Generating a stationary infinite range tractor force via a multimode   optical fiber
  Optical fibers confine and guide light almost unattenuated and thus convey light forces to polarizable nano-particles over very long distances. Radiation pressure forces arise from scattering of guided photons into free space while gradient forces are based on coherent scattering between different fiber modes or propagation directions. Interestingly, even scattering between co-propagating modes induces longitudinal forces as the transverse confinement of the light modes creates mode dependent longitudinal wave-vectors and photon momenta. We generalize a proven scattering matrix based approach to calculate single as well as inter-particle forces to include several forward and backward propagating modes. We show that an injection of the higher order mode only in a two mode fiber will induce a stationary tractor force against the injection direction, when the mode coupling to the lower order mode dominates against backscattering and free space losses. Generically this arises for non-absorbing particles at the center of a waveguide. The model also gives improved predictions for inter-particle forces in evanescent nanofiber fields as experimentally observed recently. Surprisingly strong tractor forces can also act on whole optically bound arrays. 
Christiane A. Ebongue, Daniela Holzmann, Stefan Ostermann, and Helmut   Ritsch
quant-ph physics.optics