Spin-orbital Conversion in Tightly Focused Optical Vortices with Vector Polarization

In this paper we investigated tight focusing characteristics of optical vortices with cylindrical vector polarization. The investigated beams are described by Jones vector E = e
^imϕ
(cos(nϕ); sin(nϕ))
^T
, where n denotes the cylindrical beam order, m is a topological charge of optical vortex, ϕ is the azimuthal angle at the beam cross-section. It should be noted that the initial beam has local linear polarization in its cross-section, i.e., does not have longitudinal spin angular momentum (SAM). The simulation was performed using the Richards-Wolf formulas. The wavelength of the focused light was equal to 633 nm and the numerical aperture of the focusing lens was equal to NA = 0.95. Numerically and analytically we have shown that in the tight focus longitudinal SAM-vector component occurred — there are 4(n − 1) local subwavelength regions at the focus, with the longitudinal SAM vector component changing sign in the adjacent regions.