Multidimensional Optical Fractionation of Colloidal Particles with Holographic Verification

The trajectories of colloidal particles driven through a periodic potential energy landscape can become kinetically locked-in to directions dictated by the landscape’s symmetries. When the landscape is realized with a structured light field, the path a given particle follows has been predicted to depend exquisitely sensitively on such properties as the particle’s size and refractive index. We confirm these predictions by measuring the transport of colloidal silica spheres through arrays of holographic optical traps, using holographic video microscopy to track individual spheres’ motions in three dimensions and simultaneously to measure each sphere’s radius and refractive index with part-per-thousand resolution. These measurements demonstrate optical fractionation’s ability to sort with part-per-thousand resolution on multiple characteristics simultaneously.

Figure 1

(a) Combined holographic optical trapping and holographic video microscopy system for tracking and characterizing colloidal spheres during optical fractionation. The objective lens focuses computer-generated holograms projected with a spatial light modulator (SLM) into the sample. It also collects holographic images of the sample that are recorded with a video camera. Trapping and imaging light are separated with a dichroic mirror. (b) Image of 103 holographic optical tweezers in the microscope’s focal plane. The traps are arranged in two domains of oblique lattice points with $a=3.27\mu \mathrm{m}$ and $b=2.025\mu \mathrm{m}$. One unit cell is highlighted. The domains are oppositely inclined so that ${\theta }_{[10]}=\pm 30°$, ${\theta }_{[01]}=\mp 38°$ and ${\theta }_{[11]}=\mp 13°$ with respect to the flow direction. Dashed boxes indicate input and output regions. Traces show trajectories for four representative particles measured at $1/30\mathrm{s}$ intervals. (c) Normalized holographic image of $1.5\mu \mathrm{m}$ diameter silica spheres in the same field of view. Inset: fit to the Lorenz-Mie theory of the outlined sphere’s holographic image.

Figure 2

High-resolution optical fractionation of monodisperse colloidal silica spheres demonstrated in the measured probability density $\rho (a_p,n_p)$ of particles with radius $a_p$ and refractive index $n_p$. The input sample, whose distribution is shown in (a), is separated into a smaller, low-index fraction in the side regions (b) and a larger, high-index fraction at the apex (c). The dashed curves show the marginally locked-in condition $n_c(a_p)$ for the array’s [10] direction. Plotted squares and circles indicate the properties of the four representative spheres whose trajectories are plotted in Fig. 1b.