Our paper on optical trapping using a beam with a wavefront shaped by a fractal-generated lens structure has been published as Jixiong Pu & P. H. Jones 'Devil's lens optical tweezers' Optics Express 23 8190-8199 (2015). This paper forms part of the joint Special Issue of Optics Express and JOSA B on Optical Cooling and Trapping organised by the OSA Technical Group.
From the abstract: We demonstrate an optical tweezers using a laser beam on which is
imprinted a focusing phase profile generated by a Devil’s staircase
fractal structure (Cantor set). We show that a beam shaped in this way
is capable of stably trapping a variety of micron- and submicron-sized
particles and calibrate the optical trap as a function of the control
parameters of the fractal structure, and explain the observed variation
as arising from radiation pressure exerted by unfocused parts of the
beam in the region of the optical trap. Experimental results are
complemented by calculation of the structure of the focus in the regime
of high numerical aperture.