Generation of Spiral Spin Density Vectors with A Circularly Polarized, Vortex Beam

Spiral spin density vectors refer to the spiral trajectory of the spin density vectors in three dimensional (3D) space, and similar to the polarization Mobius strip, polarization knots and photonic wheel, are also special polarization structures in 3D optical field and only exist in three dimensions. In this article, we propose a new way to generate the spiral spin density vectors with a long spiral range. This is realized by strongly focusing a circularly polarized beam with one off-axis vortex. In this field, the spiral interval of spin density vectors theoretically always exists on the propagation axis, and its position can be controlled by the beam size parameter $f/w_0$ . The polarization variation and the spiral spin density vectors are discussed analytically along the propagation direction. It is found that the spiral shape and spiral ‘speed’ can be adjusted by the off-axis distance of the vortex and the semi-aperture angle of the focusing system respectively. A special spiral behavior of the spin density vector at the geometrical focus is also observed in this focused field. The spiral spin density vectors supply a new rotational degree of freedom in 3D optical field and our finding may have applications in optical micro-manipulations.