Figure 1

(Color) Locked-in directions as a function of particle size for a sphere of fixed refractive index $n_p$ moving under a constant force ${\mathit{F}}_0\left(a_p,n_p\right)$ at angle $\theta$ through a square array of traps. Shaded regions indicate predictions of Eq. (11) for the conditions under which a sphere of radius $a_p$ becomes kinetically locked-in to particular lattice directions indicated by their Miller indices. Overlapping regions indicate opportunities for statistically locked-in transport, with higher-index directions becoming accessible as random sequences of lower-index jumps. Unshaded regions indicate conditions under which the particle freely follows the direction of the driving force. The horizontal dashed line indicates the different fates of particles with different sizes moving through a square lattice at fixed orientation $\text{tan}\theta =0.41$. The vertical dashed line indicates the lock-in transitions that a particle of radius $a_p=0.4b$ will experience as the driving direction is rotated from $\theta =0°$ to $\theta =45°$.Reuse & Permissions

Figure 2

(Color) (a) Schematic representation of the combined holographic optical trapping (HOT) and holographic video microscopy (HVM) instrument. The hologram encoding the optical tweezer array is imprinted onto a laser beam with a spatial light modulator (SLM) and relayed to the objected lens with a dichroic mirror. A second collimated laser beam illuminates the sample, and the resulting in-line holograms are collected by the same objective lens, magnified, and relayed to a video camera. (b) Image of an array of optical tweezers in the microscope’s focal plane obtained by replacing the sample with a front-surface mirror. The four superimposed traces are the measured trajectories of two particles (squares) that were locked in to the array’s [10] direction and another two (circles) that were locked in to [11]. Dashed boxes indicate the region from which particles flow into the array (input) and the two detection regions downstream of the array (apex and sides). (c) Typical holographic snapshot of the same field of view showing colloidal spheres interacting with the array of traps. Scale bar indicates $5\mu \text{m}$. Inset: fit of the indicated image to Lorenz-Mie predictions.Reuse & Permissions

Figure 3

(Color) Experimental tests of prismatic optical fractionation. (a) Bisdisperse silica sample: (left) input distribution, (center) fraction deflected to the sides along the [11] directions, (right) fraction deflected to the apex along the [10] directions. (b) Monodisperse silica sample. Symbols plotted in the center and right panels indicate the particles whose trajectories are plotted in Fig. 2b. (c) Monodisperse polystyrene sample. Dashed curves are predictions of Eq. (12) for kinetic lock-in along [10].Reuse & Permissions

Figure 4

(Color) Simulation of the experimental conditions in Fig. 3b. (a) Computed probability density of particles flowing from left to right through the array. (b) Distribution of refractive indexes and radii of the spheres in the input region, chosen to mimic the experimentally observed sample. (c) Output distribution in the side regions. (d) Output distribution in the apex region.Reuse & Permissions

Figure 5

(Color) Prismatic optical fractionation. (a) Computed probability density of particles colored by locked-in direction of trajectory through the optical trap array. The output was divided into four categories [10], [21], [31]: and undeflected. Individual traps appear as local probability maxima. (b) Map of particle properties $a_p$ and $n_p$ colored by mean transport direction through the array. Red [10], green [21], cyan [31], blue: undeflected.Reuse & Permissions