Light Streak Tracking of Optically Trapped Thin Microdisks

Nonspherical particles can uniquely probe soft system dynamics. We show that laser tweezers stably trap thin coinlike microdisks in 3D with an edge-on orientation. Scattered light forms a streak that we track using a fast camera to measure the disk’s angular displacement. Linearly polarized tweezers rotationally trap a birefringent disk, and we measure its harmonically bound Brownian rotation over 5 decades in time. Near a surface, the disk exhibits a translational-orientational switchback oscillation. Circularly polarized tweezers rotate the disk and streak, yielding a colloidal lighthouse.

Figure 1

(a) Optical micrographs of a wax microdisk suspended in water as it undergoes rotational diffusion. (b) Tweezing a microdisk. The propagation direction, $\widehat{k}$, of the laser beam is in the $z$ direction. The tweezed disk aligns edge-on with its symmetry axis, $\widehat{n}$, perpendicular to $\widehat{k}$. The angular displacement, ${\theta }_{\alpha }$, fluctuates due to Brownian thermal forces.

Figure 2

(a) The time-dependent angular displacement, ${\theta }_{\alpha }(t)$, of a wax microdisk (radius $1.2\mu \mathrm{m}$) in a rotational trap created by a LP laser tweezer at a power of $P=6.3\mathrm{m}\mathrm{W}$, measured by imaging the streak of red laser light collected by the objective lens using the high-speed camera at $5000\mathrm{\text{frames}}/\mathrm{s}$ over a duration of 10 s. Inset: Micrographs of a wax disk in a rotational harmonic trap separated by $1/6\mathrm{s}$. The backscattered light forms a streak in the plane normal to the viewing direction. (b) The time-averaged mean square angular displacement $⟨\Delta {\theta }_{\alpha }^2(t)⟩$ (points) determined from (a). The solid line is a fit using Eq. (2). Inset: $⟨\Delta {\theta }_{\alpha }^2(t)⟩$ measured using light streak tracking (LST) of the red channel of the color CCD at 30 Hz for a series of different He-Ne laser powers, $P$.

Figure 3

(a) Colloidal lighthouse created by rotation of the red light streak from a trapped wax microdisk (radius $1.5\mu \mathrm{m}$) using a CP laser tweezer ($P=10\mathrm{m}\mathrm{W}$). The counterclockwise rotation of the streak is shown in successive micrographs (1–6) separated by $1/6\mathrm{s}$. (b) The rotational frequency, $f$, as a function of laser power, $P$ (solid circles) increases linearly, as shown by the fit (solid line).

Figure 4

(a) Successive micrographs (1–6) separated by $1/6\mathrm{s}$ show the coupled translational-orientational switchback oscillation of the disk (radius $1.5\mu \mathrm{m}$) in an LP laser tweezer ($P=8\mathrm{m}\mathrm{W}$) when the focal plane is $1\mu \mathrm{m}$ away from the slide. (b) Switchback oscillation frequency, $f_s$, as a function of laser power, $P$, for several different separations between the focal plane and glass slide: $1.4\mu \mathrm{m}$ (circles), $0.4\mu \mathrm{m}$ (squares), and $-0.6\mu \mathrm{m}$—slightly inside the slide wall—(diamonds). The frequency increases linearly with laser power, $f_s\sim P$ (solid line fits).