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Metalenses can achieve diffraction-limited focusing through localized phasemanipulation of the incoming light beam. Because these structures areultrathin, less than a wavelength, this has the potential of achievingultrathin optical elements, with a thickness limited mainly by the mechanicalstrength of the transparent substrate. Recently proposed metalenses are basedon either dielectric nanofin arrays, or nanoparticles of large number, whichleads to severe manufacturing challenges. To overcome these challenges, thispaper predicts a new type of metalens with concentric-nanoring topology, wherethe number and size of the nanorings are determined using an inverse designmethod. By focusing the electrical field energy at a specified position, theconvex-like metalens is inversely predicted with desired numerical aperture anda diffraction-limited focal spot. The Poynting vector distribution founddemonstrates the mechanism of the lensing function, in which optical vorticesare generated in the nanorings to achieve a matching of the phase and impedancebetween the substrate and free space, and further, to form a sphericalwavefront and enhance the transmission of the optical energy. The inversedesign method can also be extended to predict an axicon-like metalens withfocal beam. The improved manufacturability is concluded from the geometry ofthe concentric-nanoring configurations.

Inverse design method for metalens with optical vortices towards light focusing through localized phase retardation