Single Gradientless Light Beam Drags Particles as Tractor Beams

Usually a light beam pushes a particle when the photons act upon it. We investigate the optical forces by nonparaxial gradientless beams and find that the forces can drag suitable particles all the way towards the light source. The major criterion of realizing the backward dragging force is the strong nonparaxiality of the light beam, which contributes to the pulling force owing to momentum conservation. The nonparaxiality of the Bessel beam can be manipulated to possess a dragging force along both the radial longitudinal directions, i.e., a tractor beam with stable trajectories is achieved.