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We experimentally demonstrate the focusing of visible light with ultra-thin, planar metasurfaces made of concentrically perforated, 30-nm-thick gold films. The perforated nano-voids—Babinet-inverted (complementary) nano-antennas—create discrete phase shifts and form a desired wavefront of cross-polarized, scattered light. The signal-to-noise ratio in our complementary nano-antenna design is at least one order of magnitude higher than in previous metallic nano-antenna designs. We first study our proof-of-concept ‘metalens’ with extremely strong focusing ability: focusing at a distance of only 2.5 μm is achieved experimentally with a 4-μm-diameter lens for light at a wavelength of 676 nm. We then extend our work with one of these ‘metalenses’ and achieve a wavelength-controllable focal length. Optical characterization of the lens confirms that switching the incident wavelength from 676 to 476 nm changes the focal length from 7 to 10 µm, which opens up new opportunities for tuning and spatially separating light at different wavelengths within small, micrometer-scale areas. All the proposed designs can be embedded on-chip or at the end of an optical fiber. The designs also all work for two orthogonal, linear polarizations of incident light. Scientists in the USA have developed powerful ultrathin planar lenses made from 30-nm-thick perforated gold films. These plasmonic metalenses, created by Xingjie Ni and co-workers at Purdue University, focus a beam of visible light into a spot measuring only slight larger than the wavelength of operation. The devices rely on a concentric pattern of Babinet-inverted nano-antennas (nano-avoids) in a metal film that manipulate the phase of the incident light. For example, a 4-μm-diameter lens provides a focal length of 2.5 μm at a wavelength of 676 nm. The lenses are designed to work at two orthogonal linear polarizations and in future could be suitable for use as miniature couplers or light concentrators in on-chip optical devices.