Unveiling the correlation between non-diffracting tractor beam and its singularity in Poynting vector

This paper investigates the singular optics of nonparaxial light beams in the near field when the light behaves as a tractor beam. New insights into the optical pulling force, which is usually represented by integrating the stress tensor at a black box enclosing the object, are interpreted by the optical singularity of the Poynting vector. The negative nonconservative pulling force originates from the transfer of the azimuthal Poynting vector to the longitudinal component partly owing to the presence of a scatterer. The separatrice pattern and singularity shifts of the Poynting vector unanimously exhibit a differentiable near-field distribution in the presence of optical pulling force. A new method is established to calculate the near-field optical force using the differential Poynting vector in the far field. The results obtained provide a clear physical interpretation of the light-matter interaction and manifest the significance of singular optics in manipulating objects.