Fig. 1. (a) Single-beam tweezer trap (FG, gradient force; FS, scattering force), (b) dual-beam trap (Beam 1 is shown in red and Beam 2 is shown in blue to aid in identifying from which beam these forces originated), (c) OBT, and (d) z-dependent forces at fixed x coordinate highlighted in (c); trapping occurs at zT, where the gradient force from Beam 2 is restoring.

Fig. 2. Analytically calculated forces on microbead in identical collimated beams. (a) Gradient force along z from Beam 2 and scattering force along x from Beam 1 versus transverse coordinate; curves need to intersect between the origin and location of maximum gradient force to form a stable trap [locations of maximum gradient and maximum scattering force used for (b) are shown with green arrows]. (b) Particle size dependence of forces at relevant points (symbols) and fits with second-order polynomial (lines).

Fig. 3. (a) Calculated particle trajectory exhibiting trapping at beam intersection (all dimensions to scale), (b) total force at the beam intersection, trapping point (black), w0 from Beam 1 (red), and w0 Beam 2 (blue) shown with dotted lines, and (c) time dependence of particle velocities along x and z showing acceleration due to Beam 2, followed by trapping.

Fig. 4. (a) Calculated potential profile along the direction of Beam 1 (z) and (b) trap stability plot. Symbols delineate the validity limit of the relation in Eq. (7) for a given particle size, and the line shows the linear fit.