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Tightly focused light can be used to non-invasively trap and manipulate micro-objects, a technique called "optical tweezing." By utilizing the large field gradients present in a focused laser beam, micro-particles-including biological specimens and many other materials-can become confined in all three dimensions. While optical tweezing has existed for over a decade, it has generally been limited to trapping one or two particles at a time. We have developed a technique that uses laser light to assemble large numbers of micro-particles in a highly controllable way. Here we describe, for the first time, the complete implementation of holographic optical tweezer arrays ("HOT" arrays), which offer a new means of simultaneously directing the assembly of particles into any configuration. Through calculation, and subsequent fabrication of, holographic optical devices, we can sculpt a single laser beam into a fully-configurable array of optical tweezers. Each spot in such an array is then capable of trapping and manipulating one particle, making possible simultaneous control over large collections of micro-objects. Our addition of holographic techniques has extended the basic capabilities of optical tweezing, making it a more viable tool for the assembly of nanodevices and the organization of specimens into user-defined structures. Previously, a generalized Lorentz-Mie scattering theory has been used to model single (non-holographic) optical traps. Here, we develop a simpler and more intuitive approach to examine the trapping potential as a function of particle size, the polarizability of the particle material as compared to that of the surrounding medium, the power of the laser used to trap the particles, and the angular divergence of the optics used for promoting assembly. For this calculation we incorporate an approximate form for the energy density of the laser beam-one that is appropriate both within and outside of the Rayleigh limit. We believe that our conclusions remain viable in the intermediate case, where the particles to be trapped have dimensions on the order of the wavelength of visible light; this regime is of particular interest in applications involving assembly of photonic bandgap materials and other photonically-active structures. Notably, we are the first to address the key question regarding application of holographic optical tweezer arrays, namely the number of particles that can be simultaneously incorporated and manipulated. There are many potential applications for such techniques; e.g., allowing for the construction of aggregations with tailor-made crystalline symmetries. Defects may be introduced in a controlled way allowing exploration of their role in phase transitions. Even biological specimens could be organized into useful configurations for studying how they behave in large, organized collections. In addition, there is growing interest in electronic devices, which exploit the confinement of electrons onto isolated nanoparticles. The application of our techniques might increase the yield during fabrication of these devices.



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