Three-dimensional arrays of submicron particles generated by a four-beam optical lattice

Using an optical lattice formed by four laser beams, we obtain three-dimensional light-induced crystals of 490-nm-diameter polystyrene spheres in solution. The setup yields face-centered orthorhombic optical crystals of a packing density of about 40$\%$. An alignment procedure is developed in which the crystals are first prepared near a sample wall, and then in the bulk of the sample. A series of tests is performed that demonstrate particle trapping in all three dimensions. For one case, the trapping force is measured, and good agreement with a simple theoretical model is found. Possible applications are discussed.

Figure 1

Sketch of experimental setup. OI $=$ optical isolator, $\frac{\lambda }{2}$ $=$ half-waveplate, PBS $=$ polarizing beam splitter, BD $=$ beam displacer, OBJ $=$ objective, Tz, Txy, Txyz $=$ translation stages, TL $=$ tube lens, F $=$ filter.

Figure 2

Schematic of the four-beam lattice geometry for $s$-polarized down-going and $p$-polarized up-going beams. Left: Overview showing the microscope objectives, lattice beams, and sample cell. Middle: Cross-sectional view of the lattice beams at the microscope back apertures. Right: Propagation and field vectors at the confocal point.

Figure 3

Top: 1D crystals at the beginning of the filling process (a) and near steady state (b). The arrow identifies the area where the lattice potential is deepest. The filling dynamics are explained in the text. (c)–(f): Behavior of a 2D crystal during sample translation. Arrows indicate the sample motion relative to the lattice. Particles trapped in the central lattice region are retained, while unbound or loosely bound particles are flushed out during the sample translation. (g)–(j): Behavior of a 2D lattice when scanning the relative phases of the lattice beams. The arrows indicate the direction of the phase-shift-induced motion of the lattice relative to the sample cell.

Figure 4

Demonstration of 3D optical crystals in the sample bulk volume. (a)–(c): Using lattice-beam phase shifts, the crystal is translated in the observation ($z$) direction. As a result, the trapped particles come repeatedly in and out of focus, but their relative positions do not change. (d)–(f): The particles are yanked out of the 3D lattice by jolting the sample. Comparing the numbers of particles visible in (d) and (f), the $z$-stacking depth of the crystal in (d) is estimated to be at least three. In (e), the particles appear out of focus because of their motion. (g)–(i): Behavior of a 3D crystal during sample translation in the $\mathit{xy}$ plane. The frame times are indicated. The trapped particles maintain their relative positions during the translation. The arrows identify two untrapped beads that move relative to those trapped. At 114 ms, one of them has become trapped in the lattice and one has moved away.

Figure 5

Percentage of escaping particles vs translation speed. At a critical escape speed $v_{\mathrm{x}}\approx 30\hspace{0.5em}\mu$m/s, the escape percentage jumps from 25% to 90%.