Stability Limits of Optical Capture of Transparent Spherical Nanoparticles with Account for Thermal Fluctuations and Viscous Friction

Based on expressions for radiation forces acting on a transparent spherical nanoparticle in the field of a focused Gaussian beam, an equation of motion of a nanoparticle along the optical axis in a liquid medium is constructed taking into account the viscous Stokes drag and thermal fluctuations. The Langevin equation of the first order with the initial condition is formulated. The analysis of stationary points and linearization of the resultant force near the position of stable equilibrium are carried out. Analytical expressions for the stationary distribution of the particle’s coordinate are obtained and the contribution of Brownian motion as a function of the particle’s radius is estimated. The influence of the focal length and the input beam radius on the magnitude of the maximum restoring force and the root-mean-square Brownian force is analyzed. It is shown that for particles with a radius of less than a few tens of nanometers, thermal fluctuations destroy optical capture.

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