The Hexadeca-Tweezer

The schematic diagram in Fig. 1

  

Figure 1: Schematic diagram of a practical diffractively-generated optical tweezer array.

shows one implementation of diffractively generated optical tweezer arrays. This design was used to create a $4 \times 4$ square array of tweezers-the hexadeca tweezer. The optical tweezer array is powered by a 100 mW diode-pumped frequency-doubled Nd:YAG laser operating at 532 nm. Two Keplerian telescopes arranged in series produce two planes conjugate to the back aperture of the microscope's objective lens (100 $\times$ , N.A. 1.40). The laser beam passes through eyepoints in both planes to create a conventional single optical tweezer. Introducing a diffractive $4 \times 4$ square array generator (Edmund Scientific No. P53191, angular divergence 25 mrad at $\lambda = 532$ nm) at the first eyepoint creates the pattern of rays desired for the hexadeca tweezer. A gimbal mounted mirror centered at the second eyepoint allows us to translate the entire tweezer array in the microscope's field of view and to dynamically stiffen the tweezers. A spatial filter placed in the inner focal plane of either telescope removes spurious rays created by imperfections in the low-cost diffractive optic. Conventional white-light illumination is used to form an image of the trapped particles. The image passes through a dichroic beam splitter and is captured with a video camera (NEC TI-324A) and recorded with a VCR (NEC PC-VCR) for later analysis.

For our demonstration, we used the hexadeca-tweezer to trap silica spheres ($a = 0.50 \pm 0.03 \mu$m, $\epsilon=2.3$, Duke Scientific, Palo Alto CA, Cat. No. 8100) suspended in deionized water ($\epsilon_{0}=1.7$) at room temperature. The suspension was sandwiched between a microscope slide and cover glass separated by 40 $\mu$m. The tweezer array was focused 8 $\mu$m above the lower glass wall and left in place to acquire particles.

  

Figure 2: $4 \times 4$ Optical tweezer array created from a single laser beam using a holographic array generator. (a) The tweezer array illuminates the $70\times 70$ $\mu$m² field of view with light backscattered from trapped silica particles. The scale bar represents 10$\mu$m. (b) The particle array 1/30 sec after being released. (c) The same field of view 3.1 sec later. (d) Trajectories of the particles in the field of view after being released. Dark traces indicate particles initially trapped in the array. Shorter tracks indicate particles which diffused out of the $\pm 200$ nm depth of focus.

Fig. 2(a) shows all sixteen of the primary optical traps filled with particles. Since the focal plane is several sphere diameters from the nearest wall, each sphere is trapped stably in three dimensions. Residence times in excess of 100 sec, suggest a trapping potential deeper than 6 k_BT per particle given the free spheres' self-diffusion coefficient of 0.4 $\mu$m²/sec. Comparable trapping efficiency would be expected for a single conventional optical tweezer operating at equivalent light intensity. Two additional spheres are trapped less strongly at spurious peaks in the diffraction pattern.

Fig. 2(b) shows the same field of view 1/30 sec after the laser was interrupted and before the spheres have had time to diffuse away. After 3.1 sec (Fig. 2(c)), the pattern has completely dispersed with some of the spheres wandering out of the imaging volume altogether. Fig. 2(d) shows two-dimensional projections of the particles' trajectories over this period [6]. Studying the dynamic relaxation of artificially structured colloidal crystals is just one application we foresee for manipulating soft matter with holographically patterned light.