Particle manipulation beyond the diffraction limit using structured   super-oscillating light beams
  The diffraction limited resolution of light focused by a lens was derived in 1873 by Ernst Abbe. Later in 1952, a method to reach sub-diffraction light spots was proposed by modulating the wavefront of the focused beam. In a related development, super-oscillating functions, i.e. band limited functions that locally oscillate faster than their highest Fourier component, were introduced and experimentally applied for super-resolution microscopy. Up till now, only simple Gaussian-like sub-diffraction spots were used. Here we show that the amplitude and phase profile of these sub-diffraction spots can be arbitrarily controlled. In particular we utilize Hermite-Gauss, Laguerre-Gauss and Airy functions to structure super-oscillating beams with sub-diffraction lobes. These structured beams are then used for high resolution trapping and manipulation of nanometer-sized particles. The trapping potential provides unprecedented localization accuracy and stiffness, significantly exceeding those provided by standard diffraction limited beams. 
Brijesh Kumar Singh, Harel Nagar, Yael Roichman, and Ady Arie
physics.optics