The creation of double tight focus by a concentric multi-belt pure phase filter

We demonstrate a method of constructing a concentric multi-belt pure phase filter for creating double tight focus dominated by longitudinal polarized components on the axis when a radially polarized plane wave is focused by a high numerical aperture objective. By obstructing the central part of the pure phase filter and choosing the objective with large numerical aperture, we may obtain two sub-wavelength longitudinally polarized focal spots with controllable separation. Its full-width at half-maximum (FWHM) could be less than the diffraction limit. It provides an exquisite tool for stably trapping two nanometer-sized particles and aligning them along the optical axis or manipulating biological molecules through micro-spheres attached to the molecules by chemical bonds.