Gradient and scattering forces of anti-reflection-coated spheres in an aplanatic beam

Anti-reflection coatings (ARCs) enable one to trap high dielectric spheres that may not be trappable otherwise. Through rigorously calculating the gradient and scattering forces, we directly showed that the improved trapping performance is due to the reduction in scattering force, which originates from the suppression of backscattering by ARC. We further applied ray optics and wave scattering theories to thoroughly understand the underlying mechanism, from which, we inferred that ARC only works for spherical particles trapped near the focus of an aplanatic beam, and it works much better for large spheres. For this reason, in contradiction to our intuition, large ARC-coated spheres are sometimes more trappable than their smaller counter parts. Surprisingly, we discovered a scattering force free zone for a large ARC-coated sphere located near the focus of an aplanatic beam. Our work provides a quantitative study of ARC-coated spheres and bridges the gap between the existing experiments and current conceptual understandings.