Classical and quantum properties of cylindrically polarized beams of light via a Poincaré sphere representation

Cylindrically polarized modes (CPMs) of the electro-magnetic field represent very intriguing configurations of optical beams that exhibit complex non-uniform polarization patterns. Such vector beams possess several interesting features. On the fundamental side, there is a formal analogy to the quantum entangled Bell states [1] of two indistinguishable systems, with the difference that the CPMs are composed of distinguishable systems. On the application side, there is the possibility to be focused beyond the diffraction limit for linearly polarized light [2], underlining their potential impact on applications in lithography, confocal microscopy, optical trapping as well as material processing.