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Long-distance optical pulling of nanoparticle in a low index cavity using a single plane wave

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Science Advances  20 May 2020:
Vol. 6, no. 21, eaaz3646
DOI: 10.1126/sciadv.aaz3646
  • Fig. 1 Schematic of the optical configuration of an NP-in-cavity structure facing a linearly polarized plane wave.

    kz is the wave vector, Ex is the electric field, and Fz depicts the optical force on the NP. The NP and the cavity are co-centered at the origin (O) of the coordinate.

  • Fig. 2 The coefficient terms and the forces on an NP (nnp = 1.5) as a function of incident light wavelength (λ) when the refractive index of the cavity (nc = 1) is lower than the medium (nm = 1.25).

    (A, B, and E) Electric dipole-quadrupole interaction components. (C, D, and F) Electric dipole-magnetic dipole interaction components. For all cases, |Ex| =1, rc = 150 nm, and rnp = 50 nm. In (E) and (F), the blue-shaded regions indicate that the forces are negative, and the red-shaded regions are for positive forces. Here, ed, md, and eq are the complex amplitudes of electric dipole, magnetic dipole, and electric quadrupole modes of the incoming light to the NP, respectively; See (or Sem) is the scattering coefficient consisting of electric dipole and electric quadrupole (or electric dipole and magnetic dipole) of the Lorenz-Mie scattering coefficient of the NP.

  • Fig. 3 Negative optical force on the NP inside an air cavity in the medium of liquid water.

    The calculated Fz on (A) Si NP, (D) Au NP, and (G) SiO2 NP as a function of λ. For all cases, rnp = 50 nm and rc = 150 nm. The NP and the cavity are co-centered. The insets illustrate the structure configurations. The coefficient terms as a function of λ for (B and C) Si NP, (E and F) Au NP, and (H and I) SiO2 NP; here, the blue-shaded regions indicate that the forces are negative. (J to L) The calculated Fz from FEM as a function of cz, where cz is the z coordinate of the center of the NP, for (J) Si NP, (K) Au NP, and (L) SiO2 NP. The structure configurations are illustrated on top of the contours. For all cases, |Ex| =1.

  • Fig. 4 Long-distance optical pulling of Au NP.

    (A) Calculated optical forces on the CS Au NP and the nanobubble as a function of the NP position in the nanobubble. The radius of nanobubble (rb) = 150 nm. The intensity of the incident light is set to 12 mW μm−2. Inset: The calculated temperature profile of NP at cz = −90 nm. (B) Calculated optical forces as a function of rb when the NP contacts the interface of the light-incoming side of the nanobubble. See the illustrated optical configuration on top of the graph. The two solid lines in each color correspond to the forces at the light intensity of 7.2 mW μm−2 (for the lower magnitude) and 12 mW μm−2 (for the higher magnitude). (C) The schematic of the experimental setup for observing the optical pulling motion of NPs. A 20× objective lens loosely focuses a femtosecond pulsed laser of λ = 800 nm into the suspension. The focused Gaussian beam has a beam waist of 6 μm. The fluence is 15 mJ cm−2 at the focal plane and 9 mJ cm−2 at a distance of 120 μm away from the focal plane, which correspond to the light intensities used in (A) and (B). A high-speed camera is used to record the location of the scattered light from each NPs in the water. (D) Tracked positions of representative NPs: (red) optical pulling motion, (blue) optical pushing motion, and (black) Brownian motion. Here, the symbols in each color correspond to the positions of an NP at each time frame. The NP motions are recorded at 5000 frames s−1 (or frames per second).

  • Table 1 Optical conditions of the incident light to achieve different signs of Fee and Fem.

    The shaded boxes highlight the optical conditions for the OPFs. Here, ed, md, and eq are the complex amplitudes of the electric dipole, magnetic dipole, and electric quadrupole modes of the incoming light to the NP, respectively; See (or Sem) is the scattering coefficient consisting of electric dipole and electric quadrupole (or electric dipole and magnetic dipole) of the Lorenz-Mie scattering coefficient of the NP.

    Electric dipole-electric quadrupole interactions
    Scattering coefficients of NPOptical force
    Re(See) < 0Im(See) > 0
    Amplitudes of multipole terms of incoming light to NP
    ed: electric dipole, eq: electric quadrupole
    Fee < 0
    Im(edeq*) > 0Re(edeq*) < 0
    Im(edeq*) < 0Re(edeq*) < 0
    whenRe(See)Im(edeq*)<Im(See)Re(edeq*)|
    Im(edeq*) > 0Re(edeq*) > 0
    whenRe(See)Im(edeq*)>Im(See)Re(edeq*)|
    Im(edeq*) < 0Re(edeq*) > 0Fee > 0
    Electric dipole-magnetic dipole interactions
    Scattering coefficients of NPOptical force
    Re(Sem) > 0Im(Sem) > 0
    Amplitudes of multipole terms of incoming light to NP
    ed: electric dipole, md: magnetic dipole
    Fem < 0
    Im(edmd*) < 0Re(edmd*) < 0
    Im(edmd*) > 0Re(edmd*) < 0
    whenRe(Sem)Im(edmd*)<Im(Sem)Re(edmd*)|
    Im(edmd*) < 0Re(edmd*) > 0
    whenRe(Sem)Im(edmd*)>Im(Sem)Re(edmd*)|
    Im(edmd*) > 0Re(edmd*) > 0Fem > 0

Supplementary Materials

  • Supplementary Materials

    Long-distance optical pulling of nanoparticle in a low index cavity using a single plane wave

    E. Lee and T. Luo

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