Juggling with Light

We discovered that when a pair of small particles is optically levitated, the particles execute a “dance” whose motion resembles the orbits of balls being juggled. This motion lies in a plane perpendicular to the polarization of the incident light. We ascribe the dance to a mechanism by which the dominant force on each particle cyclically alternates between radiation pressure and gravity as each particle takes turns eclipsing the other. We explain the plane of motion by considering the anisotropic scattering of polarized light at a curved interface.

Figure 1

(a) An image of a pair of optically levitated glycerol droplets and (b) their trajectories. The beam polarization vector is perpendicular to the page. Arrows indicate the instantaneous velocity at the snapshot of time corresponding to panel (a). The color bar indicates time in milliseconds.

Figure 2

The labels denote laser beam ($B$), aluminum chamber (C), LED light source (D), notch filter (F), half-wave plate ($H$), focusing lens ($L$), microscope (M), piezoelectric nozzle (N), aluminum sheet (S), and windows (W). The beam polarization is set to be in the $X$ direction.

Figure 3

Two particles juggling in a beam of light propagating with wave vector $\mathit{k}$ and polarization vector $\mathit{E}$. Black arrows denote gravity, while red or blue arrows denote the optical forces. The blue Gaussian curve at the bottom denotes the beam intensity profile. (a) Particle 1 is eclipsed by particle 2, it experiences less light and falls, while the unobstructed particle 2 receives more light than its weight and rises. (b) Particle 1 is no longer eclipsed by particle 2, the gradient force pushes it back towards the centerline. Particle 2 continues to move upward. In panels (c) and (d), the roles of particle 1 and 2 reverse.

Figure 4

Horizontal ($y$) and vertical ($z$) axes are distances measured from the beam waist at origin. The beam polarization vector is perpendicular to the page. Arrows indicate the instantaneous velocity of the particles. The color bar indicates time in milliseconds.

Figure 5

(a) Two representative equal-power, linearly polarized rays enter the sphere with different orientation of the polarization vector $\mathit{E}$. (b) Transmittances (solid lines) and reflectances (dashed lines) for $p$-polarized (purple lines) and $s$-polarized light (green lines) at an air-glycerol interface as a function of angle of incidence ${\theta }_i$. (c) Ray tracing calculation of the tangential forces ($F_T$), in units of the gravitational force $mg$, for a $28\mu \mathrm{m}$ glycerol droplet as a function of the droplet position $\mathit{r}$. The incident beam wave vector $\mathit{k}$ points out of the page. All forces point in the counterclockwise direction. They are strongest at a 45° polar angle (dashed line).