Direct Measurement of the Nonconservative Force Field Generated by Optical Tweezers

Abstract

The force field of optical tweezers is commonly assumed to be conservative, neglecting the complex action of the scattering force. Using a novel method that extracts local forces from trajectories of an optically trapped particle, we measure the three-dimensional force field experienced by a Rayleigh particle with 10 nm spatial resolution and femtonewton precision in force. We find that the force field is nonconservative with the nonconservative component increasing radially away from the optical axis, in agreement with the Gaussian beam model of the optical trap.

Perturbative theory for Brownian vortexes

“…More interesting behavior arises in a more highly structured force field of the type actually observed in optical trapping experiments [1,3,5]. Figure 1(e) shows that the computed axial force is well approximated near the plane z = 0 by a quartic polynomial,…”

“…Under these conditions, the particle is likely to remain trapped over the period of observation, and probability may be considered to be conserved. This also is the case for the experimental studies of optically trapped colloidal particles [1,3,5] that Eqs. (14) and (16) are intended to model.…”

“…The archetype for this class of systems is a colloidal sphere in an optical tweezer [1,3,4]. Trapped near the focus of a strongly converging beam of light, the particle is displaced by random thermal kicks into the nonconservative part of the optical force field arising from radiation pressure [5], which then biases its diffusion [1,3]. Assuming the particle remains localized within the trap, its time-averaged trajectory traces out a toroidal vortex.…”

Fundamental Tests of Physics with Optically Trapped Microspheres

“…If the two beams are misaligned from each other, the resulting trap will not be a simple harmonic trap. The scattering force from the laser beams is not conservative, and can do work on the microsphere under certain conditions [67,68]. When the two beams are misaligned ( Fig.…”

Potential energy profile of colloidal nanoparticles in optical confinement

“…Because optical forces on a nanoparticle are intrinsically nonconservative, the existence of a well-defined optical trapping potential is a valid approximation only when the optical gradient force (which is conservative) is much larger than the scattering force (which is nonconservative) [13][14][15][16]. Near the center of the optical trap the gradient force in the direction of the laser beam scales with magnitude CMR 3 Z∕Z 2 0 , and the scattering force scales with magnitude…”