Laser light can exert forces on matter by exchanging momentum in form of radiation pressure and refraction. Although these forces are small, they are sufficient to trap and manipulate microscopic particles [Phys. Rev. Lett. 24, 156 (1970)]. In this paper, we study the optical trapping phenomena by using computer simulation to show a detailed account of the process of momentum exchange between a focused light and a microscopic particle in an optical trapping by use of the finite difference time domain method. This approach provides a practical routine to predict the magnitude of the exchanged momentum, track the particle in a trapping process, and determine a trapping point, where dynamic equilibrium happens. Here we also theoretically describe the transfer procedure of orbital angular momentum from a focused optical vortex to the particle.
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