Displacement and localisation of a transparent nanosphere by light-pressure forces in the field of a focused laser beam

We report the results of a numerical simulation of the Langevin equation describing the motion of a transparent nanosphere under the action of a resulting light-pressure force in the field of a continuous focused Gaussian laser beam. The conditions for the localisation of the nanosphere near the focal waist of the beam focused by the lens are determined. An analytical solution of the approximate (truncated) equation of motion is found, which almost exactly coincides with the results of the numerical simulation of the initial equation.