Near-field optical trapping in a non-conservative force field

The force-field generated by a near-field optical trap is analyzed. A C-shaped engraving on a gold film is considered as the trap. By separating out the conservative component and the solenoidal component of the force-field using Helmholtz-Hodge decomposition, it was found that the force is non-conservative. Conventional method of calculating the optical potential from the force-field is shown to be inaccurate when the trapping force is not purely conservative. An alternative method is presented to accurately estimate the potential. The positional statistics of a trapped nanoparticle in this non-conservative field is calculated. A model is proposed that relates the position distribution to the conservative component of the force. The model is found to be consistent with numerical and experimental results. In order to show the generality of the approach, the same analysis is repeated for a plasmonic trap consisting of a gold nanopillar. Similar consistency is observed for this structure as well.