The ability to control the amplitude, phase and polarization states of light on subwavelength scales established metasurfaces as miniaturized alternatives to standard, the relatively large optical components. So far, most of these ultrathin elements operate in the linear regime, and do not change the frequency of the light transmitted or reflected from them. Using our better control over the response of the metasurfaces, we demonstrate a special class of metasurfaces that act as frequency-converting optical components [1-3]. Through nonlinear generation, plasmonic meta-atoms are used as the metasurfaces’ building blocks and a 2π phase shift can be imparted on the nonlinear wave. Similar to the linear metasurfaces case, the laws governing nonlinear optics can be generalized to include nonlinear phase gradients. In phase matched interactions for example, the anomalous signal generated in a collinear wave mixing scheme is emitted into another direction . We demonstrate optical elements such as blazed gratings and lenses operating through four-wave mixing and third-harmonic generation. Additionally, we devise a novel type of computer-generated hologram that can reconstruct complex images at the third harmonic frequency of the reading beam . Polarization-multiplexed, three-dimensional and dynamical nonlinear holograms are fabricated in ultrathin elements by multilayer nanolithography, paving the way to a class of devices that can manipulate optical beams in unprecedented ways.
 E. Almeida and Y. Prior. Scientific Reports 5, 10033 (2015)
 E. Almeida, G. Shalem and Y. Prior, Nature Communications 7, 10367 (2016)
 E. Almeida, O. Bitton and Y. Prior, Nature Communications 7, 12533 (2016)
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