# Morphological properties of 2D symmetric Airy beams extracted from the stationary wave approximation

## TL;DR

This paper analyzes the morphological properties of symmetric 2D Airy beams in both paraxial and nonparaxial regimes using geometrical optics, stationary wave approximation, and numerical simulations to identify features like phase singularities.

## Contribution

It introduces a comprehensive approach combining geometrical optics and stationary wave approximation to analyze 2D symmetric Airy beams in different regimes, including nonparaxial.

## Key findings

- Roots of the beam's structure can be of order 3 in paraxial and up to 6 in nonparaxial regimes.
- The method identifies features like optical vortices and dislocations.
- Numerical simulations confirm the analytical results.

## Abstract

We explore the morphological properties of symmetric Airy beams in the paraxial and nonparaxial regimes. We consider a 2D electromagnetic realization with a single transverse component of the electric field, and in the nonparaxial regime, the longitudinal component along the optic axis. The general structure of these beams is analyzed with the combination of several approaches: geometrical optics through the use of caustics, the asymptotic wave properties of the light field using the stationary wave approximation and numerical integration. The geometrical optics approach involves locating the critical points that are later used in the stationary phase approximation. In the paraxial regime the highest order of the roots is 3, while in the nonparaxial regime, the order can be of up to 6. The technique yields conditions to identify interesting features on the beam, like the number of waves interfering constructively/destructively at the critical positions. The results are confirmed by the numerical simulations. In this way it is possible to distinguish and classify phase singularities like optical vortices and dislocations. The developed algorithm could be used to study any structured light field.