Backward force exerted on a nanoparticle in a non-paraxial beam near zero intensity

Using finite-difference time-domain simulation, we demonstrate that if an absorbing nanoparticle (e.g., gold, approximately 20 nm in diameter) is positioned near an isolated intensity null in the autofocus plane, both in a two-dimensional and three-dimensional non-paraxial laser beam, the particle experiences a force of the order of femtonewtons, causing it to move back near the zero intensity. Along part of this trajectory, the force is negative and pulls the particle backward. The direction of the absorbing nanoparticle's rotation around the zero intensity is the same as the direction of the canonical energy flux vector. The absorbing nanoparticle is, as it were, captured by the energy flux and moves with it, in both the positive and negative directions.