Fractional-order hybridly polarized vector beams: generation, focusing, propagation, and spatial self-phase...

As a class of integer-order vector beams, hybridly polarized vector beams (HPVBs) are widely used in focus shaping, femtosecond laser filamentation, linear and nonlinear polarization evolution, etc. Recently, fractional-order vector beams have gained widespread interest due to their more control parameters, rich photophysical properties, and novel nonlinear optical phenomena. In this work, we report the experimental generation, focusing and propagation characteristics, and spatial self-phase modulation (SSPM) phenomenon of fractional-order HPVBs. It is shown that during the focusing and propagation processes, the intensity pattern of fractional-order HPVBs develops from a near-Gaussian structure in the incident plane to an asymmetric structure in both the focal field and the far field. Meanwhile, their distributions of state of polarization (SoP) also evolve, although it remains a hybrid polarization distribution overall. When the focused fractional-order HPVBs pass through the nonlinear optical sample, the far-field self-diffraction intensity pattern displays an irregular concentric multi-ring structure with a hybrid polarization distribution. It is found that the nonlinear medium not only modulates the far-field intensity pattern of fractional-order HPVBs but also controls their SoP distribution. This symmetric breaking HPVB has potential application prospects in optical micro-manipulation, light-matter interaction, optical spin-orbit conversion, etc.