Electromagnetic Equivalence Principle Formulation for Optical Forces on Particles in Arbitrary Fields

The computation of the fields scattered by a dielectric sphere illuminated by a plane wave and the evaluation of the resultant optical forces is a classical problem that can be analytically solved using Mie theory. Whereas extending said formulation to arbitrary incident fields does not pose any conceptual difficulty, the actual computation of the scattering coefficients and force components substantially grows in complexity as soon as interactions beyond the electric dipole arise. By formulating an equivalent electromagnetic problem, we derive a set of computationally efficient formulas for the evaluation of scattering and optical forces exerted by arbitrary incident fields upon dielectric spheres in the Mie regime. As opposed to force calculations by direct integration of the Maxwell's Stress Tensor, the present formulation relies on a set of universal interaction coefficients that do not require any problem-specific integration and can therefore be all precomputed and tabulated. The proposed methods can be easily integrated with the T-Matrix method to calculate forces on non-spherical dielectric objects.