Optical Acutators

Figure 5: Optical pump (a) and valve (b) constructed of colloidal particles in microfluidic channels activated with optical tweezers. The flow of water created by the colloidal peristaltic pump is visualized by the tracer particle indicated with an arrow. The colloidal valve flap is flipped with an optical tweezer and directs particles either downward (top) or downward (bottom). Adapted from Refs. (57) and (58).

Using conventional optical tweezers as actuators for micromachines is likely to speed the adoption of lab-on-a-chip and related technologies for medical diagnostics, environmental testing, and point-of-use microfabrication. Dynamic optical tweezers can both organize and drive devices such as the micrometer-scale hydraulic pump shown in Fig. 5(c). The microscopic valve flap in Fig. 5(b) is an example of a photopolymerized colloidal heterostructure both assembled and actuated with optical tweezers (58).

Modifying the optical tweezers' wavefronts transforms them into whole new categories of optical traps, some of which already have found applications as actuators for unconventional micromachines. Some of the most useful of these are based on exotic modes of light whose properties only recently have been elucidated.

Figure 6: (a) The helical phase profile $\varphi(\ensuremath{\vec \rho}\xspace ) = \ell \theta$ converts a TEM₀₀ laser beam into a helical mode whose wavefronts resemble an $\ell$-fold corkscrew. (b) Rather than focusing to a point, a helical mode focuses to an optical vortex whose radius R_$\ell$ is proportional to its pitch, $\ell$. (c) A single colloidal particle trapped on the optical vortex travels around its circumference, driven by the helical beam's orbital angular momentum. This multiple exposure shows 11 stages in one 0.8 nm particle's transit in 1/6 sec intervals. Adapted from Ref. (59).

Figure 6(a) demonstrates how the deceptively simple phase profile $\varphi(\ensuremath{\vec \rho}\xspace ) = \ell \theta$ transforms the parallel wavefronts of a TEM₀₀ laser mode into the corkscrew topology of a helical mode (60). Here, $\theta$ is the azimuthal angle around the optical axis and $\ell$ is an integer winding number also known as the topological charge. The modified beam no longer focuses to a point because the helical topology fosters destructive interference along the optical axis. Instead, it converges to a ring of light, as shown in Fig. 6(b). The dark focus is suitable for trapping reflecting (61), absorbing (62), or low-dielectric-constant (63,64) objects that would be damaged or repelled by conventional optical tweezers. Because such traps lack the radiation pressure due to axial rays, they also can make more efficient traps for large dielectric objects than conventional optical tweezers (66,67,65). Smaller dielectric particles are drawn to the ring's circumference, as shown in Fig. 6(c).

What really distinguishes these ring-like optical traps is their ability to exert torques as well as forces (61,68,62). Just a decade ago, Allen demonstrated that each photon in a helical mode carries an orbital angular momentum $\ell$$\hbar$ in addition to its intrinsic spin angular momentum (60). This orbital angular momentum takes the form of a tangential component to the beam's linear momentum density that can be transferred to illuminated objects (59,70,69). A single colloidal microsphere is shown circulating around such a topological ring-trap under the influence of the optical angular momentum flux in the time-lapse photograph of Fig. 6(c). Such toroidal torque-exerting traps have come to be known as optical vortices (71) or optical spanners (72) and they have potentially widespread technological applications. Studying objects' motions in optical vortices also has provided valuable insights into the interplay of photon spin and orbital angular momentum (61,59,70,68,73,69) which have been useful in elucidating the quantum mechanical nature of helical beams.

An optical vortex's radius, R_$\ell$, increases with topological charge (59,74), so that the intensity pattern can be tailored to different applications. For example, a properly scaled ring of light can be projected onto the teeth of a microfabricated gear thereby creating a reliable micrometer-scale motor. The distributed drive made possible by projecting multiple optical vortices also should help to alleviate problems associated with friction in micromechanical systems. The spin angular momentum carried by circularly polarized optical tweezers similarly has been used to apply torques to birefringent components (76,75,77). Using an SLM to control the polarization of multiple optical tweezers then opens up still more possibilities for extensive micromachines assembled and driven with light.

Figure 7: Generalizations of the optical vortex principle. (a) An array of $\ell$ = 30 optical vortices created from a superposition of helical beams, from Ref. (1). (b) An optical rotator created by interfering an $\ell$ = 3 optical vortex with a plane wave. From Ref. (78). (c) An optical rotator created with a 5-fold modulation of the helicity of an $\ell$ = 60 optical vortex. From Ref. (59).

Some micromechanical applications may require no microfabrication at all. Rapidly circulating particles entrain flows that can mix and pump extremely small volumes of fluid. This solves a problem in microfluidic systems whose laminar flows are ideal for transporting minuscule quantities of reagents, but do not promoting mixing when needed. Furthermore, the holographic optical tweezer technique can project multiple optical vortices, such as the 3×3 array in Fig. 7(a), each with an individually specified intensity and topological charge (1). Cooperative flows in such arrays can be reconfigured dynamically by modifying the trap-forming hologram, opening up the possibility of adaptive microfluidics on length scales ranging all the way do to tens of nanometers.

Other variations on this theme yield a family of distinct optical micromanipulators, each with its own applications. For example, superposing a helical beam with a conventional beam not only visualizes the helical wavefronts' structure, as in Fig. 7(b), but also creates an oriented intensity pattern useful for orienting asymmetric objects (78). Superposing instead a helical mode with its mirror-image counterpart creates three-dimensional arrays of discrete traps that can be rotated arbitrarily in three dimensions by varying the beams' relative phase (79). Modulating the helical pitch of an optical vortex results in another class of optical rotators (80), an example of which appears in Fig. 7(c). Further generalizations create intensity patterns related to the caustics seen at the bottom of swimming pools and can move objects along complex trajectories transverse to the optical axis, all with static holograms and no moving parts. Still other superpositions focus to micrometer-scale dark regions surrounded by light on all sides known as optical bottles (81). These are useful for trapping very small dark-seeking objects, including clouds of ultracold atoms (81). Holographic arrays of optical bottles therefore should be useful for manipulating atoms (82), perhaps for quantum computing applications, and will help to extend pioneering efforts to apply optical tweezers in atomic physics (84,83).

Whereas azimuthal phase modulations extend optical tweezers into optical micromanipulators transverse to the optical axis, radial modulations create axial devices, again with an intriguing twist. The simplest nontrivial radial phase profile modification, $\varphi(\ensuremath{\vec \rho}\xspace ) = \gamma \rho$, transforms a TEM₀₀ beam into an approximation to a Bessel mode, a beam that propagates without diffracting even when focused to a wavelength-scale cross-section. The associated optical trap can extend for millimeters along the optical axis, as demonstrated in Fig. 8, and can push particles precisely over very large distances (85). The extended range of Bessel-beam arrays should increase the throughput of optical fractionation by orders of magnitude. Still more remarkably, Bessel beams are impervious to distortions by intervening particles and surfaces (86), reconstructing their wavefronts as they propagate away from disturbances. Combining Bessel beams' robustness against diffraction with helical modes' orbital angular momentum yields optical devices that can reach deeply into complex systems to apply both forces and torques where needed.

Figure 8: The radial phase profile $\varphi(\ensuremath{\vec \rho}\xspace ) = \gamma \rho$ creates a diffractionless Bessel beam that focuses to a long axial trap. Here, the same beam is shown trapping multiple colloidal particles in two separate sample chambers separated by 3 mm. Distortions due to a particle trapped in plane (a) heal themselves in planes (b) and (c). The process is repeated for the same beam in planes (d), (e) and (f). From Ref. (86).