Mapping of three-dimensional optical force field on a micro-particle trapped in a fiber-optical dual-beam trap

摘要

We report the first direct experimental mapping of three-dimensional optical force field on a silica micro-particle trapped in a counter-propagating dual-beam trap. We tracked the three-dimensional Brownian motion of the trapped particle (by optical position sensing) and analyzed the particle position distribution to obtain the force constant of the optical force field on the particle along each direction. The trapping beams scattered by the trapped particle along two directions (mutually orthogonal to each other and also to the trapping beams) were projected on a pair of quadrant photo-detectors (QPDs) to facilitate high-speed (20 KHz) three-dimensional position tracking. Position tracking over two mutually orthogonal planes intrinsically provides one set of redundant data for a self-consistency check. At optical wavelength λ = 532nm, the force constants of the three-dimensional optical force field on a silica micro-particle (diameter = 2.58 μm) were determined to be k_x = 1.61x10~(-1) pN/μm, k_y = 1.49x10~(-1) pN/μm, and k_z = 4.43x10~(-2) pN/μm when the total trapping power was about 21mW and the distance between the two fiber end-faces was 125 μm. The set of force constants (k_x, k_y, and k_z) completely defines the optical force field E(x, y, z) = [k_xx~2 + k_yy~2 + k_zz~2]/2 (in the parabolic potential approximation) on the trapped particle.