Abstract
Diffraction of light limits the resolution of beam focusing with conventional lenses, as dictated by the Abbe limit, that is, approximately half the wavelength. Numerous techniques have been explored to overcome this limit. One of the most intensively explored approaches is to design a lens that operates in the near-field region, that is, with a focal length on the order of 10 nm, where evanescent fields can carry and project large in-plane wave-vectors (greater than free-space wave-vectors) to a focal plane. From a practical perspective, however, the requirement of such an ultra-short focal length puts too much constraint, since much longer focal length is commonly desired for intermediate or far-field operation. Here we report a method to beat the Abbe limit while operating with focal length greater than wavelength λ. Our approach is to tailor the radiation patterns of nanoaperture transmission by tilting aperture axes away from the surface of a metal film such that each slanted aperture transmits a highly directed, tilt-oriented beam onto a common focal point carrying maximal in-plane wave-vector components. The proposed nanoaperture array lens was fabricated by forming tilted nanoslits in a Ag, Al, or Cr film. We demonstrate minimal spot size of λ/3 (210-nm or 110-nm full-width half-maximum at λ = 633 nm or 325 nm, respectively) with 1-4λ focal length in air, beating the Abbe limit.