Particle manipulation beyond the diffraction limit using structured super-oscillating light beams

Abstract

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, that is, 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.

Keywords: beam shaping; optical tweezers; optical vortex; super-oscillating beams.

Figure 1

Super-oscillating (SO) beams generation. (a) A schematic of the optical setup; optical wave-fronts are modulated by the phase mask and focused through a microscopic objective lens to generate SO beams. (b–e) Three-dimensional (3D) volumetric profiles of the generated SO-structured beams—SO-Gaussian beam (SO-GB), SO-vortex beam with l=1, SO-Hermite–Gauss (SO-HG₁₀) beam, and SO-Airy beam, respectively. Beams were created with relatively large features to better image their structure. The threshold intensity levels for the contour plots in b–e are 0.43, 0.34, 0.36 and 0.31 of the maximum intensity, respectively.

Figure 2

Gallery of generated SO beams: Gaussian beam, vortex beam of charge l=1 and l=3, HG₁₀ beam and Airy beam. All the SO phase masks, their corresponding simulation and their experimental realizations are given in the first, second and third columns, respectively, while the experimental realizations of their counterpart normal beams are given in the last column. One-dimensional intensity plots of SO beams and their equivalent normal beams used to measure the FWHM are given in the fourth column in red and blue colors, respectively. Each beam profile is normalized to its own maximum.

Figure 3

Particle manipulation with structured SO beams. (a) Trapping of single polystyrene bead of size 500 nm in diameter with the SO-Gaussian beam (SO-GB). (b, c) corresponds to 2D probability distribution of position of a single trapped bead of the normal Gaussian beam (GB) and SO-Gaussian beam, respectively. (d–f) Multiple particle manipulations with the SO-vortex l=1, SO-HG₁₀ and SO-HG₁₁ beams, respectively. (g–i) A time series showing the anticlockwise rotation of beads trapped in a SO-vortex beam of charge l=1, due to the transfer of orbital angular momentum from the SO-vortex beam to the trapped beads.

Figure 4

Trapping results with the infrared laser. (a) Normalized experimental (dots) and simulation (lines) 1D beam profile of the SO (red) and normal (blue) beams for equal peak intensity. (b) Computed gradient force of SO (red) and normal (blue) beams, where the vertical lines show the maximal gradient force of the central lobes of both the beams. (c) Experimental 1D probability distribution of the single particle trapped in the central lobes of SO (red) and normal (blue) beams.