# Nonparaxial Cartesian and azimuthally symmetric waves with concentrated wavevector and frequency spectra

## TL;DR

This paper introduces a theoretical framework for analyzing nonparaxial waves with concentrated spectra, enabling the description of complex azimuthally symmetric fields beyond traditional paraxial limits.

## Contribution

It extends the paraxial formalism to handle superpositions of nonparaxial waves, especially azimuthally symmetric Bessel beam superpositions with large cone angles.

## Key findings

- Describes nonparaxial Bessel-Gauss beams with enhanced curvature
- Demonstrates superpositions produce complex transverse patterns
- Provides analytical tools for azimuthally symmetric wave analysis

## Abstract

In this paper, we develop a theoretical analysis to efficiently handle superpositions of waves with concentrated wavevector and frequency spectra, allowing an easy analytical description of fields with interesting transverse profiles. First, we analyze an extension of the paraxial formalism that is more suitable for superposing these types of waves, as it does not rely on the use of coordinate rotations combined with paraxial assumptions. Second, and most importantly, we leverage the obtained results to describe azimuthally symmetric waves composed of superpositions of zero-order Bessel beams with close cone angles that can be as large as desired, unlike in the paraxial formalism. Throughout the paper, examples are presented, such as Airy beams with enhanced curvatures, nonparaxial Bessel-Gauss beams and Circular Parabolic-Gaussian beams (which are based on the Cartesian Parabolic-Gaussian beams), and experimental data illustrates interesting transverse patterns achieved by superpositions of beams propagating in different directions.