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

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.