The evolutions of spin density of tightly focused vector fields with spatially-variant uniform and non-uniform ellipticities

Recently, the emergence of transverse spin has aroused enormous interest research. Here, we present general analytical formulas of the tightly focused electric fields and spin densities for polarized beams with spatially-variant uniform and non-uniform ellipticities. We explore the evolution of spin densities from the Poincaré sphere view using the tightly focused azimuthal-variant first-order cylindrically polarized beams and azimuthal-variant first-order hybrid polarized beams as examples. This reveals the roles and contributions of the relative intensity fraction and initial phase in the modulation of spin density. These two degrees of freedom have different effects on the polarization distribution of these two types of input fields, and thus on the spin density of tightly focused fields. These findings enrich the spin structure of the light field and contribute to the modulation of the spin density. •General analytical formulas of the tightly focused electric fields and spin densities for polarized beams with spatially-variant uniform and non-uniform ellipticities are presented.•The evolution of spin densities from the Poincaré sphere view using the tightly focused azimuthal-variant first-order cylindrically polarized beams and azimuthal-variant first-order hybrid polarized beams as examples are explored.•This reveals the roles and contributions of the relative intensity fraction and initial phase to the modulation of spin density in these two types of fields, respectively.