Orbital motion of optically trapped particles in Laguerre-Gaussian beams

A theoretical examination of off-axial trapping in non-paraxial Laguerre-Gaussian beams is presented for both the Rayleigh and Mie regimes. It is well known that the force acting on a particle may be divided into a term proportional to the intensity gradient and another representing the scattering force. The latter term may be further sub-divided into a dissipative radiation force and a term dependent on the electric field gradient. For Rayleigh particles in Laguerre-Gaussian beams, it is shown that the field gradient term contributes exactly half of the scattering force. This may be compared with a plane wave, in which it makes zero contribution. The off-axis trapping positions for spheres with radii varying from 0.1 to 0.5 mum and a range of refractive indices are calculated numerically in the Mie regime, using a conjugate gradient approach. Azimuthal forces and orbital torques are presented for particles in their trapping positions, for beams with different orbital angular momentum and polarization states. The components of a "spin" torque, acting through the center of the particle, are also computed for absorbing particles in the Mie regime.