Three-dimensional forces in GPC-based counterpropagating-beam traps

We theoretically investigate the three-dimensional (3D) trapping force acting on a microsphere held in a pair of counterpropagating beams produced by the generalized phase contrast (GPC) method. In the case of opposing beams of equal power, we identify the range of beam waist separation s that results in a stable 3D optical potential-well by assessing the dependence of the axial and transverse force curves on s. We also examine how the force curves are influenced by other parameters such as size and refractive index of the microsphere. Aside from force curves of beam tandems with equal powers, we also numerically calculate force curves for cases of beam pairs having disparate relative strengths. These calculations enable us to elucidate the large dynamic range for axial position control of microparticles in GPC-based counterpropagting-beam traps.