On the overall polarisation properties of Poincare beams

We analyse the polarisation properties of Poincare beams. We consider different configurations, such as Laguerre-Poincare (LP), Bessel-Poincare (BP), and Lambert-Poincare (LaP) beams. The former considers the well-known cylindrical vector beams and full-Poincare beams 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, BP 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 Poincare pattern, one which is generated by a Lambert projection of the Poincare sphere on the transverse plane, and hence we call them LaP. This configuration, contrary to the LP, provides a finite region containing all polarisation states uniformly distributed on the Poincare sphere.