Wave-optics description of self-healing mechanism in Bessel beams

TL;DR

This paper provides a wave-optics explanation for the self-healing property of Bessel beams, deriving expressions for the reconstruction distance and clarifying the underlying physics in terms of plane wave propagation.

Contribution

It offers a rigorous wave-optics framework for understanding Bessel beam self-healing, aligning with geometrical optics predictions and elucidating the physical mechanism.

Findings

Derived expressions for the minimum reconstruction distance.

Confirmed agreement with geometrical optics predictions.

Explained self-healing via propagation of plane waves on a ring.

Abstract

Bessel beams' great importance in optics lies in that these propagate without spreading and can reconstruct themselves behind an obstruction placed across their path. However, a rigorous wave-optics explanation of the latter property is missing. In this work we study the reconstruction mechanism by means of a wave-optics description. We obtain expressions for the minimum distance beyond the obstruction at which the beam reconstructs itself, which are in close agreement with the traditional one determined from geometrical optics. Our results show that the physics underlying the self-healing mechanism can be entirely explained in terms of the propagation of plane waves with radial wave vectors lying on a ring.