Dynamic optical manipulation of colloidal systems using a spatial light modulator

Abstract

A method and mathematical foundation are presented for generating multiple-beam optical tweezers capable of introducing complex trapping beam configurations that enable optical manipulation for a variety of colloidal structures. The method is based on the generalized phase contrast technique for generating high intensity beam patterns from an input phase modulation encoded on a spatial light modulator. The mathematical foundation describes issues concerning how the method provides high photon efficiency adequate for generating large array traps while maintaining dynamic features. Experimental results show multiple trapping of up to 25 particles using a 200 mW laser diode operating at 830 nm. Arbitrary array beam configurations are also shown where the shape, position and size can easily be reconfigured and applied for dynamic manipulation of colloidal particles.     

Synthesis of Colloidal SU‐8 Polymer Rods Using Sonication

The bulk synthesis of fluorescent colloidal SU‐8 polymer rods with tunable dimensions is described. The colloidal SU‐8 rods are prepared by shearing an emulsion of SU‐8 polymer droplets and then exposing the resulting non‐Brownian rods to ultrasonic waves, which breaks them into colloidal rods with typical lengths of 3.5–10 µm and diameters of 0.4–1 µm. The rods are stable in both aqueous and apolar solvents, and by varying the composition of apolar solvent mixtures both the difference in refractive index and mass density between particles and solvent can be independently controlled. Consequently, these colloidal SU‐8 rods can be used in both 3D confocal microscopy and optical trapping experiments while carefully tuning the effect of gravity. This is demonstrated by using confocal microscopy to image the liquid crystalline phases and the isotropic–nematic interface formed by the colloidal SU‐8 rods and by optically trapping single rods in water. Finally, the simultaneous confocal imaging and optical manipulation of multiple SU‐8 rods in the isotropic phase is shown.     

Calibration of sound forces in acoustic traps

A two-dimensional or transverse acoustic trapping and its capability to noninvasively manipulate micrometersized particles with focused sound beams were experimentally demonstrated in our previous work. To apply this technique, as in optical tweezers, for studying mechanical properties of and interactions among biological particles such as cells, the trapping forces must be calibrated against known forces, i.e., viscous drag forces exerted by fluid flows. The trapping forces and the trap stiffness were measured under various conditions and the results were reported in this paper. In the current experimental arrangement, because the trapped particles were positioned against an acoustically transparent mylar membrane, the ultrasound beam intensity distribution near the membrane must be carefully considered. The total intensity field (the sum of incident and scattering intensity fields) around the droplet was thus computed by finite element analysis (FEA) with the membrane included, and it was then used in the ray acoustics model to calculate the trapping forces. The membrane effect on trapping forces was discussed by comparing effective beam widths with and without the membrane. The FEA results found that the broader beam width, caused by the scattered beams from the neighboring membrane and the droplet, resulted in the lower intensity, or smaller force, on the droplet. The experimental results showed that the measured forces were as high as 64 nN. The trap stiffness, approximated as a linear spring, was estimated by linear regressions and found to be 1.3 to 4.4 nN/μm, which was on a larger scale than that of optical trapping estimated for red blood cells, a few tenths of piconewtons/nanometer. The experimental and theoretical results were in good agreement.     

High trapping forces for high-refractive index particles trapped in dynamic arrays of counterpropagating optical tweezers

We demonstrate the simultaneous trapping of multiple high-refractive index (n > 2) particles in a dynamic array of counterpropagating optical tweezers in which the destabilizing scattering forces are canceled. These particles cannot be trapped in single-beam optical tweezers. The combined use of two opposing high-numerical aperture objectives and micrometer-sized high-index titania particles yields an at least threefold increase in both axial and radial trap stiffness compared to silica particles under the same conditions. The stiffness in the radial direction is obtained from measured power spectra; calculations are given for both the radial and the axial force components, taking spherical aberrations into account. A pair of acousto-optic deflectors allows for fast, computer-controlled manipulation of the individual trapping positions in a plane, while the method used to create the patterns ensures the possibility of arbitrarily chosen configurations. The manipulation of high-index particles finds its application in, e.g., creating defects in colloidal photonic crystals and in exerting high forces with low laser power in, for example, biophysical experiments.     

Optical trapping with focused Airy beams

Airy beams are attractive owing to their two intriguing properties--self-bending and nondiffraction--that are particularly helpful for optical manipulation of particles. We perform theoretical and experimental investigations into the focusing property of Airy beams and provide insight into the trapping ability of tightly focused Airy beams. Experiment on optical tweezers demonstrates that the focused Airy beams can create multiple traps for two-dimensional confining particles, and the stable traps exist in the vicinity of the main intensity lobes in the focused beams. The trapping pattern can be varied with changes in the cross section of the focused beam. The focused Airy beam offers a novel way of optically manipulating microparticles.     

Spatial light modulator-controlled alignment and spinning of birefringent particles optically trapped in an array

We demonstrate the use of a phase-only liquid-crystal spatial light modulator (SLM) for polarization-controlled rotation and alignment of an array of optically trapped birefringent particles. A collimated beam incident upon a two-dimensional lenslet array yields multiple foci, scaled to produce optical gradient traps with efficient three-dimensional trapping potentials. The state of polarization of each trapping beam is encoded by the SLM, which acts as a matrix of wave plates with computer-controlled phase retardations. Control of the rotation frequency and alignment direction of the particles is achieved by the transfer of tunable photon spin angular momentum.     

Dynamic motion analysis of optically trapped nonspherical particles with off-axis position and arbitrary orientation

We present a general computational method of determining radiation pressure forces and torques exerted on small particles by a converging beam of light. This method, based on a ray optics model of optical trapping, allows time-series dynamic motion analysis to be performed on nonspherical objects that are initially positioned off the optical axis with arbitrary orientation. Comparison tests of computer simulation with experimental results prove that the proposed model can be used to predict complicated trapping behavior of microfabricated objects.     

Microfluidic sorting with a moving array of optical traps

Optical sorting was demonstrated by selective trapping of a set of microspheres (having specific size or composition) from a flowing mixture and guiding these in the desired direction by a moving array of optical traps. The approach exploits the fact that whereas the fluid drag force varies linearly with particle size, the optical gradient force has a more complex dependence on the particle size and also on its optical properties. Therefore, the ratio of these two forces is unique for different types of flowing particles. Selective trapping of a particular type of particles can thus be achieved by ensuring that the ratio between fluid drag and optical gradient force on these is below unity whereas for others it exceeds unity. Thereafter, the trapped particles can be sorted using a motion of the trapping sites towards the output. Because in this method the trapping force seen by the selected fraction of particles can be suitably higher than the fluid drag force, the particles can be captured and sorted from a fast fluid flow (about 150 μm/s). Therefore, even when using a dilute particle suspension, where the colloidal trafficking issues are naturally minimized, due to high flow rate a good throughput (about 30 particles/s) can be obtained. Experiments were performed to demonstrate sorting between silica spheres of different sizes (2, 3, and 5 μm) and between 3 μm size silica and polystyrene spheres.     

Confocal Raman microscopy for monitoring chemical reactions on single optically trapped,solid-phase support particles

Optical trapping of small structures is a powerful tool for the manipulation and investigation of colloidal and particulate materials. The tight focus excitation requirements of optical trapping are well suited to confocal Raman microscopy. In this work, an inverted confocal Raman microscope is developed for studies of chemical reactions on single, optically trapped particles and applied to reactions used in solid-phase peptide synthesis. Optical trapping and levitation allow a particle to be moved away from the coverslip and into solution, avoiding fluorescence interference from the coverslip. More importantly, diffusion of reagents into the particle is not inhibited by a surface, so that reaction conditions mimic those of particles dispersed in solution. Optical trapping and levitation also maintain optical alignment, since the particle is centered laterally along the optical axis and within the focal plane of the objective, where both optical forces and light collection are maximized. Hour-long observations of chemical reactions on individual, trapped silica particles are reported. Using two-dimensional least-squares analysis methods, the Raman spectra collected during the course of a reaction can be resolved into component contributions. The resolved spectra of the time-varying species can be observed, as they bind to or cleave from the particle surface.     

Three-dimensional laser trapping on the base of binary radial diffractive optical element

A radially symmetric binary diffractive optical element to generate an optical bottle beam is designed, fabricated, and characterized. Analysis of the numerical simulation and experimental research results shows that the fabricated element is well suited for solving three-dimensional (3D) laser trapping problems.     

Microlens-array-enabled on-chip optical trapping and sorting

An on-chip optical trapping and sorting system composed of a microchamber and a microlens array (MLA) is demonstrated. The MLA focuses the incident light into multiple confocal spots to trap the particles within the microchamber. The SiO(2)/ZrO(2) solgel material is introduced in the fabrication of MLA for its unique optical and chemical characters. Moreover, in order to prove the effectiveness of the system, experimental demonstration of multibeam trapping and locked-in transport of micropolymer particles in the microchamber is implemented. The system may easily be integrated as microfluidic devices, offering a simple and efficient solution for optical trapping and sorting of biological particles in lab-on-a-chip technologies.     

Adaptive beam shaping by controlled thermal lensing in optical elements

We describe an adaptive optical system for use as a tunable focusing element. The system provides adaptive beam shaping via controlled thermal lensing in the optical elements. The system is agile, remotely controllable, touch free, and vacuum compatible; it offers a wide dynamic range, aberration-free focal length tuning, and can provide both positive and negative lensing effects. Focusing is obtained through dynamic heating of an optical element by an external pump beam. The system is especially suitable for use in interferometric gravitational wave interferometers employing high laser power, allowing for in situ control of the laser modal properties and compensation for thermal lensing of the primary laser. Using CO(2) laser heating of fused-silica substrates, we demonstrate a focal length variable from infinity to 4.0 m, with a slope of 0.082 diopter/W of absorbed heat. For on-axis operation, no higher-order modes are introduced by the adaptive optical element. Theoretical modeling of the induced optical path change and predicted thermal lens agrees well with measurement.     

Structured light spots projected by a Dammann grating with high power efficiency and uniformity for optical sorting

We report a method for microfluidic multiple trapping and continuous sorting of microparticles using an optical potential landscape projected by a Dammann grating, enabling a high power-efficient approach to forming a composite two-dimensional spots array with high uniformity. The Dammann grating is fabricated in a photoresist by optical lithography. It is employed to create an optical lattice for multiple optical trapping and sorting in a mixture of polymer particles (n = 1.59) and silica particles (n = 1.42) with the same diameters of 3.1 μm. In addition to the exponential selectivity by the projected optical landscapes, the proposed microfluidic sorting system has advantages in terms of high power efficiency and high uniformity due to the Dammann grating.     

Controlled assembly of jammed colloidal shells on fluid droplets

Assembly of colloidal particles on fluid interfaces is a promising technique for synthesizing two-dimensional microcrystalline materials useful in fields as diverse as biomedicine, materials science, mineral flotation and food processing. Current approaches rely on bulk emulsification methods, require further chemical and thermal treatments, and are restrictive with respect to the materials used. The development of methods that exploit the great potential of interfacial assembly for producing tailored materials have been hampered by the lack of understanding of the assembly process. Here we report a microfluidic method that allows direct visualization and understanding of the dynamics of colloidal crystal growth on curved interfaces. The crystals are periodically ejected to form stable jammed shells, which we refer to as colloidal armour. We propose that the energetic barriers to interfacial crystal growth and organization can be overcome by targeted delivery of colloidal particles through hydrodynamic flows. Our method allows an unprecedented degree of control over armour composition, size and stability.     

Liquid crystal-on-silicon implementation of the partial pixel three-dimensional display architecture

We report the implementation of a liquid crystal-on-silicon, three-dimensional (3-D) diffractive display based on the partial pixel architecture. The display generates multiple stereoscopic images that are perceived as a static 3-D scene with one-dimensional motion parallax in a manner that is functionally equivalent to a holographic stereogram. The images are created with diffraction gratings formed in a thin liquid crystal layer by fringing electric fields from transparent indium tin oxide interdigitated electrodes. The electrodes are controlled by an external drive signal that permits the 3-D scene to be turned on and off. The display has a contrast ratio of 5.8, which is limited principally by optical scatter caused by extraneous fringing fields. These scatter sources can be readily eliminated. The display reported herein is the first step toward a real-time partial pixel architecture display in which large numbers of dynamic gratings are independently controlled by underlying silicon drive circuitry.     

Axial optical trapping forces on two particles trapped simultaneously by optical tweezers

Optical tweezers, which utilize radiation pressure to control and manipulate microscopic particles, are used for a large number of applications in biology and colloid science. In most applications a single optical tweezers is used to control one single particle. However, two or more particles can be trapped simultaneously. Although this characteristic has been used in applications, no theoretical analysis of the trapping force or the status of the trapped particles is available to our knowledge. We present our calculation, using a ray optics model, of the axial trapping forces on two rigid particles trapped in optical tweezers. The spherical aberration that results from a mismatch of the refractive indices of oil and water is also considered. The results show that the forces exerted by the optical tweezers on the two particles will cause the two particles to touch each other, and the two particles can be stably trapped at a joint equilibrium point. We also discuss the stability of axial trapping. The calculation will be useful in applications of optical tweezers to trap multiple particles.     

Computation of the optical trapping force on small particles illuminated with a focused light beam using a FDTD method

According to the electromagnetic momentum interpretation due to Minkowski, the optical trapping force is determined by momentum transfer. The computation details related to computing the forces of optical radiation pressure on small particles using the scattered field three-dimensional (3D) grid finite difference time domain (FDTD) algorithm are presented. The technique is based on propagating the focused electromagnetic fields through the grid and determining the changes in the optical energy flow with and without the trapped object in the system. The Richards–Wolf vector field equations are applied to the scattered FDTD approach to specify an incident focused beam. We show computational results for a high refractive index particle. These results are in agreement with published experiments and are similar to other computational methods. Compared with some other calculation results using the FDTD method, our results are more consistent with the results measured.     

Controlled simultaneous rotation of multiple optically trapped particles

Abstract

We present a method for the controlled alignment or rotation of birefringent particles trapped in multiple optical trap sites of an interference pattern between two Laguerre—Gaussian laser modes. Controlled spin or alignment of the particles within each individual trap site is achieved independently of the lateral or rotational motion of the interference pattern as a whole. This technique may lead to driving arrays of micro-machines and micro-fluidic studies and can be used in combination with dynamically generated trapping arrays for uniformly distributed stirring throughout microscopic volumes of fluid.     

Significantly improved trapping lifetime of nanoparticles in an optical trap using feedback control

We demonstrate an increase in trapping lifetime for optically trapped nanoparticles by more than an order of magnitude using feedback control, with no corresponding increase in beam power. Langevin dynamics simulations were used to design the control law, and this technique was then demonstrated experimentally using 100 nm gold particles and 350 nm silica particles. No particle escapes were detected with the controller on, leading to lower limits on the increase in lifetime for 100 nm gold particles of 26 times (at constant average beam power) and 22 times for 350 nm silica particles (with average beam power reduced by one-third). The approach described here can be combined with other techniques, such as counter propagating beams or higher-order optical modes, to trap the smallest nanoparticles and can be used to reduce optical heating of particles that are susceptible to photodamage, such as biological systems.     

Dynamic Assembly of Small Parts in Vortex–Vortex Traps Established within a Rotating Fluid

Stable, purely fluidic particle traps established by vortex flows induced within a rotating fluid are described. The traps can manipulate various types of small parts, dynamically assembling them into high‐symmetry clusters, cages, interlocked architectures, jammed colloidal monoliths, or colloidal formations on gas bubbles. The strength and the shape of the trapping region can be controlled by the strengths of one or both vortices and/or by the system's global angular velocity. The system exhibits a range of interesting dynamical behaviors including a Hopf‐bifurcation transition between equilibrium‐point trapping and the so‐called limit cycle in which the particles are confined to circular orbits. Theoretical considerations indicate that these vortex–vortex traps can be further miniaturized to manipulate objects with sizes down to ≈10 µm.