We describe a method for projecting single-beam optical traps whose potential energy wells are extended along one-dimensional curves. This technique exploits shape-phase holography in which computer-generated phase-only diffractive optical elements are used to implement complex and amplitude-only holograms. The resulting optical traps can have specified intensity and phase profiles along their lengths and can extend along curves in three dimensions. We demonstrate the extended traps' operation and characterize their potential energy profiles through digital video microscopy of trapped colloidal spheres.
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