Optical trapping by Laguerre-Gaussian beams: Far-field matching, equilibria, and dynamics

By using the method of far-field matching we obtain the far-field expressions for the optical (radiation) force exerted by Laguerre-Gaussian (LG) light beams on a spherical (Mie) particle and study the optical-force-induced dynamics of the scatterer near the trapping points represented by the equilibrium (zero-force) positions. The regimes of linearized dynamics are described in terms of the stiffness matrix spectrum and the damping constant of the ambient medium. Numerical analysis is performed for both nonvortex and optical-vortex LG beams. For the purely azimuthal LG beams, the dynamics is found to be locally nonconservative and is characterized by the presence of conditionally stable equilibria (unstable zero-force points that can be stabilized by the ambient damping). We also discuss effects related to the Mie resonances (maxima of the internal field Mie coefficients) that under certain conditions manifest themselves as the points changing the trapping properties of the particles.