Fig. 1. Experimental setup for diffractive steering of optical tweezers at an inverted (“hanging”) air-liquid interface. A photograph of the object chamber is displayed at the upper left corner. The object chamber consists of a plastic disc of 1 cm height with a conical drill in its center. At the bottom the chamber has a circular opening with a diameter of about 200 microns. If the chamber is filled with a liquid, surface tension prevents leaking through the tiny hole. The air-liquid surface can manipulated by optical tweezers from below by an inverted microscope. For the laser tweezers a high resolution (1920×1200 pixels) reflective spatial light modulator (SLM) is illuminated by an expanded collimated laser beam. At the SLM various image windows displaying computer-designed off-axis holograms (two examples displayed in the figure)are displayed. Only laser light diffracted from these holograms into the desired first order is guided by a lens to the rear input aperture of a microscope objective, and creates a programmed light field distribution at the air-liquid interface.

Fig. 2. (Movie fig2.avi 2.1 MB) High-speed rotation of multiple particles in a doughnut mode of helical index 20 induces a flow of the whole surface, as seen by the rotation of particles in the surroundings of the “vortex pump”. The corresponding movie is displayed in real time.

Fig. 3. (Movie fig3.avi 2.4 MB) Generation of surface flow into interactively selectable directions. Four doughnut modes with the same helical index but selectable rotation orientations (indicated by yellow and orange semicircles in the figures) are projected onto the surface. The light modes are “filled” with trapped beads which rotate into the selected directions and create a corresponding surface flow (direction of flow also indicated in the pictures by arrows). By changing the rotational direction of one of the doughnut modes from sequence to sequence (indicated by orange arrows) the surface flow can be controlled. This is demonstrated by the transport of unbound beads in the corresponding movie, which indicate the flow of the liquid in the surface.

Fig. 4. (Movie fig4.avi 1.5 MB) Efficient mixing of fluid and particles trapped in a light field consisting of two concentric doughnut modes with different diameter and helicity, and two different signs of their respective helical indices. The particles trapped at the inner and outer light ring are rotating in opposite directions (indicated by yellow semi-circles in the figure), creating vortices of the liquid at the surface in the area between the two light rings. In the movie these vortices are demonstrated to mix a bunch of micro-beads in the area between the two circles.

Fig. 5. (Movie fig5.avi 1.2 MB) Two doughnut modes with different helicities and different diameters are excentrically arranged. The two helicities have the same sign, such that their induced rotations have the same orientations. The inner light ring is filled with beads, such that a surface flow is induced. The movie shows the hydrodynamic coupling between the vortex surface flow induced by the inner rotating ring of beads and the outer orbiting bead. The velocity of the single bead depends on its distance from the inner ring. The right inset is a plot of the tangential bead velocity as a function of its angular position. The closest distance between the two rings is obtained at the zero angle position. The plot shows that the maximal bead velocity is obtained before the bead actually reaches the zero angle position (note that the positive angle direction is measured counter-clockwise, whereas the beads rotate clockwise).

Fig. 6. (Movie fig6.avi 2.5 MB) Long range interaction of beads moving in a light field and a hydrodynamic flow field induced by a rotating vortex pump (center). Two beads are trapped in the light potential of an outer doughnut ring which induces a counter-clockwise rotation. However, an inner ring filled with beads induces a clockwise surface flow. At a certain position one of the two outer beads is stopped due to a balance between the counterclockwise acting optical scattering force and the clockwise acting surface flow. However, the bead is released from its equilibrium position as soon as the second bead approaches to a distance of several bead diameters. In the following, the two beads change their roles, i.e. the travelling bead becomes trapped, whereas the formerly trapped bead advances around the orbit. The whole movement repeats periodically, as can be seen in the attached movie.

Fig. 7. (Movie fig7.avi 1.3 MB) Clocked bead traffic. Beads are orbiting at two intersecting doughnut modes of different helicities and rotational directions (indicated by yellow semi-circles). The two intersection points (indicated by arrows) are stable traps for beads. The movie shows that the trapped beads are pushed away by other beads circling around the doughnut modes, which subsequently get trapped themselves.

Fig. 8. (Movie fig8.avi 1.9 MB) Size selective splitting of the pathes of micro beads. The movie shows two beads of different sizes (indicated by orange arrows) circling around a doughnut mode with a high helical index of 80 (indicated by the outer dashed yellow circle). As the beads approach an excentrically arranged inner light ring (doughnut mode with a helical index of 30) the larger bead is drawn into the inner circle, whereas the smaller bead proceeds on its orbit on the outer circle.