper, the propagation of a beam blocked by a transparent obstacle is modeled. As a special case, an analytical expression for an Airy beam blocked by a transparent obstacle is derived, and the evolution of its intensity in free space is studied and discussed. Study shows that the disturbed phase of Airy beam due to the transparent obstacle may cause many phase singularities during propagation. However, with the increase of the propagation distance, a disturbed Airy beam exhibits a similar property as the self-healing of its intensity.