Transverse force profiles of individual dielectric particles in an optical trap

The transverse force profile of a particle in an optical trap is important for the designs of optical trapping-based force transducers. We mapped these force profiles for micron-size polystyrene beads using a pair of overlapping optical traps produced by two highly focused Gaussian beams with unequal intensity; the stronger trap serves as a force transducer to measure the force of the weaker trap in both linear and nonlinear regimes. For particles with size smaller or comparable to the laser wavelength, the force profiles follow closely the gradient of the Gaussian profile, but as the particle size increases, the force profiles deviate from the shape of the gradient of Gaussian for the distance beyond the position of the maximum force. The distance from the center of the trap to the position of the maximum trapping force was found to increase linearly with the particle size. The experimental results are in good agreements with our theoretical model, based on a combination of the Mie theory, vector Debye integral, and Maxwell stress tensor; except that the experimental particle-size dependence of the maximum trapping forces was found to be weaker than that predicted by the theory.