Localization of a Dielectric Spherical Nanoparticle Under the Action of Two Radiation Forces in the Field of a Focused Gaussian Laser Beam

We have solved the Lagrange equation by numerical methods with zero initial conditions, describing the motion of a transparent spherical nanoparticle under the action of the resultant force from the light pressure in the field of a continuous-wave focused Gaussian laser beam. We have determined the focal length of the lens needed for localization of the spherical nanoparticle near a point on the focal waist of the beam, and the coordinates at which the components of the radiation forces take on extremal values. We have also analyzed their dependence on the focal length of the lens.