Spatial self-phase modulation excited by fractional-order linearly polarized vector fields

Compared to the integer-order vector field, the fractional-order vector field has an additional degree of control freedom, which will bring rich photophysical properties and what we believe to be novel nonlinear optical phenomena. In this work, we theoretically and experimentally investigate the focusing, propagation, and spatial self-phase modulation (SSPM) of fractional-order linearly polarized vector fields (FLPVFs). It is shown that the weak focusing field of FLPVF exhibits an asymmetric intensity distribution. Intriguingly, its state of polarization (SoP) has a hybrid polarization distribution. When this focused FLPVF propagates to the far field in free space, its SoP degenerates into a localized linearly polarization distribution. However, after the focused FLPVF passes through an isotropic nonlinear Kerr medium, its SoP exhibits a hybrid polarization distribution. Additionally, unlike the self-diffraction intensity pattern of integer-order linearly polarized vector field (ILPVF) with a concentric multi-ring structure, the SSPM pattern of FLPVF is a symmetry broken self-diffraction intensity pattern. The presented work provides a nonlinear optics approach for manipulating both the SoP and intensity distributions of the light field.