Based on the vectorial angular spectrum theory, we optimize superoscillatory lenses (SOLs) for focusing circularly polarized and radially polarized beams below the diffraction limits. Our simulations show that in comparison to the circularly polarized beam, the radially polarized beam can realize a smaller superfocusing hotspot at a longer distance from the SOL. Compared with the amplitude-type SOL, the phase-type SOL can realize a much brighter hotspot without increasing the size of the hotspot. (C) 2015 Optical Society of America
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