Spontaneous generation of singularities in paraxial optical fields

TL;DR

This paper explores how certain smooth optical fields can spontaneously develop singularities at focal points, using an analogy with quantum mechanics, potentially enabling new technological applications.

Contribution

It introduces a new class of paraxial optical fields that develop singularities at focal points, based on a novel analogy with quantum wave functions.

Findings

Fields develop singularities at focal points

Singularity nature depends on a real parameter

Potential for diverse scientific applications

Abstract

In nonrelativistic quantum mechanics the spontaneous generation of singularities in smooth and finite wave functions, is a well understood phenomenon also occurring for free particles. We use the familiar analogy between the two-dimensional Schroedinger equation and the optical paraxial wave equation to define a new class of square-integrable paraxial optical fields which develop a spatial singularity in the focal point of a weakly-focusing thin lens. These fields are characterized by a single real parameter whose value determines the nature of the singularity. This novel field enhancement mechanism may stimulate fruitful researches for diverse technological and scientific applications.