Parametric Force Analysis for Measurement of Arbitrary Optical Forces on Particles Trapped in Air or Vacuum

We demonstrate a new method to measure arbitrary optical forces on particles trapped in gaseous or vacuum environments using the ring down of a trapped particle following electrostatic excitation of particle motion in the trap. The method is not limited to the common constraints of linear forces for small oscillations or conservative forces, allows for a wide displacement range, and measures forces directly from trajectories in near-real time. We use transient response analysis to model the nearly ideal response for small oscillations, and illustrate the more general case by demonstrating a nonlinear response to impulse excitation at a displacement where the optical force is linear. Simulations verify the applicability to nonlinear forces from a general potential, and comparison to traditional thermodynamic measures shows good agreement. Combined with in situ microscopy to measure the particle diameter, this allows for the estimation of all system parameters assuming only the manufacturer's value for the particle density.