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Optical metasurfaces are engineered 2D electromagnetic structures enabling flat optical elements with properties not readily found in nature. Their unit cells, meta-atoms, usually are represented by a set of electric and magnetic multipoles. All-dielectric-based metasurfaces have recently attracted significant attention owing to their virtually lossless transmission properties at optical frequencies. A majority of reported dielectric metamaterials are composed of relatively simple meta-atoms such as spheres, cubes, and cylinders, whose electromagnetic response is dominated by the electric dipole. However, magnetic dipoles and higher-order multipoles may enable new optical properties and functionalities, including directional scattering, beam steering, and new frequency generation. Despite impressive progress in the field of optical metamaterials and nanofabrication technologies, engineering meta-atoms that support such higher-order resonances is still challenging. Here, we demonstrate that designed titanium dioxide meta-atoms can enable dominant magnetic dipole response. We apply a machine-learning model to predict a meta-atom shape with a strong magnetic dipole resonant mode at the operating wavelength of 750 nm. Using finite-element-based numerical simulations implemented in COMSOL Multiphysics, we found that the optimized meta-atom is robust against experimental variations and conditions such as a non-perfectly collimated incident beam, nanofabrication inaccuracies, and an added substrate. The meta-atoms have been fabricated using two approaches, focused ion beam lithography and an electron beam lithography followed by reactive ion etching, and characterized using white light spectroscopy. To the best of our knowledge, this is the first experimental realization of a machine-learning-based optimization of a magnetic dipole mode at optical frequencies.
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