# On the overall polarisation properties of full Poincar\'e beams

## TL;DR

This paper investigates the polarization characteristics of various full Poincaré beams, including Laguerre-, Bessel-, and Lambert-Poincaré types, revealing their properties, behaviors under propagation, and introducing a new Lambert-Poincaré pattern.

## Contribution

It introduces a novel Lambert-Poincaré beam configuration based on a Poincaré sphere projection, expanding the understanding of polarization distributions in complex beam structures.

## Key findings

- Bessel-Poincaré beams act as polarization attractors transforming elliptical to linear polarization.
- Lambert-Poincaré beams provide a finite, uniformly distributed polarization region on the Poincaré sphere.
- The study describes the statistical and invariant properties of Laguerre-Poincaré beams.

## Abstract

We analyse the polarisation properties of full Poincar\'e beams. We consider different configurations, such as Laguerre-Poincar\'e, Bessel-Poincar\'e, and Lambert-Poincar\'e beams. The former is the original Poincar\'e beam produced by a collinear superposition of two Laguerre-Gauss beams with orthogonal polarisations. For this configuration, we describe the Stokes statistics and overall invariant parameters. Similarly, Bessel-Poincar\'e beams are produced by the collinear superposition of Bessel beams with orthogonal polarisations. We describe their properties under propagation and show that they behave as a free-space polarisation attractor transforming elliptical polarisations to linear polarisations. We also propose a novel type of full Poincar\'e pattern, one which is generated by a Lambert projection of the Poincar\'e sphere on the transverse plane, and hence we call them Lambert-Poincar\'e. This configuration, contrary to the Laguerre-Poincar\'e, provides a finite region containing all polarisation states uniformly distributed on the Poincar\'e sphere.