Optical trapping of dielectric particles in arbitrary fields

We present a new method to calculate trapping forces of dielectric particles with diameters $D⩽\lambda$ in arbitrary electromagnetic, time-invariant fields. The two components of the optical force, the gradient force and the scattering force, are determined separately. Both the arbitrary incident field and the scatterer are represented by plane-wave spectra. The scattering force is determined by means of the momentum transfer in either single- or double-scattering processes. Therefore the second-order Born series is evaluated and solved in the frequency domain by Ewald constructions. Numerical results of our two-force-component approach and an established calculation method are compared and show satisfying agreement. Our procedure is applied to investigate axial trapping by focused waves experiencing effects of aperture illumination and refractive-index mismatch.