Research ArticleOPTICS

Optical pulling at macroscopic distances

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Science Advances  29 Mar 2019:
Vol. 5, no. 3, eaau7814
DOI: 10.1126/sciadv.aau7814
  • Fig. 1 Illustration of the series of mechanisms applied, in turn, to achieve the OPF.

    The yellow particle is illuminated by a transversely isotropic Bessel beam, which propagates in the direction of the gray arrow, and its constituting k vectors lie on the cone formed by the revolution of the blue arrows about the partial axis. The green layer represents the ARC, and the semitransparent black cone is the pulling cone. In (A), the scattered fields are represented by the pink arrows. In (B) to (E), the scattered fields are represented by the cone formed by the revolution of the red arrows about the partial axis. (A) Scattering by a general particle. Light is scattered everywhere. (B) Introducing transverse isotropy to eliminate the diffraction in the azimuthal direction. (C) Introducing ARC to eliminate reflection. (D) Snell’s law approximately aligns the scattered field to the edge of the pulling cone. (E) The diffracted light is collimated by the interference. (F) Half-cone angles achieved in the literature.

  • Fig. 2 Pulling enhanced by transversely isotropic beam.

    The blue color indicates the phase space region where the OPF exists. The insets are schematic illustrations of a sphere (np = 1.6) in water (nb = 1.33) illuminated by a different beam. (A) m = 0 azimuthally polarized Bessel beam (transversely isotropic) (see Eq. 3). (B) m = 0 radially polarized Bessel beam (transversely isotropic) (see Eq. 4). (C) m = 0 linearly polarized Bessel beam (nontransversely isotropic) (see Eq. 5). (D) Propagation-invariant beam formed by a pair of plane waves (nontransversely isotropic) (see Eq. 6).

  • Fig. 3 Pulling enhanced by transversely isotropic particle.

    The OPF induced by an m = 0 azimuthally polarized Bessel beam (transversely isotropic) acting on a transversely isotropic circular cylinder (solid line) with diameter D and length L and nontransversely isotropic rectangular blocks (dashed line) with different aspect ratios (b1/b2) and length L. Inset: Schematic illustration of the geometries.

  • Fig. 4 OPF acting on a dielectric cylinder of diameter D and length L.

    Schematic illustration without ARC (A) and with ARC (D). (B and E) Phase space plots for the OPF acting on the dielectric cylinders without [see (A)] and with [see (D)] ARC, respectively, with D0) shown in (G). Blue and gray regions indicate pulling and pushing forces, respectively. (C) Optical forces acting on the cylinder shown in (A) versus the length of the cylinder L when θ0 = 2o. (F) Black: Optical forces acting on the cylinder shown in (D) versus the length of the cylinder L when θ0 = 2o. Red: The OPF acting on a metamaterial cylinder made of εr = npnb and μr = np/nb. (G) Diameter D0) of the cylinder at which the FWM is excited. (H) Range of the Bessel beam versus θ0. (I) Angular distribution of the scattered fields for pulling (blue) and pushing (others) forces, marked by arrows in (F) with corresponding colors.

  • Fig. 5 Pulling force induced by diffraction.

    The diffracted field emerging from a circular aperture of diameter D0 = 2o) = 14 μm illuminated by one (Eq. 10) or two (Eq. 11) plane waves. The constructive interference between the two plane waves (PWs) at −2° < θ < 2° collimates the beam such that |θ| < 2°, which induces the OPF. a.u., arbitrary units.

  • Fig. 6 Robustness of the OPF.

    The incident beam is the azimuthally polarized Bessel beam (Eq. 3). (A) Schematic illustration for a circular cylinder (yellow) coated with ARC (green) and irregular additional structures (purple) with a maximum thickness h (the relative heights of the additional structure are drawn to scale). The incident beam is the m = 0 azimuthally polarized Bessel beam with θ0 = 35o, and D is chosen such that FWM is excited. (B) Optical force for the structure shown in (A) at various h when n3 = 1.6. Here, n3 is the refractive index for the additional structures. (C) Optical force for the structure shown in (A) at various h when n3 = 2.0. (D) Optical force for three bare cylinders of different sizes versus θ0. (E) Optical force for two bare cylinders of different size versus light frequency (θ0 = 30o). (F) Optical force versus length for ARC-coated cylinders made of materials with different absorption levels (θ0 = 35o).

Supplementary Materials

  • Supplementary material for this article is available at http://advances.sciencemag.org/cgi/content/full/5/3/eaau7814/DC1

    Section S1. OPF acting on a spheroid

    Section S2. Small-angle approximation to the diameter associated with the FWM

    Section S3. Diffraction theory for slit and circular aperture to explain the negative recoil force induced by a pair of nearly forward propagating plane wave

    Section S4. Tolerance of the optical pulling on the misalignment of the particle due to Brownian motion

    Section S5. Tolerance of the optical pulling on the thickness and nonuniformity of the ARCs

    Fig. S1. OPF exerted on a spheroid by the m = 0 azimuthally polarized Bessel beam with θ0 = 30o.

    Fig. S2. Collimation of two nearly forward propagating plane waves through single-slit diffraction.

    Fig. S3. Collimation of two nearly forward propagating plane waves through diffraction through a circular aperture.

    Fig. S4. Robustness of OPF versus orientation.

    Fig. S5. Robustness of OPF versus thickness and nonuniformity of ARC.

  • Supplementary Materials

    This PDF file includes:

    • Section S1. OPF acting on a spheroid
    • Section S2. Small-angle approximation to the diameter associated with the FWM
    • Section S3. Diffraction theory for slit and circular aperture to explain the negative recoil force induced by a pair of nearly forward propagating plane wave
    • Section S4. Tolerance of the optical pulling on the misalignment of the particle due to Brownian motion
    • Section S5. Tolerance of the optical pulling on the thickness and nonuniformity of the ARCs
    • Fig. S1. OPF exerted on a spheroid by the m = 0 azimuthally polarized Bessel beam with θ0 = 30o.
    • Fig. S2. Collimation of two nearly forward propagating plane waves through single-slit diffraction.
    • Fig. S3. Collimation of two nearly forward propagating plane waves through diffraction through a circular aperture.
    • Fig. S4. Robustness of OPF versus orientation.
    • Fig. S5. Robustness of OPF versus thickness and nonuniformity of ARC.

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