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$$zzzzzzWe investigate the optical trapping of a Rayleigh particle by a linearly or radially polarized Gaussian beam beyond the paraxial approximation based on a description of beam by the mixed dipole model. The Mie theory is applied to abtain a full solution, and the approximate analytical expressions for the optical force, equilibrium position, and trap stiffness are presented for a Rayleigh particle. Our results suggest that at equilibrium the displacement of the particle from the focus scales like EMBED Equation.DSMT4 (where a is the radius) for a transparent particle, owing to scattering, while for an absorptive particle it scales like EMBED Equation.DSMT4 , owing to absorption. The trap stiffness is found to be proportional to EMBED Equation.DSMT4 , in good agreement with the recent experiment. In addition, the radially polarized trapping beam is shown to be superior to the linearly polarized one in the Rayleigh regime as far as their trapping capabilities are concerned.
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