Optically Induced Sieve Effect for Nanoparticles near a Nanofiber Taper

We demonstrate size-selective optical trapping and transport for nanoparticles near an optical nanofiber taper. Using a two-wavelength counterpropagating mode configuration, we show that 100-nm-diameter and 150-nm-diameter gold nanospheres (GNSs) are trapped by the evanescent field in the taper region at different optical powers. Conversely, when one nanoparticle species is trapped the other may be transported, leading to a sievelike effect. Our results show that sophisticated optical manipulation can be achieved in a passive configuration by taking advantage of mode behavior in nanophotonic devices.

Figure 1

The concept and physical principles. A conceptual diagram showing the trapping and transport of 100- and 150-nm-diameter gold nanospheres along a 500-nm-diameter optical nanofiber. The green and red arrows depict the optical force due to the 640-nm ${\mathrm{HE}}_{11}$ mode and the 785-nm ${\mathrm{HE}}_{11}$ mode, respectively. Inset (a) shows FDTD-simulated force along the fiber axis for 640-nm light and 785-nm light as indicated in the legend, with the inset showing their ratio. Inset (b) shows how the light intensity at the fiber surface depends on the fiber diameter.

Figure 2

Numerical predictions. (a),(b) The dependence of the optical forces along the nanofiber axis with $P_2=12$ mW (as in the experiments) and given force-balance conditions for a 100-nm-diameter GNS and a 150-nm-diameter GNS, respectively. In all cases, the blue curve shows the nanofiber taper diameter profile (left-hand vertical axis) and the black and magenta curves show the optical forces on 100- and 150-nm-diameter GNSs, respectively (right-hand vertical axis). (c) Variation of the force difference (i.e., total force) on a 100-nm GNS for $P_1=1.7$ mW (force-balance condition, solid line), $P_1=2.0$ mW (dashed line), and $P_1=2.25$ mW (dash-dotted line). As before, the blue curve shows the nanofiber taper diameter profile (left-hand vertical axis). The blue circles show points where stable trapping is possible, whereas red circles show points where antitrapping (i.e., a local potential maximum) exists. (d) The calculated potential energy of a 100-nm GNS as a function of $z$ associated with $P_1=1.7$ mW (no trap, solid line), $P_1=2.0$ mW (dashed line), and $P_1=2.25$ mW (dash-dotted line). For $z>0$, we see that trapping potential minima occur, whereas for $z<0$, antitrapping potential maxima occur. Note that the potential minimum has been assigned to zero energy in each case to allow simple comparison of the trap depths. The inset shows a calculation using the approximate theoretical expressions Eq. (1) for a power of $P_1=2.5$ mW.

Figure 3

The experiment. (a) The experimental setup. An optical nanofiber is immersed in a droplet containing colloidal gold nanoparticles. Counterpropagating 640- and 785-nm-wavelength guided modes are introduced into the fiber from diode laser sources, with a short-pass filter (SPF) and long-pass filter (LPF) employed to keep counterpropagating light from entering the laser diodes. Each field passes through a half-wave plate (HWP) and a polarizing beam splitter (PBS) before entering the fiber. Light scattered from particles trapped by the nanofiber guided modes is collected by an objective lens, attenuated by a neutral density filter (NDF) and detected by a CMOS camera. The inset shows the scanning-electron-microscope-measured nanofiber diameter. (b) Example frames from a particle transported along the nanofiber. The frame number is indicated at the bottom of each frame. (c) The 1D data extracted from the frames in (b) by taking only the pictures that lie along the fiber line. The red dots indicate peaks, which are detected and used to create a reduced data set (see text for details).

Figure 4

Experimental data: the transport of 150-nm-diameter GNSs. (a) Combined 1D cross sections for each captured frame in the data set for parameters $P_1=0$ mW, $P_2=12$ mW, and 150-nm GNSs only. (b) Detected peaks (red points) in the 1D cross-section data along with five lines detected by a Hough analysis of the data (dashed black lines). The inset depicts the polar representation of a line (shown in red) used by the Hough analysis and the detected angle $\theta$ is shown beside each detected line. (c) GNS trajectories detected in the data using the correlation technique explained in the text. The associated mean velocity is shown beside each trajectory.

Figure 5

Experimental data: size-selective trapping. (a) The upper row shows the power dependence of transport in the case where only 150-nm-diameter GNSs are present in solution, with $P_1$ as indicated and $P_2$ fixed at 12 mW. The onset of trapping is observed at $P_1=8$ mW. The lower row shows the power dependence of transport for a mixture of 100-nm-diameter and 150-nm-diameter GNSs. The onset of trapping is now observed at $P_1=3$ mW, corresponding to trapping conditions for the 100-nm-diameter GNSs. In each case, a black dotted line shows the dominant line of the Hough spectrum, while dashed horizontal lines indicate the nominal position of the nanofiber center. The black arrow in the lower row of the 8-mW data indicates a particle stuck to the fiber surface. This is ignored for the purposes of the Hough analysis. For movie file data for similar parameters, see the Supplemental Material [37]. (b) The power dependence of the mean velocity for trajectories detected in each data set shown in the upper row of (a). The error bars show plus or minus one standard deviation. (c) The angle $\mathrm{\Theta }$ of the top-ranked line detected by Hough analysis for each data set shown in the upper row of (a) (blue points) and the bottom row of (a) (red points). (d) The same as (c), but for a data set where there is no control over the polarization of the fields entering the nanofiber.