Abstract
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.
Highlights
Spiral structure is a basic structure of the world, which can be found from the double helix of DNA to a galaxy
When we examine the spiral structure of the spin density vector, it is convenient to adopt the normalized spin density vector for analysis
Our result shows that this spiral spin density vectors is mainly caused by the Gouy phase difference which is a result of spin-orbit interactions (SOI) in a strongly focusing system
Summary
Spiral structure is a basic structure of the world, which can be found from the double helix of DNA to a galaxy. The electric field vector of a circularly polarized field generates a spiral trajectory on propagation, while the wavefront of the electric field has a spiral shape in a vortex beam Because of these two spiral behaviors, the optical beams can carry spin angular momentum (SAM) and orbital angular momentum (OAM), which is one of the fundamental theories in optics [1], [2]. As one result of the SOI in a strongly focused field, the spinning spin density vectors ( named SAM density vectors) compose a new spiral structure in a three-dimensional (3D) optical field [8]. A special spiral behavior of the spin density vector will be observed in this focused field
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