Evolution of C-point singularities and polarization coverage of Poincaré-Bessel beam in self-healing process

As a vector version of scalar Bessel beams, Poincaré-Bessel beams (PBBs) have attracted a great deal of attention due to their non-diffracting and self-healing properties as well as the presence of polarization singularities. Previous studies of PBBs have focused on cases that consist of a superposition of Bessel beams in orthogonal circular polarization states; here, we present a theoretical and experimental study of PBBs for which the polarization states are taken to be linear, which we call a linear PBB. Using a mode transformation of a full Poincaré beam constructed from linear polarization states, we observe the linear PBB as providing an in-principle infinite number of covers of the Poincaré sphere in the transverse plane and with an infinite number of C-points with positive and negative topological indices. We also study the dynamics of C-point singularities in a linear PBB in the process of self-healing after being obstructed by an obstacle, providing insight into "Hilbert Hotel" style evolution of singularities in light beams. The present study can be useful for imaging in the presence of depolarizing surroundings, studying turbulent atmospheric channels, and exploring the rich mathematical concepts of transfinite numbers.