Nonparaxial accelerating Talbot effect

TL;DR

This paper explores the fractional Talbot effect in nonparaxial accelerating beams, revealing how interference of solutions to the Helmholtz equation creates self-imaging phenomena at specific angles, enhancing understanding of nonparaxial beam behavior.

Contribution

It introduces the fractional nonparaxial Talbot effect based on Helmholtz solutions, demonstrating self-imaging in nonparaxial accelerating beams with potential applications.

Findings

Fractional Talbot images form at specific angles.

Nonparaxial accelerating beams exhibit self-imaging properties.

The effect is controllable by beam component coefficients.

Abstract

We demonstrate the fractional Talbot effect of nonpraxial accelerating beams, theoretically and numerically. It is based on the interference of nonparaxial accelerating solutions of the Helmholtz equation in two dimensions. The effect originates from the interfering lobes of a superposition of the solutions that accelerate along concentric semicircular trajectories with different radii. Talbot images form along certain central angles, which are referred to as the Talbot angles. The fractional nonparaxial Talbot effect is obtained by choosing the coefficients of beam components properly. A single nonparaxial accelerating beam possesses duality --- it can be viewed as a Talbot effect of itself with an infinite or zero Talbot angle. These results improve the understanding of nonparaxial accelerating beams and the Talbot effect among them.