Vortex Dynamics and Structured Darkness of Laguerre-Gaussian Beams Transmitted Through Q-Plates Under Weak Axial-Asymmetric Incidence

We describe the rich vortex dynamics at normal and near-normal or off-centered Laguerre-Gaussian beam transmission through the q-plate – a waveplate capable of generating vortex beams from circularly polarized incident beams. First, we explore the basics of the spin-to-orbit angular momentum conversion and show the vortex constellations under normal incidence for the case of quarter-wave retardation. Second, we analyze the optical Gaussian and vortex beam profile transformations accompanying the giant beam shifts under axial-asymmetric incidence. Namely, we consider the near-normal (for the Fourier-space q-plate) and off-centered (for the real-space q-plate) incidence, when the incident angle becomes comparable with beam angular divergence and off-center distance becomes comparable with beam width, respectively. In this regime, one can control the positions of the single-charge vortices with the specified polarization components of the beam, including those residing in its structured darkness. All mentioned effects arise due to the extreme spin-orbit coupling. The results obtained form a novel platform for a plethora of optical vortex transformation and structured light phenomena.