Enhanced force measurement techniques to extend optical trapping towards nanoscale manipulation

We have developed a new force measurement technique based on the random thermal motion of a nanoparticle in an optical trap. We demonstrate this method, in one-dimension, through numerical simulations and laboratory experiments. We show that computer simulations successfully recover the profile of the optical trapping force, beyond the inflection point of the trapping potential for a range of particle sizes. We show, through laboratory experiments, that this technique is effective in recovering higher order terms, in a power series expansion of the trapping force, beyond the widely reported linear trap stiffness. We also show that the first order (stiffness) term in our series expansion is consistent with values reported in the literature.