Trapping forces, force constants, and potential depths for dielectric spheres in the presence of spherical aberrations

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Abstract
We present and verify a theoretical model that predicts trapping forces (escape forces), force constants (trap stiffnesses), and trapping potential depths for dielectric spheres with diameters smaller than or equal to the wavelength of the trapping light. Optical forces can be calculated for arbitrary incident light distributions with a two-component approach that determines the gradient and the scattering force separately. We investigate the influence of spherical aberrations that are due to refractive-index mismatch on the maximum trapping force, the force constant, and the potential depth of a trap, which are important for optical tweezer applications. The relationships between the three parameters are explained and studied for different degrees of spherical aberration and various spheres (refractive indices n s = 1.39–1.57, radii a = 0.1–0.5 µm, λ0 = 1.064 µm). We find that all three parameters decrease when the distance to the coverslip increases. Effects that could make the interpretation of experimental results ambiguous are simulated and explained. Computational results are compared with the experimental data found in the literature. A good coincidence can be established.