We demonstrate a scheme that can produce a three-dimensional (3D) focus spot array in a 3D lattice structure, called a 3D Dammann array, in focal region of an objective. This 3D Dammann array is generated by using two separate micro-optical elements, a Dammann zone plate (DZP) that produces a series of coaxial focus spots and a conventional two-dimensional (2D) Dammann grating (DG). A simple, fast, and clear method is presented to design this binary pure-phase DZP in vectorial Debye theory regime. Based on this kind of DZP, one can always obtain a 3D Dammann array both for low and high numerical aperture (NA) focusing objectives. For experimental demonstration, an arrangement combining a DZP, a 2D DG, and a pair of opposing lenses is proposed to generate a Dammann array in focal region of an objective with and another Dammann array for an objective of . It is shown that this arrangement makes it possible to achieve 3D Dammann arrays with micrometer-sized focus spots and focus spacings of tens of micrometers for various practical applications, such as 3D parallel micro- and nanomachining, 3D simultaneous optical manipulation, 3D optical data storage, and multifocal fluorescence microscope, etc.
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