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.

中文翻译：

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倾斜纳米孔径金属透镜：中间场区域的光的亚衍射限制聚焦。

光的衍射限制了传统透镜的光束聚焦分辨率，如阿贝极限（即大约一半波长）所规定的。人们已经探索了许多技术来克服这一限制。最深入探索的方法之一是设计一种在近场区域工作的透镜，即焦距约为 10 nm，其中渐逝场可以携带和投射大的面内波矢（大于自由空间波矢量）到焦平面。然而，从实际角度来看，这种超短焦距的要求带来了太多限制，因为中场或远场操作通常需要更长的焦距。在这里，我们报告了一种在焦距大于波长 λ 的情况下打破阿贝极限的方法。我们的方法是通过将孔径轴倾斜远离金属膜表面来定制纳米孔径传输的辐射图案，使得每个倾斜孔径将高度定向、倾斜定向的光束传输到承载最大面内波矢的公共焦点上成分。所提出的纳米孔径阵列透镜是通过在银、铝或铬薄膜中形成倾斜的纳米狭缝来制造的。我们证明了空气中焦距为 1-4λ 的最小光斑尺寸为 λ/3（在 λ = 633 nm 或 325 nm 时分别为 210 nm 或 110 nm 半峰全宽），突破了阿贝极限。