Radiation force exerted on a sphere by focused Laguerre-Gaussian beams

The generalized Lorenz-Mie theory is employed to calculate the force exerted on a sphere by focused Laguerre-Gaussian beams. The key parameters of the theory, namely, the multipole coefficients of the beams, are exactly derived from the beams' angular spectra in terms of some auxiliary coefficients. Several recurrence formulas, which can improve the calculation of the auxiliary coefficients and accordingly the force, are also derived. According to the calculated force, the trapping performances of the beams are investigated in the Mie regime. It is found that low(high)-azimuthal-order beams usually have advantages in the radial trapping of the high(low)-refractive-index sphere and the axial trapping of the low(high)-refractive-index sphere. The influences of the parameters of the beams, lens, and sphere on the trapping performance are also investigated.