Trapping forces in a multiple-beam fiber-optic trap.

Transverse and axial trapping forces are calculated in the ray optics regime for a multiple-beam fiber-optic light-force trap for dielectric microspheres located both on and off axis relative to the beam axis. Trap efficiencies are evaluated as functions of the effective index of refraction of the microspheres, normalized sphere radius, and normalized beam waist separation distance. Effects of the linear polarization of the electric field and of beam focusing through microlenses are considered. In the case of a counterpropagating two-beam fiber-optic trap, using microlenses at the distal ends of the fiber to focus the beams may somewhat increase the trapping volume and the axial stability if the fiber spacing is sufficiently large but will greatly reduce the stiffness of the transverse force. Trapping forces produced in a counterpropagating two-beam fiber-optic trap are compared with those generated in multiple-beam fiber-optic gradient-force traps. Multiple-beam fiber-optic traps use strong gradient forces to trap a particle; therefore they stabilize the particles much more firmly than do counterpropagating two-beam traps.