Possible sorting mechanism for microparticles in an evanescent field

Mie scattering theory is used to calculate radiation forces on a dielectric microsphere illuminated by evanescent waves, produced by laser light transmitted obliquely through a flat horizontal dielectric surface. The incident field is identified with the evanescent field, and both $p$ and $s$ polarizations are considered. Our investigation consists of three parts. First, after highlighting the basic formalism, we report results for the radiation force published in an earlier paper [J. Opt. Soc. Am. B {\bf 12}, 2429 (1995)], correcting a few trivial calculational errors. Second - the main objective of our paper - is to show how the vertical (lifting) force on microspheres, typically via a proper adjustment of the laser frequency, can be used to separate spheres differing by a slight amount in their refractive index. This is caused by an oscillatory behavior in the force with respect to the nondimensional wave number $\alpha$ in the surrounding medium. Fine-tuning the wave number $\alpha$, relative to the given refractive indices in the system, may lead to particle expulsion. The sorting mechanism turns out to be feasible when $\alpha$ is about 18-20 or larger, which actually is in the region of practical interest. Finally, we investigate how variations in the angle of incidence $\theta_1$ for the laser beam influences the resulting radiation force.