Coherent and incoherent nonparaxial self-accelerating Weber beams

TL;DR

This paper explores the properties of coherent and incoherent nonparaxial Weber beams, revealing their inability to produce the accelerating Talbot effect due to lobes not accelerating in unison, and extends insights to similar Mathieu beams.

Contribution

It provides a theoretical and numerical analysis of nonparaxial Weber beams, clarifying their coherence properties and their relation to the accelerating Talbot effect, with implications for Mathieu beams.

Findings

Superposition of coherent Weber beams does not produce the Talbot effect.

Incoherent Weber beams can display nonparaxial accelerating properties.

Similar conclusions apply to nonparaxial Mathieu beams.

Abstract

We investigate the coherent and incoherent nonparaxial Weber beams, theoretically and numerically. We show that the superposition of coherent self-accelerating Weber beams with transverse displacement cannot display the nonparaxial accelerating Talbot effect. The reason is that their lobes do not accelerate in unison, which is a requirement for the appearance of the effect. While for the incoherent Weber beams, they naturally cannot display the accelerating Talbot effect but can display the nonparaxial accelerating properties, although the transverse coherence length is smaller than the beam width, based on the second-order coherence theory. Our research method directly applies to the nonparaxial Mathieu beams as well, and one will obtain similar conclusions as for the Weber beams, although this is not discussed in the paper. Our investigation identifies families of nonparaxial accelerating beams that do not exhibit the accelerating Talbot effect, and in addition broadens the understanding of coherence properties of such nonparaxial accelerating beams.