Our work on a novel optical trapping system using fractal optics and spatially inhomogneous polarisation of light has been published as Zhirong Liu and P. H. Jones, 'Fractal conical lens optical tweezers', IEEE Photonics Journal 9 6500111 (2017)
From the abstract: We propose a novel optical tweezers composed of an annular beam with
alternate radially and azimuthally polarized rings modulated by a
fractal conical lens (FCL) and demonstrate its optical forces on
Rayleigh dielectric particles both analytically and numerically. Owing
to the optical system's particular focusing properties, which could
generate a dark-centered or peak-centered intensity distribution in the
focal region when selecting an appropriate truncation parameter in front
of the focusing lens, the proposed FCL optical tweezers could
selectively trap and manipulate dielectric mesoscopic particles with
low- or high-refractive indices by appropriately adjusting the radius of
the pupil or the beam. Finally, the stability conditions for effective
trapping and manipulation Rayleigh particles are analyzed.