Influence of permittivity on gradient force exerted on Mie spheres

In optical trapping, whether a particle could be stably trapped into the focus region greatly depends on the strength of the gradient force. Individual theoretical study on gradient force exerted on a Mie particle is rare because the mathematical separation of the gradient force and the scattering force in the Mie regime is difficult. Based on the recent forces separation work by Du et al. [Sci. Rep. 7, 18042 (2017)], we investigate the influence of permittivity (an important macroscopic physical quantity) on the gradient force exerted on a Mie particle by cooperating numerical calculation using fast Fourier transform and analytical analysis using multipole expansion. It is revealed that gradient forces exerted on small spheres are mainly determined by the electric dipole moment except for certain permittivity with which the real part of polarizability of the electric dipole approaches zero, and gradient forces exerted on larger spheres are complex because of the superposition of the multipole moments. The classification of permittivity corresponding to different varying tendencies of gradient forces exerted on small spheres or larger Mie particles are illustrated. Absorption of particles favors the trapping of small spheres by gradient force, while it is bad for the trapping of larger particles. Moreover, the absolute values of the maximal gradient forces exerted on larger Mie particles decline greatly versus the varied imaginary part of permittivity. This work provides elaborate investigation on the different varying tendencies of gradient forces versus permittivity, which favors more accurate and free optical trapping.