Optically bound matter in a tractor beam

In a `tractor beam’ a particle may experience an optical recoil force directed against the total field momentum. This effect occures either with isolated particles, or mutiple-particle structures spontaneusly formed due to secondary light scattering (`optical binding’). We investigate conditions yielding the `negative’ force for the simplest stucture, a pair of identical spheres, using numerical simulations based on the exact theory of multiple particle scattering and low-Reynolds-number hydrodynamics, To model the tractor beam in our calculations, we use a wide Gaussian beam counter-reflected at a small angle, thus forming a standing wave. In such beam the pairs end up with their centers moving uniformly, separated in space roughly by an integer number of wavelenghts, while spanning none or several fringes. We show that, for a large interval or sphere radii and their specific alignment, the tractoring can be provoked by adjusting the beam angle of incidence and/or its polarisation. In addition, we find pairs which move even faster than a single sphere in its optimal beam settings.