Self-healing of Gaussian and Bessel beams: a critical comparison

TL;DR

This paper investigates the self-healing property of optical beams, providing a new universal expression for the minimum reconstruction distance and introducing a witness function to quantify self-reconstruction capabilities.

Contribution

It offers a novel, general formula for the minimum reconstruction distance applicable to all beam types and proposes a new measure to quantify self-healing ability.

Findings

Derived a universal expression for the minimum reconstruction distance.

Introduced a witness function to quantify self-healing capability.

Clarified the physics underlying the self-healing mechanism.

Abstract

Contrarily to a common belief, any beam of light possesses to a some extent the ability to "reconstruct itself" after hitting an obstacle. The celebrated Arago spot phenomenon is nothing but a manifestation of this property. In this work we analyze the self-healing mechanism from both a mathematical and a physical point of view, eventually finding a new expression for the minimum reconstruction distance, which is valid for \emph{any} kind of beam, including Gaussian ones. Finally, a witness function that quantify the self-reconstruction capability of a beam is proposed and tested. The results presented here help clarifying the physics underlying self-healing mechanism in optical beams.